Over the years, various researchers have suggested connections between the octonions and the standard model of particle physics. The past few years, in particular, have been marked by an upsurge of activity on this subject, stimulated by the recent observation that the standard model gauge group and fermion representation can be elegantly characterized in terms of the octonions. This workshop, which will be the first ever on this topic, is intended to bring this new community together in an attempt to better understand these ideas, establish a common language, and stimulate further progress.
The workshop will consist of an hour-long talk every Monday at noon (EST), with the first talk on Monday February 8, and the final talk on Monday May 17.
Format results
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Welcome and Opening Remarks
Kirill Krasnov - University of Nottingham
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Finite quantum geometry, octonions and the theory of fundamental particles.
Michel Dubois-Violette - University of Paris-Saclay
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Supersymmetry and RCHO revisited
Paul Townsend - University of Cambridge
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Spin (8,9,10), Octonions and the Standard Model
Kirill Krasnov - University of Nottingham
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Gravity as the square of gauge theory
Leron Borsten - Heriot-Watt University
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A Magic Pyramid of Supergravity Theories from Yang-Mills Squared
Mia Hughes - Imperial College London
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Division algebraic symmetry breaking
Cohl Furey - Humboldt University of Berlin , Mia Hughes - Imperial College London
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Clifford algebra of the Standard Model
Ivan Todorov - Bulgarian Academy of Sciences
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The Higher Algebra of Supersymmetry
John Huerta - University of Lisbon
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Can We Understand the Standard Model?
John Baez - University of California, Riverside
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Can We Understand the Standard Model Using Octonions?
John Baez - University of California, Riverside
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Spin(11,3), particles and octonions
Kirill Krasnov - University of Nottingham
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Finite quantum geometry, octonions and the theory of fundamental particles.
Michel Dubois-Violette - University of Paris-Saclay
We will describe an approach to the theory of fundamental particlesbased on finite-dimensional quantum algebras of observables. We will explain why the unimodularity of the color group suggests an interpretation of the quarklepton symmetry which involves the octonions and leads to the quantum spaces… -
Supersymmetry and RCHO revisited
Paul Townsend - University of Cambridge
Various links between supersymmetry and the normed division algebras R,C,H,O were found in the 1980s. This talk will focus on the link between K=R,C,H,0 and supersymmetric field theories in a Minkowski spacetime of dimension D=3,4,6,10. The first half will survey the history starting with a 1944/5… -
Spin (8,9,10), Octonions and the Standard Model
Kirill Krasnov - University of Nottingham
"I will start by explaining how the (Weyl) spinor representations of the pseudo-orthogonal group Spin(2r+s,s) are the spaces of even and odd polyforms on Cr x Rs. Then, the triality identifies the Majorana-Weyl spinors of Spin(8) with octonions. Combining the two constructions one finds that the… -
Gravity as the square of gauge theory
Leron Borsten - Heriot-Watt University
Can gravity, in certain regards, be the `product' of two gauge theories, such as those appearing in the Standard Model? I will begin by reviewing the Bern—Carrasco—Johansson colour—kinematics duality conjecture, which implies that one can write the scattering amplitudes of Einstein-Hilbert gravity… -
A Magic Pyramid of Supergravity Theories from Yang-Mills Squared
Mia Hughes - Imperial College London
"I will begin by reviewing the unified description of pure Super Yang-Mills (SYM) Theory (consisting of just a gauge field and gaugino) in dimensions 3, 4, 6, and 10 over the four normed division algebras R, C, H, and O. Dimensionally reducing these initial theories into dimensions 3, 4, 5, 6, 7, 8… -
Division algebraic symmetry breaking
Cohl Furey - Humboldt University of Berlin , Mia Hughes - Imperial College London
Can the 32C-dimensional algebra R(x)C(x)H(x)O offer anything new for particle physics? Indeed it can. Here we identify a sequence of complex structures within R(x)C(x)H(x)O which sets in motion a cascade of breaking symmetries: Spin(10) -> Pati-Salam -> Left-Right symmetric -> Standard model + B-L… -
Clifford algebra of the Standard Model
Ivan Todorov - Bulgarian Academy of Sciences
We explore the Z2 graded product C`10 = C`4⊗ˆC`6 (introduced by Furey) as a finite quantum algebra of the Standard Model of particle physics. The gamma matrices generating C`10 are expressed in terms of left multiplication by the imaginary octonion units and the Pauli matrices. The subgroup of Spin… -
The Higher Algebra of Supersymmetry
John Huerta - University of Lisbon
We have already met the octonionic Fierz identity satisfied by spinors in 10-dimensional spacetime. This identity makes super-Yang-Mills "super" and allows the Green-Schwarz string to be kappa symmetric. But it is also the defining equation of a "higher" algebraic structure: an L-infinity algebra… -
Can We Understand the Standard Model?
John Baez - University of California, Riverside
40 years trying to go beyond the Standard Model hasn't yet led to any clear success. As an alternative, we could try to understand why the Standard Model is the way it is. In this talk we review some lessons from grand unified theories and also from recent work using the octonions. The gauge group… -
Can We Understand the Standard Model Using Octonions?
John Baez - University of California, Riverside
Dubois-Violette and Todorov have shown that the Standard Model gauge group can be constructed using the exceptional Jordan algebra, consisting of 3×3 self-adjoint matrices of octonions. After an introduction to the physics of Jordan algebras, we ponder the meaning of their construction. For example… -
Spin(11,3), particles and octonions
Kirill Krasnov - University of Nottingham
The fermionic fields of one generation of the Standard Model, including the Lorentz spinor degrees of freedom, can be identified with components of a single real 64-dimensional semi-spinor representation S of the group Spin(11,3). I will describe an octonionic model for Spin(11,3) in which the semi…