An Exceptionally Simple Theory of Everything

An Exceptionally Simple Theory of Everything

"An Exceptionally Simple Theory of Everything" is a preprint proposing a basis for a unified field theory, named "E8 Theory", which attempts to describe all known fundamental interactions in physics, and to stand as a possible theory of everything. The preprint was posted to the physics arXiv by Antony Garrett Lisi in November 2007,cite arXiv |author=A. G. Lisi |eprint=0711.0770 |title=An Exceptionally Simple Theory of Everything |year=2007 ] and has not been published in a formally peer-reviewed scientific journal. The title is a pun on the algebra used, the Lie algebra of the largest "simple," "exceptional" Lie group, E8.

The theory "received accolades from a few physicists amid a flurry of media coverage," but also "widespread skepticism."cite news |author=Amber Dance |title=Outsider Science |url=http://www.symmetrymagazine.org/cms/?pid=1000607 |work=Symmetry Magazine |date=2008-04-01 |accessdate=2008-06-15 ] Scientific American reported in March 2008 that the theory was being "largely but not entirely ignored" by the mainstream physics community, with a few physicists picking up the work to develop it further. However, as of July 2008, the paper had nine citations from other arXiv preprints, [cite web |url=http://arxiv.org/cits/0711.0770 |title=Citations for 0711.0770 |accessdate=2008-07-30 |date=2007-06-20 |work=arXiv ] and was the most downloaded preprint on the arXiv.

Overview

Lisi's model is a variant and extension of a Grand Unification Theory (a "GUT," describing electromagnetism, the weak interaction and the strong interaction) to include gravitation, a Higgs boson and fermions in an attempt to describe all fields of the Standard Model and gravity as different parts of one field over four dimensional spacetime. More specifically, Lisi combines the left-right symmetric Pati-Salam GUT with a MacDowell-Mansouri description of gravity, using the spin connection and gravitational frame combined with a Higgs boson, necessitating a cosmological constant. The model is formulated as a gauge theory, using a modified BF action, with E8 as the Lie group. Mathematically, this is an E8 principal bundle, with connection, over a four dimensional base manifold. Lisi's embedding of the Standard Model gauge group in E8 leads him to predict the existence of 22 new bosonic particles at an undetermined mass scale.

The fermions enter, via an unconventional use of the BRST technique, as Grassmann number fields valued in part of the E8 Lie algebra. The bosons are combined with these fermions as one-form and Grassmann number parts of a sort of superconnection, each valued in separate parts of the E8 Lie algebra. The curvature of this superconnection is calculated, producing the Riemann curvature, gauge field curvature, gravitational torsion, covariant derivative of the Higgs, and the covariant Dirac derivative of the fermions. This curvature is used to build the modified BF action by hand, in an attempt to match the dynamics of the Standard Model and gravity.

In the paper, Lisi describes several deficiencies in this model. The most important deficiency is noted as an incorrect, or "poorly understood," inclusion of the second and third generations of fermions in E8, relying on triality. This deficiency, and the incomplete nature of the model, prevents the prediction of masses for new or existing particles. Also, Lisi notes the use of explicit symmetry breaking in building his action, rather than offering a more desirable spontaneous symmetry breaking mechanism. And, no attempt is made to provide a quantum description of the theory—this being left for future work.

In a follow-up paper, Lee Smolin proposes a spontaneous symmetry breaking mechanism for obtaining the action in Lisi's model, and speculates on the path to its quantization as a spin foam.

Non-technical overview

Consider a wavy, two-dimensional surface, with many different spheres glued to the surface—one sphere at each surface point, and each sphere attached by one point. This geometric construction is a fiber bundle, with the spheres as the "fibers," and the wavy surface as the "base." A sphere can be rotated in three different ways: around the x-axis, the y-axis, or around the z-axis. Each of these rotations corresponds to a symmetry of the sphere. The fiber bundle connection is a field describing how spheres at nearby surface points are related, in terms of these three different rotations. The geometry of the fiber bundle is described by the curvature of this connection. In the corresponding quantum field theory, there is a particle associated with each of these three symmetries, and these particles can interact according to the geometry of a sphere.

In Lisi's model, the base is a four-dimensional surface—our spacetime—and the fiber is the E8 Lie group, a complicated 248 dimensional shape, which some mathematicians consider to be the most beautiful shape in mathematics.cite web |url=http://www.aimath.org/E8/ |title=Mathematicians Map E8 |accessdate=2007-12-30 |work=AIM ] In this theory, each of the 248 symmetries of E8 corresponds to a different elementary particle, which can interact according to the geometry of E8. As Lisi describes it: "The principal bundle connection and its curvature describe how the E8 manifold twists and turns over spacetime, reproducing all known fields and dynamics through pure geometry."

The complicated geometry of the E8 Lie group is described graphically using group representation theory. Using this mathematical description, each symmetry of a group—and so each kind of elementary particle—can be associated with a point in a diagram. The coordinates of these points are the quantum numbers—the charges—of elementary particles, which are conserved in interactions. Such a diagram sits in a flat, Euclidean space of some dimension, forming a polytope, such as the 421 polytope in eight-dimensional space.

In order to form a theory of everything, Lisi's model must eventually predict the exact number of fundamental particles, all of their properties, masses, forces between them, the nature of spacetime, and the cosmological constant. Much of this work is still in the conceptual stage—in particular, quantization and predictions of particle masses have not been done. And Lisi himself acknowledges it as a work-in-progress: "The theory is very young, and still in development."cite news |author=Roger Highfield |title=Surfer dude stuns physicists with theory of everything |url=http://www.telegraph.co.uk/earth/main.jhtml?view=DETAILS&grid=&xml=/earth/2007/11/14/scisurf114.xml |work=The Daily Telegraph |date=2007-11-14 |accessdate=2008-06-15 ]

Description

Lisi's model attempts to describe all known fields—the gravitational spin connection, frame, Higgs, gauge bosons, and three generations of fermions—as different parts of a single superconnection over a four-dimensional base manifold.

uperconnection

Lisi's superconnection is built by formally adding a connection 1-form field to a Grassmann number 0-form field, both valued in different parts of a Lie algebra, mathfrak{g},
underset{-cdot}{A} = underset{-}{H} + underset{cdot}{Psi} = underset{-}{dx^i} H_i{}^A T_A + underset{cdot}{Psi^A} T_A

The bosonic part of the superconnection, underset{-}{H}, is valued in a reductive subalgebra, mathfrak{h}, of mathfrak{g}, i.e. satisfying the Lie bracket relations,
[ mathfrak{h}, mathfrak{h} ] = mathfrak{h}

[ mathfrak{h}, mathfrak{k} ] = mathfrak{k}
The fermionic part of the superconnection, underset{cdot}{Psi}, is valued in the remainder of the Lie algebra, mathfrak{k}=mathfrak{g}-mathfrak{h}. Lisi states this superconnection is a kind of "BRST extended connection," in which the mathfrak{k} valued part of a 1-form connection has been replaced by BRST ghosts valued in mathfrak{k}. In Lisi's model the relevant Lie algebra is the split real form of mathfrak{g} = e8 and the bosonic subalgebra iscite web |url=http://golem.ph.utexas.edu/~distler/blog/archives/001532.html |title=A Little More Group Theory |accessdate=2008-08-30 |author=Jacques Distler |date=2007-12-09 |work=Musings ]
mathfrak{h} = mathrm{so}(7,1) + mathrm{so}(1,7)

Algebraic breakdown

Lisi proposes a decomposition of e8, the 248 dimensional Lie algebra of E8, into parts accommodating the gravitational and standard model fields according to the following schema:



Under this decomposition, Lisi's e8 valued superconnection for everything is
egin{align}underset{-cdot}{A} & = (underset{-}{H}{}_1 + underset{-}{H}{}_2) + underset{cdot}{Psi} \ & = (( frac{1}{2}underset{-}{omega} + frac{1}{4}underset{-}{e}phi + underset{-}{W} + underset{-}{B}{}_1)+(underset{-}{g} + underset{-}{B}{}_2 + underset{-}{w} +underset{-}{x}Phi)) \ & + ((underset{cdot}{ u}{}_e + underset{cdot}{e} + underset{cdot}{u} + underset{cdot}{d})+(underset{cdot}{ u}{}_mu + underset{cdot}{mu} + underset{cdot}{c} + underset{cdot}{s})+(underset{cdot}{ u}{}_ au + underset{cdot}{ au} + underset{cdot}{t} + underset{cdot}{b}))end{align}

in which underset{-}{omega} is the spin connection, underset{-}{e} is the gravitational frame, phi , is the Higgs boson, underset{-}{W} is a weak gauge field, underset{-}{B}{}_1 is the right partner to the weak gauge field, underset{-}{g} is the strong gauge field, underset{-}{B}{}_2 is the baryon minus lepton number gauge field, underset{-}{w} +underset{-}{x}Phi are new gauge bosons, and the rest of the fields are the standard model fermions. Lisi's detailed description of the spin connection, frame-Higgs and fermions, as parts of e8, relies heavily on the Clifford algebra "C"ℓ7, 1(R). Lisi says this left-right symmetric model, similar to the Pati-Salam model, must be broken to obtain the standard model. Notably, Lisi includes fermions along with bosons in the same representation, and also proposes tentatively that the three generations of fermions of the standard model may be described by a triality rotation (relating to the three-fold symmetry of mathrm{SO}(8)). He notes that the second and third generations of fermions do not obviously have the correct quantum numbers in this model—and that this stands as the least understood aspect of the theory, and the largest outstanding problem.

Visual representation

The algebraic structure of the standard model and gravitational fields may be described using group representation theory, with roots and weights corresponding to the charge quantum numbers of elementary particle states. Different kinds of charge correspond to the different fundamental forces, with weak hypercharge and weak isospin of the electroweak force combining to produce electric charge, and two kinds of charge quantum numbers associated with the color charge of the strong force. These four kinds of standard model charge are conserved in all elementary particle interactions. In Lisi's theory, the spin of elementary particles are the charges with respect to the gravitational force, with a different spin charge for the left and right chiral parts of the gravitational spin connection. The quantum numbers of all elementary particles is a pattern of points in six dimensional charge space, which may be projected down to two dimensions and plotted, creating a visual representation of the algebraic structure. In Lisi's E8 Theory these charges in six dimensions are a projection of some of the E8 root system in eight charge dimensions. The standard model or E8 system of charges and allowed particle interactions may be rotated in eight dimensions and visualized via an online tool, the "Elementary Particle Explorer".cite web |url=http://deferentialgeometry.org/epe/ |title=Elementary Particle Explorer |accessdate=2008-09-04 |author=Troy Gardner |date=2008-08-09 |work=Deferential Geometry ]

Curvature

The dynamics in Lisi's model depends on the supercurvature of the superconnection,
egin{align}underset{=cdot}{F} & = underset{-}{d} underset{-cdot}{A} + frac{1}{2} [ underset{-cdot}{A}, underset{-cdot}{A} ] \ & = underset{-}{d} (underset{-}{H}+underset{cdot}{Psi}) + frac{1}{2} [ (underset{-}{H}+underset{cdot}{Psi}), (underset{-}{H}+underset{cdot}{Psi}) ] \ & = (underset{-}{d} underset{-}{H} + frac{1}{2} [ underset{-}{H}, underset{-}{H} ] )+ (underset{-}{d} underset{cdot}{Psi} + [ underset{-}{H},underset{cdot}{Psi}) ] )+ ( frac{1}{2} [ underset{cdot}{Psi}, underset{cdot}{Psi} ] ) \ & = underset{=}{F} + underset{-}{D} underset{cdot}{Psi} + underset{cdot}{Psi} underset{cdot}{Psi}end{align}

in which underset{=}{F} is the bosonic curvature form and underset{-}{D} underset{cdot}{Psi} is the exterior covariant derivative of the fermions. Under Lisi's algebraic breakdown of e8, the supercurvature decomposes into parts,



in which underset{=}{R} = underset{-}{d} underset{-}{omega} + frac{1}{2}underset{-}{omega} underset{-}{omega} is the Riemann curvature 2-form, underset{=}{T}=underset{-}{d} underset{-}{e} + frac{1}{2} [underset{-}{omega},underset{-}{e}] is the torsion 2-form, and underset{-}{D} underset{cdot}{Psi} is the massive covariant derivative of the fermions, as Dirac spinors, in curved spacetime.

Action

To specify dynamics matching general relativity and the standard model, Lisi postulates a modified BF theory action,
egin{align}S & = int underset{=cdot}{F}+ frac{pi G}{4}underset{=}{B}^Gunderset{=}B^Ggamma-underset{=}{B}'*underset{=}{B}'> \ & = int underset{-}{D}underset{cdot}{Psi} + underset{=}{e} frac{1}{16 pi G} phi^2 (R - frac{3}{2} phi^2) - frac{1}{4} underset{=}{F}'*underset{=}{F}'>end{align}
producing the Einstein-Hilbert action for gravity, the Yang-Mills action for gauge fields, the action for the Higgs boson, and the action for fermions in curved spacetime. The cosmological constant in Lisi's model is necessarily related to the vacuum expectation value of the Higgs, Lambda = frac{3}{4} phi^2.

It should be noted that this action breaks the E8 symmetry by hand. However, Lee Smolin has proposed a way to obtain the bosonic part of Lisi's action (plus higher-order terms) from a fully E8-symmetric theory, by starting with the action:
S = int >

Vector-form notation

Lisi employs an unusual mathematical notation in his work with vectors and differential forms. He denotes the grade of a differential form by underlines, as in the curvature 2-form,
underset{=}{F} = frac{1}{2} underset{-}{dx^i} underset{-}{dx^j} F_{ij}
in which he does not write the wedge—taking the coordinate basis 1-forms to always anti-commute. For the interior product between a vector, vec{v}, and a form, Lisi writes
vec{v} underset{-}{f} = v^i vec{partial_i} underset{-}{dx^j} f_j = v^i f_i
taking the coordinate basis vectors and their dual coordinate basis 1-forms to contract as vec{partial_i} underset{-}{dx^j} = delta_i^j. This is similar to Dirac's Bra-ket notation for vectors in Hilbert space, and Lisi uses the order-dependent nature of this contraction to describe vector valued forms similar to "ket-bra"'s, such as
vec{underset{-}{H = underset{-}{dx^i} H_i{}^j vec{partial_j}
Also, Lisi uses an under-dot, as in underset{cdot}{Psi}, to denote the Grassmann grade of a field.

Predictions

By matching 226 known standard model particles to some of the 248 symmetries of E8, Lisi is able to predict the existence and quantum numbers of 22 new particles. Three of these, the B_1^pm , and B_2 ,, are the same new mathrm{su}(2)_R , and mathrm{u}(1)_{B-L} , gauge bosons as predicted in the Pati-Salam model, the W' and Z' bosons. Another, the w ,, is a new mathrm{u}(1) , gauge boson, with a corresponding new quantum number. And the remaining 18 new bosons predicted, the x Phi ,, are new colored fields, interacting with the strong force. Lisi states that some of these 22 particles might be seen at the Large Hadron Collider.cite news |title=The Big Bang: what will we find? |url=http://www.telegraph.co.uk/earth/main.jhtml?xml=/earth/2008/03/25/scicomments125.xml |work=The Daily Telegraph |date=2008-03-25 |accessdate=2008-06-15 ]

It is important to note that Lisi does not specify masses for these predicted particles. This implies these predictions are not falsifiable, because the masses can always be speculated to be beyond the reach of a given experiment. However, the discovery of new particles that do not fit in Lisi's classification, such as superpartners, would fall outside the model, and falsify Lisi's match to E8. Also, because the matching of the three fermion generations is tentative and problematic in the model, Lisi places a low confidence in these predictions.

Chronology and reaction

Three previous arXiv preprints by Lisi dealt with related questions. "Clifford Geometrodynamics," (2002) [cite arXiv |author=A. G. Lisi |eprint=gr-qc/0212041 |title=Clifford Geometrodynamics |year=2002 ] "Clifford bundle formulation of BF gravity generalized to the standard model," (2005) [cite arXiv |author=A. G. Lisi |eprint=gr-qc/0511120 |title=Clifford bundle formulation of BF gravity generalized to the standard model |year=2005 ] "Quantum mechanics from a universal action reservoir,"(2006) [cite arXiv |author=A. G. Lisi |eprint=physics/0605068 |title=Quantum mechanics from a universal action reservoir |year=2006 ]

In 2007 Lisi further discussed his work on an FQXi forum, [cite web |url=http://fqxi.org/community/forum/topic/68 |title=Pieces of E8 |accessdate=2008-06-15 |author=A. G. Lisi |date=2007-06-09 |work=FQXi forum ] ; at an FQXi conference, [cite web |url=http://fqxi.org/conference/talkslides.html |title=Standard model and gravity |accessdate=2008-06-15 |author=A. G. Lisi |date=2007-07-21 |work=inaugural FQXi conference ] ;and in an FQXi article.cite news |author=Scott Dodd |title=Surfing the Folds of Spacetime |url=http://fqxi.org/community/download.php?url=/community/data/articles/Lisi_Garrett.pdf |work=FQXi article |format=PDF |date=2007-10-26 |accessdate=2008-06-15 ] He also gave talks at the Loops '07 conference in Morelia, Mexico [cite web |url=http://www.matmor.unam.mx/eventos/loops07/cont_abs.html#lisi |title=Deferential Geometry |accessdate=2008-06-15 |author=A. G. Lisi |date=2007-06-25 |work=Loops '07 conference ] ; and the url=http://pirsa.org/07100001 |title=An Exceptionally Simple Theory of Everything |accessdate=2008-06-15 |author=A. G. Lisi |date=2007-10-04 |work=Perimeter Institute talk ] Commentary on his work was found in John Baez's "This Week's Finds in Mathematical Physics (Week 253)," [cite web |url=http://math.ucr.edu/home/baez/week253.html |title=This Week's Finds in Mathematical Physics (Week 253) |accessdate=2008-06-15 |author=John Baez |date=2007-06-27 ] and he is interviewed on Sabine Hossenfelder "Backreaction," blog. [cite web |url=http://backreaction.blogspot.com/2007/08/garrett-lisis-inspiration.html |title=Garrett Lisi's Inspiration |accessdate=2008-06-15 |author=Sabine Hossenfelder |date=2007-08-06 |work=Backreaction ]

Lisi's arXiv preprint, "An Exceptionally Simple Theory of Everything," appears on November 6, 2007 where Lisi describes how gravity, the standard model bosons, and three generations of fermions can be unified using an E8 superconnection.cite arXiv |author=A. G. Lisi |eprint=0711.0770 |title=An Exceptionally Simple Theory of Everything |year=2007 ]

Lisi's paper attracted a great deal of attention after its release and spun-off a variety of debates across various blogs and online discussion groups. Numerous news sites from all over the world reported this new theory, noting the personal background of Lisi, and the controversy in the physics community surrounding the preprint.

Mainstream and scientific press coverage included:
The Daily Telegraph, November 14, 2007;cite news |author=Roger Highfield |title=Surfer dude stuns physicists with theory of everything |url=http://www.telegraph.co.uk/earth/main.jhtml?view=DETAILS&grid=&xml=/earth/2007/11/14/scisurf114.xml |work=The Daily Telegraph|date=2007-11-14 |accessdate=2008-06-15 ]
New Scientist, November 15, 2007;cite news |author=Zeeya Merali |title=Is mathematical pattern the theory of everything? |url=http://www.newscientist.com/channel/fundamentals/dn12891-is-mathematical-pattern-the-theory-of-everything.html |work=New Scientist |date=2007-11-15 |accessdate=2008-06-15 ]
Wired News, November 16, 2007; [cite news |author=John Borland |title=Surfer-Physicist Offers A New Way To Explain Everything |url=http://blog.wired.com/wiredscience/2007/11/surfer-physicis.html |work=Wired News |date=2007-11-16 |accessdate=2008-06-15 ]
Le Monde, November 19, 2007; [cite news |author=Stéphane Foucart |title=The theory is mathematically and aesthetically superb |url=http://www.lemonde.fr/cgi-bin/ACHATS/acheter.cgi?offre=ARCHIVES&type_item=ART_ARCH_30J&objet_id=1013839&clef=ARC-TRK-D_01 |work=Le Monde |date=2007-11-19 |accessdate=2008-06-16 ]
The Economist, November 22, 2007; [cite news |title=Geometry is all |url=http://www.economist.com/science/displaystory.cfm?story_id=10170958 |work=The Economist |date=2007-11-22 |accessdate=2008-06-15 ] [The Daily Telegraph] , January 22, 2008; [cite news |author=Marcus du Sautoy |title=Garrett Lisi: This surfer is no Einstein... |url=http://www.telegraph.co.uk/earth/main.jhtml?xml=/earth/2008/01/22/scieinstein122.xml |work=The Daily Telegraph |date=2008-01-22 |accessdate=2008-06-15 ]
Discover Magazine, February 26, 2008; [cite news |title=Could the Next Einstein Be a Surfer Dude? |url=http://discovermagazine.com/2008/mar/13-e-nste-n |work=Discover Magazine |date=2008-02-26 |accessdate=2008-06-15 ]
Wired Magazine, February 27, 2008; [cite news |author=Kim Zetter |title=Surfer-Physicist's Unified Theory Leads to Fame, Backlash |url=http://www.wired.com/science/discoveries/news/2008/02/ted_lisi |work=Wired Magazine |date=2008-02-27 |accessdate=2008-06-15 ]
Scientific American, March 1, 2008;cite journal |last=Collins |first=Graham P. |authorlink= |coauthors= |year=2008 |month=March |title="Wipeout?" |journal=Scientific American |volume= |issue= |pages=30–32 |id= |url=http://www.sciam.com/article.cfm?id=wipeout-theory |accessdate=2008-06-18 |quote= ]
Physics World, July 1, 2008;cite news |author=Stephen Maxfield |title=Symmetry's physical dimension |url=http://physicsworld.com/cws/article/print/34784 |work=Physics World |date=2008-07-01 |accessdate=2008-07-10 ] and The New Yorker, July 21, 2008.cite news |author=Benjamin Wallace-Wells |title=Surfing the Universe |url=http://www.newyorker.com/reporting/2008/07/21/080721fa_fact_wallacewells |work=The New Yorker |date=2008-07-21 ]

Numerous blogs and forums also discussed the work includingSabine Hossenfelder's "Backreaction", [cite web |url=http://backreaction.blogspot.com/2007/11/theoretically-simple-exception-of.html |title=A Theoretically Simple Exception of Everything |accessdate=2008-06-15 |author=Sabine Hossenfelder |date=2007-11-06 |work=Backreaction ]
Lubos Motl's "The Reference Frame", which objects to the addition of bosons and fermions in Lisi's superconnection, and to the violation of the Coleman-Mandula theorem, [cite web |url=http://motls.blogspot.com/2007/11/exceptionally-simple-theory-of.html |title=Garrett Lisi: An exceptionally simple theory of everything |accessdate=2008-06-15 |author=Lubos Motl |date=2007-11-07 |work=The Reference Frame ]
Peter Woit's "Not Even Wrong", [cite web |url=http://www.math.columbia.edu/~woit/wordpress/?p=617 |title=An Exceptionally Simple Theory of Everything? |accessdate=2008-06-15 |author=Peter Woit |date=2007-11-09 |work=Not Even Wrong ]
Sean Carroll's "Cosmic Variance", [cite web |url=http://cosmicvariance.com/2007/11/16/garrett-lisis-theory-of-everything/ |title=Garrett Lisi’s Theory of Everything! |accessdate=2008-06-15 |author=Sean Carroll |date=2007-11-16 |work=Cosmic Variance ]
Steinn Sigurðsson's "Dynamics of Cats", [cite web |url=http://scienceblogs.com/catdynamics/2007/11/red_boson_blue_fermion.php |title=red boson, blue fermion |accessdate=2008-06-16 |author=Steinn Sigurðsson |date=2007-11-20 |work=Dynamics of Cats ] Physics Forums [cite web |url=http://www.physicsforums.com/showthread.php?t=196498 |title=An Exceptionally Simple Theory of Everything! |accessdate=2008-06-15 |date=2007-11-06 |work=Physics Forums ]
Slashdot, [cite web |url=http://science.slashdot.org/article.pl?sid=07/11/15/2322225 |title=A New Theory of Everything? |accessdate=2008-06-15 |date=2007-11-15 |work=Slashdot ]
Digg, [cite web |url=http://digg.com/general_sciences/Surfer_Dude_Stuns_Physicists_With_Theory_of_Everything_2 |title=Surfer Dude Stuns Physicists With Theory of Everything |accessdate=2008-06-16 |date=2007-11-15 |work=Digg ] and Reddit. [cite web |url=http://www.reddit.com/info/60msi/comments/ |title=Surfer dude stuns physicists with theory of everything |accessdate=2008-06-15 |date=2007-11-15 |work=Reddit ] Woit, Smolin are generally supportive whereas Moit, Marcus du Sautoy are critical.

Jacques Distler's "Musings" is one of the strongest criticism to Lisi's approach, identifying problems with the inclusion of the second and third generations of fermions using E8 and is acknowledged by Lisi in the paper as the largest problem, requiring work.cite web |url=http://golem.ph.utexas.edu/~distler/blog/archives/001505.html |title=A Little Group Theory |accessdate=2008-06-15 |author=Jacques Distler |date=2007-11-21 |work=Musings ] And the group blog, "The n-Category Cafe," provides the some of the more technical discussions with posts by Lisi, Urs Schreiber,cite web |url=http://golem.ph.utexas.edu/category/2008/05/e8_quillen_superconnection.html |title=E8 Quillen Superconnection |accessdate=2008-06-15 |author=Urs Schreiber |date=2008-05-10 |work=The n-Category Cafe ] Kea [http://golem.ph.utexas.edu/category/2008/05/e8_quillen_superconnection.html#c016877] and Jaques Distler. [http://golem.ph.utexas.edu/category/2008/05/e8_quillen_superconnection.html#c016877]

Lisi has made further presentations at International Loop Quantum Gravity Seminar on November 13, 2007 [cite web |url=http://relativity.phys.lsu.edu/ilqgs/ |title=A Connection With Everything |accessdate=2008-06-15 |author=A. G. Lisi |date=2007-11-13 |work=International Loop Quantum Gravity Seminar ] and responded to press enquiries on an FQXi forum in November 20, 2007 [cite web |url=http://fqxi.org/community/forum/topic/107 |title=An Exceptionally Simple FAQ |accessdate=2008-06-15 |author=A. G. Lisi |date=2007-11-20 |work=FQXi forum ]

Several arXiv preprints build on Lisi's work:
Lee Smolin "The Plebanski action extended to a unification of gravity and Yang-Mills theory," December 6, 2007, proposes a symmetry breaking mechanism to go from an E8 symmetric action to Lisi's action for the standard model and gravity. cite arXiv |author=Lee Smolin |eprint=0712.0977 |title=The Plebanski action extended to a unification of gravity and Yang-Mills theory |year=2007 ]
Roberto Percacci "Mixing internal and spacetime transformations: some examples and counterexamples," [cite arXiv |author=Roberto Percacci |eprint=0803.0303 |title=Mixing internal and spacetime transformations: some examples and counterexamples |year=2008 ] and Bertram Kostant discusses in a colloquium presentation at UC Riverside [cite web |url=http://math.ucr.edu/home/baez/kostant/ |title=On Some Mathematics in Garrett Lisi's 'E8 Theory of Everything' |accessdate=2008-06-15 |author=Bertram Kostant |date=2008-02-12 |work= UC Riverside mathematics colloquium ]

In the presentation "What's new at the arXiv?" on May 20 2008,Simeon Warner stated that Lisi's paper is the most downloaded article on the arXiv.cite web |url=http://indico.desy.de/conferenceOtherViews.py?confId=800#2008-05-20 |title=What's new at the arXiv? |accessdate=2008-07-22 |author=Simeon Warner |date=2008-05-20 |work=HEP Information Resource Summit (The slide containing this statement was subsequently removed from the presentation file.)] cite web |url=http://www.math.columbia.edu/~woit/wordpress/?p=693 |title=INSPIRE |accessdate=2008-08-05 |author=Peter Woit |date=2008-05-28 |work=Not Even Wrong ]

FQXi awarded Lisi a grant for further development of "E8 Theory" on 4 August 2008.cite web |url=http://www.fqxi.org/large-grants/awardee/details/2008/lisi |title=E8 Theory |accessdate=2008-08-05 |date=2008-08-04 |work=FQXi ] cite web |url=http://www.fqxi.org/grants |title=FQXi Grants |accessdate=2008-08-08 |date= |work=FQXi ]

References

External links

* [http://deferentialgeometry.org/ Deferential Geometry] - Lisi's wiki, containing detailed mathematical background.
* [http://uk.youtube.com/watch?v=-xHw9zcCvRQ Animation of E8] - a New Scientist video describing the theory using a visual representation.
* [http://deferentialgeometry.org/epe/ The Elementary Particle Explorer] - an online E8 investigation tool for rotating and examining the particle assignments, charges, and interactions in the standard model and Lisi's E8 Theory.
* [http://theoryofeverything.org/TOE/JGM/e8Flyer.nbp E8Flyer] - An interactive [http://theoryofeverything.org/TOE/JGM/ece2.mht E8 investigation tool] based on the free Mathematica Notebook Player) (* see [http://theoryofeverything.org/TOE/JGM/E8Favorites.pdf] for screen shots *)
* [http://www.physicsforums.com/showthread.php?t=202439 An Exceptionally Technical Discussion of AESToE] - a thread at "Physics Forums," started by Garrett Lisi, devoted to discussing the mathematics used in the AESToE paper.


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