8 problems

The full quantum differential is the BV differential … Let $\mathcal{V}$ denote the cohomology of the underlying free and classical theory, and let $\mathbf{Q}$ be a differential o…

Let $\mathcal E_{\mathrm{twist}}$ be the Courant algebroid over the Dolbeault complex associated to a twist datum. The Costello–Li twist of type I supergravity is the perturbative…

In the BV formalism, let $I$ be a local interaction for a UV-finite theory, and let $r\to 0$ denote the removal of the regularization. Write $l_n^\hbar$ for the multilinear operati…

Fix a canonical $2$-framing $\phi$ of $M$, let $\mathcal{M}_j=S_{CS}^{-1}(c_j)$ be the moduli-space preimage of the Chern–Simons invariant $c_j$, and let $\mathcal{M}'$ be the modu…

Let $M$ be a spacetime, let $g \in [\mathrm{Lor}(M)/\mathrm{Diff}^{+}(M)]$ be an asymptotically flat and stationary black-hole solution, and let $\mathscr{E}_g$ be the differential…

Let $(F,Q,(-,-),W)$ be a free BV field theory, and suppose its Green's witness $W$ is obtained by truncating an $L_{\infty}$ algebra to its underlying cochain complex. Green-witnes…

Let $(M,\alpha)$ be a Poisson manifold equipped with a volume form $\Omega$, and let $\Delta_{(\Omega,\alpha)}$ be the corresponding BV operator. Denote by…

Let the Poisson sigma model on the sphere be reduced to the finite-dimensional BV theory describing constant configurations, with reduced BV action and path integral obtained by co…