15 problems

Figueroa-O'Farrill's conjecture. The BRST cohomology of any string theory and, more generally, of any two-dimensional topological conformal field theory is isomorphic to the chiral…

Let $S$ and $T$ be smooth complex submanifolds of $X$ with intersection $S\cap T$, and let ${\cal E}$ and ${\cal F}$ be twisted holomorphic bundles on $S$ and $T$. The paper constr…

Let $\omega\in H^2(X,\mathcal{O}_X^*)$ define the $B$ field, let $i:S\hookrightarrow X$ and $j:T\hookrightarrow X$ be smooth complex submanifolds with $T\subseteq S$, and let…

Let $S$ be a smooth complex submanifold of $X$, let $i:S\hookrightarrow X$, and let ${\cal E}$ and ${\cal F}$ be twisted holomorphic bundles on $S$. The spectral sequence relating…

Let $p$ be a momentum, let $H$ be its stabiliser, and let $\mathsf{H}^n(p)$ denote the absolute BRST cohomology at ghost number $n$, regarded as an $H$-module. Write…

Let $p$ be a momentum, let $H$ be its stabiliser, and let $\mathsf{H}^n(p)$ and $\mathsf{H}_{\mathrm{rel}}^n(p)$ denote the absolute and relative BRST cohomology groups at ghost nu…

Let $\mathsf{H}^n(0)$ denote the absolute BRST cohomology at ghost number $n$ and zero momentum, regarded as a representation of $\operatorname{SO}(25,1)$, and let $\mathbb{V}$ be…

Let $Q$ be the nilpotent BRST-type operator, let $H^0(Q)$ denote its zeroth cohomology, let ${\cal F}$ be the gauge-fixing space, let ${\cal B}(L^2(M,S))$ be the relevant algebra o…

For $g\in\mathrm{Co}_0$, let the twisted fake monster algebra be the generalized Kac–Moody superalgebra obtained by twisting the fake monster algebra by $g$. Let $V$ be a suitable…

Let $\det X$ be a determinant operator, and consider its BRST-closed modifications at leading order in $N$. The four towers are the modifications generated by the two bosonic const…

Beem–Rastelli conjecture. The single-trace BRST cohomology is generated by the symmetrized traces $A^{(n)}$ and their global super-conformal partners $B^{(n)}$, $C^{(n)}$, and…

Let $\mathfrak g$ be the constructed BKM superalgebra, and consider the quotient of the space of BRST-exact, $Q_L$-closed states by its subspace of $Q_L$-exact states. BRST realiza…

BRST–Lie–Rinehart cohomology conjecture. One has

Let $(KT^\bullet_{|Z},d)$ be the vertical complex obtained from the BRST differential in the homological reduction setup. Its construction may depend on the choice of generator spa…

The BRST algebra and, respectively, the vertical complex arise from the homological reduction setup described in the source. A $P_\infty$-quasiisomorphism is understood in the sens…