58 problems

Let the $A_{N-1}$ $(2,0)$ superconformal field theory be the six-dimensional theory labelled by the simply laced Lie algebra $A_{N-1}$, and let $N$ denote the number of units of 4-…

In the infinite momentum frame, let $N$ point-like D0-branes be described by quantum mechanics, with their dynamics governed by a supersymmetric matrix model. BFSS M-theory conject…

Let $M$ be a three-dimensional twisted torus, let $\widetilde{M}=M\times S^1$ be the corresponding trivial circle bundle with coordinates $x^\mu=(x^i,x^4)$, and let $p_\mu$ be the…

Let $k$ be the orbifold order, let $S^{7}/\mathbb{Z}_{k}$ denote the quotient of the seven-sphere by the action $y^{A}\mapsto e^{2\pi i/k}y^{A}$ on its four complex coordinates, an…

Let $N$ denote the number of D0-branes, and let the low-energy dynamics of D0-branes be described by dimensionally reduced supersymmetric Yang–Mills quantum mechanics. Large-$N$ M-…

The $K3\times S^1$ compactification of type-IIB superstring theory is a candidate dual theory, and let $T^5/{\mathbb Z}_2$ denote the corresponding orbifold of M-theory. K3–M-theor…

Let M-theory be compactified on $T^{d+1}$ with $d\leq4$, let $H$ denote the resulting three-form field strengths, and let $M(\mathrm{string})$ be the mass matrix in the string repr…

M-theory is described, at least in the infinite momentum frame, by the dimensional reduction to one dimension of ten-dimensional supersymmetric Yang--Mills theory, denoted…

Consider the five basic superstring theories and the web of $S$, $T$, and $U$ dualities relating certain pairs of them. M-theory unification conjecture. The five superstring theori…

M2-brane duality conjecture. The dual theory is the $2+1$-dimensional $N=8$ superconformal field theory living on the M2 brane.

Loop-index conjecture. The effective action of F-theory compactified on $S^1$ could be computed by the same index-theoretical method as the effective action of M-theory, with loop-…

Critical-fraction conjecture. The critical fraction is

The IIA partition function admits an elliptic refinement, equivalently obtainable from the M-theory $G_4$ description. An $M2$-brane may intersect an $M5$-brane in a fundamental st…

For $d>2$, let $G(\mathrm{spacelike})$, $G(\mathrm{timelike})$, and $G(\mathrm{null})$ denote the groups obtained respectively from spacelike, timelike, and null dimensional reduct…

Let the $D=11$ supergravity fields be the graviton $g_{MN}$, gravitino $\Psi_M$, and three-form gauge field $A_{MNP}$. The equations of motion are considered without compactificati…

Matroid bundles are combinatorial analogues of vector bundles, with oriented matroids playing the role of tangent spaces or, more generally, vector spaces. The authors introduce th…

Let matrix quantum mechanics denote the BFSS matrix model, and let full eleven-dimensional M-theory denote the corresponding nonperturbative theory of quantum gravity in eleven dim…

Let $B$ be the base of a genus-one fibration, let $N$ be the degree of its multisection, and let $N_k$, for $k=1,\ldots,N-1$, denote the numbers of fibral curves intersecting the…

Let $X^6$ be the six-dimensional M5-brane worldvolume, let $[athsf{G}_4]_{\mathbb{Z}}$ denote its integral four-form flux class, and let $\beta$ be the Bockstein homomorphism assoc…

The paper considers 11-dimensional supergravity and its conjectured ultraviolet completion, referred to as M-theory. M-theory conjecture. Some completion of 11-dimensional supergra…

Cohomotopy theory assigns cohomology classes to charges carried by branes in M-theory. Cohomotopy conjecture. Cohomotopy theory is conjectured to be the actual cohomology theory of…

Let $Z$ be a Calabi–Yau five-fold with a $\mathbb{C}^{\times}$ action, and let $X$ be a threefold arising as a fixed point of this action. The M-theory index of $Z$ is conjectured…

In the DFM model, let the additional generators of the Dolbeault cohomology groups of the holomorphic non-abelian bundle be modes that are non-smooth on the singular space and have…

Let $\mathscr{X}_{\vec{n}}$ be a noncompact Calabi–Yau fivefold obtained from the superposition of KK monopoles, and let the displayed expression…

The K-theoretic tetrahedron instanton partition-function conjecture. The partition function admits the closed-form expression