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M-Theory and Mathematics

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mtheorymath.org

A conference series on M-theory and mathematics.

These workshops bring together experts on the mathematical aspects of M-theory, the main candidate for a theory of everything, with implications to string theory and quantum field theory and interactions with geometry and algebraic topology.

M-Theory and Mathematics 2020

• January 27-30, 2020

• Event webpage

• Program

Confirmed speakers:

• David Berman

• Bianca Cerchiai

• Martin Cederwall

• Michael Duff

• José Figueroa-O’Farrill

• Domenico Fiorenza

• Pietro Grassi

• Fei Han

• Yang-Hui He

• Chris Hull

• Branislav Jurčo

• Neil Lambert

• William Linch III

• Varghese Mathai

• Du Pei

• Christian Saemann

• Henning Samtleben

• Hisham Sati

• Urs Schreiber

• Ashoke Sen

• Eric Sharpe

• Dmitri Sorokin

• Meng-Chwan Tan

Abstracts, Slides and Talk notes:

• Bianca Cerchiai

  Supergravity in a pencil

  download: pdf slides

  Abstract: In the spirit of the gauge-gravity correspondence, we derive a 2+1 dimensional model with “unconventional” supersymmetry at the boundary of a 4-dimensional Anti de Sitter N-extended supergravity, which in the case N=2 reproduces the AVZ model [P.D. Alvarez, M. Valenzuela, J. Zanelli, JHEP 1204 (2012) 058, arXiv:1109.3944 hep-th]. The extended supersymmetry of the boundary model is instrumental to describe the electronic properties of graphene, in particular at the two Dirac points. The two valleys correspond to the two independent sectors of the OSp(p|2)×OSp(q|2) boundary model in the p=q case, which are related by a parity transformation. The Semenoff and the Haldane masses entering the corresponding Dirac equations for the graphene pseudoparticles are identified with supergravity torsion parameters.

• Michael Duff:

  Perspectives on M-Theory

  download: video stream

• José Figueroa-O’Farrill

  Lie superalgebra deformations and d=11 supergravity backgrounds

  download: pdf slides

  Abstract: To every (supersymmetric) background of d=11 supergravity there is associated a filtered Lie superalgebra. For ($\gt 1/2$)-BPS backgrounds, this Lie superalgebra determines the background up to local isometry. I will then report on an algebraic reformulation of this classification problem. This is joint work with Andrea Santi.

• Domenico Fiorenza:

  Twisted Cohomotopy implies level quantization of the 6d WZ term of the M5-brane

  download: pdf slides

  Abstract: The 6d Wess-Zumino term in the action functional for the M5-brane is anomalous as traditionally defined. What has been missing is a condition implying a higher analogue of level quantization familiar from the 2d Wess-Zumino term. We prove that such an anomaly cancellation condition is implied by the hypothesis that the C-field is charge-quantized in twisted Cohomotopy theory. The proof follows by a twisted/parametrized generalization of the Hopf invariant, after identifying the 6d Wess-Zumino term with a twisted homotopy Whitehead integral formula, which we establish. Joint work with Hisham Sati and Urs Schreiber, arXiv:1906.07417.

• Yang-Hui He,

  Universes as Bigdata

  download: pdf slides

  Abstract: We review how historically the problem of string phenomenology lead theoretical physics first to algebraic/differential geometry, and then to computational geometry, and now to data science and AI. With the concrete playground of the Calabi-Yau landscape, accumulated by the collaboration of physicists, mathematicians and computer scientists over the last 4 decades, we show how the latest techniques in machine-learning can help explore problems of physical and mathematical interest.

• Neil Lambert,

  Lagrangians with (2,0) Supersymmetry

  download: pdf slides

  Abstract: We will discuss free and interacting six-dimensional actions which admit $(2,0)$ supersymmetry including their application to abelian and non-abelian M5-branes.

• Hisham Sati,

  M-theory and cohomotopy

  download: pdf slides

  Abstract Cohomotopy theory has recently emerged as the proper generalized cohomology theory to describe the fields in M-theory. It is hoped that viewing M-theory from a mathematical perspective will shed the light on the nature of the theory and will allow for progress. I will survey this area, illustrating how cohomotopy captures the nature of the C-field and its dual as well as of the M-branes, allows for cancellation of various anomalies, and provides a firm grounding for further study of M-theory. This is joint work Urs Schreiber and Domenico Fiorenza.

• Urs Schreiber:

  Microscopic Brane Physics from Cohomotopy

  download: pdf slides

  Abstract: As reviewed in H. Sati‘s talk, assuming that the C-field is charge-quantized in the generalized cohomology theory called J-twisted Cohomotopy (“Hypothesis H”) implies a list of M-theoretic anomaly cancellation conditions, such as shifted C-field flux quantization, DMW anomaly cancellation and C-field tadpole cancellation on 8-manifolds. In this talk I review the further geometric refinement of the cohomology theory to equivariant Cohomotoy theory and to differential Cohomotopy theory. Now we find that Hypothesis H implies also the Witten mechanism of multiple M5-branes on MO5-orientifolds in heterotic M-theory on ADE-orbifolds, hence RR-field tadpole cancellation in type I' string theory; as well as a multitude of effects associated with Dp/D(p+2)-brane intersections: Chan-Paton factors, BMN matrix model fuzzy funnel states and BLG 3-algebras, the Hanany-Witten rules, AdS3-gravity observables, supersymmetric indices of Coulomb branches as well as gauge/gravity duality between all these. This suggests that Hypothesis H is a correct assumption about the elusive mathematical fomulation of M-theory. This is joint work with H. Sati (arxiv:1909.12277, arxiv:1912.10425).

more to appear here…

Related events:

• Higher Structures in M-Theory 2018

category: reference