nLab M-Theory and Mathematics



String theory

Quantum systems

quantum logic

quantum physics

quantum probability theoryobservables and states

quantum information

quantum computation


quantum algorithms:

quantum sensing

quantum communication

This page collects material related to:

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 2024

on January 15 - 17, 2024

at CQTS @ New York University, Abu Dhabi


Alfonsi\,Giotop. Malek Saemann Minasian Lambert Hull Schreiber He Sati X Han Tan Singh Shahbazi Myers Hohm


  • 15 Jan 2024

    Eric Sharpe:

    Decomposition of 2D Pure Yang-Mills and the Gross- Taylor String Theory

    slides: pdf

    video: kt

    cf.: arXiv:2307.08729

    In this talk, we will attempt to reconcile two different results on two-dimensional pure Yang-Mills theory. Specifically, we will discuss how the fact that 2d pure Yang-Mills is equivalent to a disjoint union of theories, is related to the Gross-Taylor description of 2d pure Yang-Mills as the target-space field theory of a string theory. The Gross-Taylor picture can be understood by first rewriting the Yang-Mills partition function (in a large N N limit) as a sum of correlation functions in Dijkgraaf-Witten theories for the symmetric group S nS_n, and then interpreting those Dijkgraaf-Witten correlation functions in terms of branched covers, which leads to the string theory description. We first observe that the decomposition of the pure Yang-Mills aligns perfectly with the decomposition of S nS_n Dijkgraaf-Witten theory, and then discuss decomposition and the branched covers interpretation. We encounter two puzzles, and to solve them, propose that the Gross-Taylor string theory has a higher-form symmetry.

  • 16 Jan 2024

    Ruben Minasian:

    Constraining and Un-constraining Supergravities

    slides: pdf

    video: kt

    I will review various aspects and somewhat surprising consequences of cancellation of (different types of) anomalies in supergravity theories in eight and six dimensions. I will also discuss appearance and importance of exotic (singular, non-spin, non-orientable) backgrounds.

  • 16 Jan 2024

    Emanuel Malek:

    Kaluza-Klein Spectrometry for String Theory Compactifications

    slides: pdf

    video: kt

    cf.: arXiv:2212.01135

    I will present a powerful new method that for the first time allows us to compute the Kaluza-Klein spectrum of a large class of string theory compactifications, including those arising in maximal gauged supergravities and beyond. This includes geometries with little to no remaining (super-)symmetries, completely inaccessible by previous methods. I will show how these insights can be used to holographically compute the anomalous dimensions of protected and unprotected operators in strongly-coupled CFTs, as well as to study global properties of their conformal manifolds. I will also show how the method can be used to determine the perturbative stability of non supersymmetric AdS vacua. We will see the importance of higher Kaluza-Klein modes to the physics of string compactifications, e.g. in realising the compactness of moduli spaces, restoring supersymmetry that is lost in a consistent truncation, and in destabilising vacua that appear to stable in lower-dimensional supergravities.

  • 16 Jan 2024

    Fei Han:

    Cubic Forms, Anomaly Cancellation and Modularity

    video: kt

    cf.: arXiv:2005.02344

    Freed and Hopkins developed an algebraic theory of cubic forms, which is an analogy to the theory of quadratic forms in topology. They are motivated by the Witten-Freed-Hopkins anomaly cancellation formula in M-theory, which equals a cubic form arising from an E 8 E_8 bundle over a 12 dimensional spin manifold to the indices of twisted Dirac operators on the manifold. In this talk, we will first review the Witten-Freed-Hopkins anomaly cancellation formula and the algebraic theory of cubic forms, and then show that the cubic forms as well as the anomaly cancellation formula can be naturally derived from modular forms that we construct inspired by the Witten genus and the basic representation of affine 𝔢 8 \mathfrak{e}_8 . Following this approach, we obtain new cubic forms and anomaly cancellation formulas on non-spin manifolds and thus provide a unified way to obtain anomaly cancellation formulas of this type. This is based on our joint work with Prof. Ruizhi Huang, Prof. Kefeng Liu and Prof. Weiping Zhang.

  • 16 Jan 2024

    Christian Saemann:

    Atiyah Algebroids for Higher and Groupoid Gauge Theories

    slides: pdf

    video: kt

    We present an Atiyah algebroid picture for higher and groupoid gauge theories. Common to both is the fact that straightforward definitions of curvatures are only suitable for partially flat cases. Instead, one has to adjust the underlying cocycle relations, leading to new curvatures and gauge transformations. The Atiyah algebroid picture I sketch provides a good idea about the origin of adjustments and why they are required even in the relative conventional case of groupoid gauge theories.

  • 17 Jan 2024

    Chris Hull:

    Self-Dual pp-Form Gauge Fields and the Topology of the Graviton

    slides: pdf

    video: kt

    cf.: arXiv:2307.04748

    Sen’s action for a p p -form gauge field with self-dual field strength coupled to a spacetime metric involves an explicit Minkowski metric and the presence of this raises questions as to whether the action is coordinate independent and whether it can be used on a general spacetime manifold. A natural generalisation of Sen’s action is presented in which the Minkowski metric is replaced by a second metric on spacetime. The theory is covariant and can be formulated on any spacetime. The theory describes a physical sector, consisting of the chiral p p -form gauge field coupled to the dynamical metric gg, plus a shadow sector consisting of a second chiral pp-form and the second metric. The resulting theory is covariant and can be formulated on any spacetime. A spacetime with two metrics has some interesting geometry and some of this is explored here and used in the construction of the interactions. The action has two diffeomorphism-like symmetries, one acting only on the physical sector and one acting only on the shadow sector, with the spacetime diffeomorphism symmetry arising as the diagonal subgroup.

  • 17 Jan 2024 (talk canceled last minute and postponed to 31 Jan)

    Chris Blair:

    Geometry and Dualities of Decoupling Limits in String Theory and M-Theory

    cf.: arXiv:2311.10564

    Our understanding of M-theory is based on a duality web connecting different limits of the theory. I’ll discuss the extension of this duality web to a wide variety of decoupling limits related by duality to the null reduction of M-theory (and hence to the proposal that M-theory can be described by Matrix theory). From a modern perspective, these limits involve non-relativistic geometries, leading to new variants of supergravity in 11- and 10-dimensions. I’ll discuss how to systematically explore these corners of M-theory, following the roadmap of

M-Theory and Mathematics 2023

  • on: January 12-15, 2023

    at: CQTS @ New York University, Abu Dhabi

    see: event webpage

\phantom{-----} (logo adapted from JMP 62 (2021) 042301)


(from left to right: Valera, Jurčo, Berman, Alfonsi, Han, Schreiber, Mathai, Saemann, Sati, Voronov, Lambert, Bah, Tsimpis, Hull, Marrani, He, Singh, Giotopoulos, Szabo, )

Titles, Abstracts, and Slides for M-Theory & Math 2023 (in chronological order of talks delivered):

  • Dimitrios Tsimpis:

    Universal accelerating cosmologies from 10d supergravity

    slides: pdf

    video: YT

    cf.: arXiv:2210.10813

    4d Friedmann-Lemaître-Robertson-Walker cosmologies are obtained from time-dependent compactifications of Type IIA 10d supergravity on various classes of 6d manifolds. These cosmologies are universal in that they do not depend on the detailed features of the compactification manifold, but only on the properties which are common to all the manifolds belonging to that class. Once the equations of motion are rewritten as an appropriate dynamical system, the existence of solutions featuring a phase of accelerated expansion is made manifest. Some of the resulting cosmologies exhibit eternal or semi-eternal acceleration, whereas others allow for a parametric control on the number of e\mathrm{e}-foldings. Moreover, we find several smooth accelerating cosmologies without Big Bang singularities: the universe is contracting in the cosmological past (T<0T \lt 0), expanding in the future (T>0T \gt 0), while in the vicinity of T=0T = 0 it becomes de Sitter in hyperbolic slicing. We also obtain several cosmologies featuring an infinite number of cycles of alternating periods of accelerated and decelerated expansions.

  • Fei Han:

    Graded T-duality with H-flux for 2d sigma models

    slides: pdf

    cf.: arXiv:2207.03134

    T-duality in string theory can be realised as a transformation acting on the worldsheet fields in the two-dimensional nonlinear sigma model. Bouwknegt-Evslin-Mathai established the T-duality in a background flux for the first time upon compactifying spacetime in one direction to a principal circle by constructing the T-dual maps transforming the twisted cohomology of the dual spacetimes. In this talk, we will describe our recent work on how to promote the T-duality maps of Bouwknegt-Evslin-Mathai in two aspects. More precisely, we will introduce (1) graded T-duality, concerning the graded T-duality maps of all levels of twistings; (2) the 2-dimensional sigma model picture, concerning the double loop space of spacetimes. This represents our joint work with Mathai.

  • Eric Sharpe:

    An introduction to decomposition

    slides: pdf

    video: YT

    cf.: arXiv:2204.09117

    In this talk I will review work on ‘decomposition’, a property of 2d theories with 1-form symmetries and, more generally, d-dim’l theories with ( d 1 ) (d-1) -form symmetries. Decomposition is the observation that such quantum field theories are equivalent to (‘decompose into’) disjoint unions of other QFTs, known in this context as “universes”.

    Examples include two-dimensional gauge theories and orbifolds with matter invariant under a subgroup of the gauge group. Decomposition explains and relates several physical properties of these theories – for example, restrictions on allowed instantons arise as a “multiverse interference effect” between contributions from constituent universes.

    First worked out in 2006 as part of efforts to understand string propagation on stacks, decomposition has been the driver of a number of developments since. I will walk through general aspects of 2d gauge theories that exhibit decomposition, dive into specifics in orbifold examples, and as time permits, discuss recent work in progress.

  • Meer Ashwinkumar:

    Matrix Quantization of Classical Nambu Brackets and Super pp-Branes

    video: YT

    cf.: arXiv:2103.06666

    We will present an explicit matrix algebra quantization of the algebra of volume-preserving diffeomorphisms of the nn-torus. That is, we approximate the corresponding classical Nambu brackets using 𝔰𝔩(N n/2,)\mathfrak{sl}\big(N^{\lceil n/2\rceil}, \mathbb{C}\big)-matrices equipped with the finite bracket given by the completely anti-symmetrized matrix product, such that the classical brackets are retrieved in the NN \to \infty limit. We then apply this approximation to the super 4-brane in 9 dimensions and give a regularized action in analogy with the matrix quantization of the supermembrane. This action exhibits a reduced gauge symmetry that we discuss from the viewpoint of L L_\infty -algebras in a slight generalization to the construction of Lie 2-algebras from Bagger-Lambert 3-algebras.

  • Alessio Marrani:

    Exceptional super Yang-Mills in 27+327 + 3 and worldvolume M-theory

    slides: pdf

    video: YT

    cf.: arXiv:1906.10709

    Some time ago, Bars and Sezgin proposed a super Yang-Mills theory in D=s+t=11+3D=s+t=11+3 space-time dimensions, with an electric 3-brane that generalizes the 2-brane of M-theory. More recently, Rios, Chester and the speaker found an infinite family of “exceptional” super Yang-Mills theories in D=s+t=(8n+3)+3D=s+t=(8n+3)+3. A particularly interesting case occurs for n=3n=3, namely in signature D=27+3D=27+3, in which the superalgebra is centrally extended by an electric 11-brane and its 15-brane magnetic dual. The worldvolume symmetry of the 11-brane has signature D=11+3D=11+3 and can reproduce super Yang-Mills theory in D=11+311+3. Upon reduction to D=26+2D=26+2, the 11-brane reduces to a 10-brane with 10+210+2 worldvolume signature. A single time projection gives a 10+110+1 worldvolume signature, and it can serve as a model for D=10+1D=10+1 M-theory as a reduction from the D=26+1D=26+1 signature of the bosonic M-theory of Horowitz and Susskind; this is further confirmed by the reduction of chiral (1,0)(1,0), D=11+3D=11+3 superalgebra to the 𝒩=1\mathcal{N}=1 superalgebra in D=10+1D=10+1, as found by Rudychev, Sezgin and Sundell some time ago. Extending previous results of Dijkgraaf, Verlinde and Verlinde, I will also put forward the realization of spinors as total cohomologies of (the largest spatially extended) branes which centrally extend the (1,0)(1,0) superalgebra underlying the corresponding “exceptional” super Yang-Mills theory. Moreover, by making use of an “anomalous” Dynkin embedding, I will present further evidence about Ramond‘s and Sati’s argument that M-theory has hidden Cayley plane fibers.

M-Theory and Mathematics 2020

Confirmed speakers:

Abstracts, Slides and Talk notes:

This is joint work with H. Sati (arxiv:1909.12277, arxiv:1912.10425).

  • Neil Lambert,

    Lagrangians with (2,0)(2,0) Supersymmetry

    slides: pdf

    video: YT

    cf.: arXiv:1908.10752

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

  • Yang-Hui He:

    Universes as Bigdata

    slides: pdf

    video: YT

    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.

category: reference

Last revised on May 8, 2024 at 09:00:44. See the history of this page for a list of all contributions to it.