7 problems

Let $M$ be the moduli space of instantons, let $S(TM)$ denote its chiral spin bundle, and let ${\cal L}^{(I)}$ be a line-bundle object over $M$ for which only…

Let the holomorphic theory be the ten-dimensional theory whose anomaly polynomials factorise as the heterotic-supergravity anomaly polynomials for gauge group $SO(32)$ or…

In six dimensions, let $(2,0)$ conformal supergravity be coupled to $26$ copies of the $(2,0)$ tensor multiplet $\mathrm T$. The $a$-anomaly and Casimir energy are the quantities w…

Dual Coxeter number conjecture. The coefficient $b_i$ is conjectured to equal minus the dual Coxeter number of the symmetry algebra supported on $\Sigma_i$:

Let type I Kodaira–Spencer theory be coupled to $\operatorname{SO}(32)$ holomorphic Chern–Simons theory. Localization conjecture. This coupled theory is a supersymmetric localizati…

An anomaly is a global anomaly in dimension $3$, and an invariant partition function is a partition function unchanged by the relevant symmetry. Witten's conjecture. The existence…

Let $X\to B$ be an elliptic Calabi–Yau threefold with $\mathbb{Q}$-factorial terminal singularities $\{P\}$, the relative minimal model of a Weierstrass model $W\to B$. Assume that…