BV Quantization of Topological Open Membranes

Abstract

We study bulk-boundary correlators in topological open membranes. The basic example is the open membrane with a WZ coupling to a 3-form. We view the bulk interaction as a deformation of the boundary string theory. This boundary string has the structure of a homotopy Lie algebra, which can be viewed as a closed string field theory. We calculate the leading order perturbative expansion of this structure. For the 3-form field we find that the C-field induces a trilinear bracket, deforming the Lie algebra structure. This paper is the first step towards a formal universal quantization of general quasi-Lie bialgebroids.

A minimal BV action for Vasiliev’s four-dimensional higher spin gravity

“…As for boundary conditions [24], the undeformed ones (96) (imposed off shell in order to have a globally-defined bulk action) are compatible with those following the variational principle provided that the off-shell extensions are super-field extensions V r = V r (X, dX) of topological vertex operators as defined in (64), i.e.…”

“…therein); interestingly, the BF model without Poisson structure on a non-commutative manifold was studied in [20,21]. Further developments of the AKSZ formalism can be found in [22,23,24] and [25,26,27,28,29,30,31,32,33], and its close ties to unfolded dynamics have been stressed in [34,35,36,37,38,39]. For related treatments of more general dynamical systems, not necessarily based on differential algebras, see [40,41] and references therein.…”

Sigma models for genuinely non-geometric backgrounds

“…Additionally, the condition in the fourth row is also standard and it corresponds to the H-twisted Poisson sigma model [29,30,61]. This table can also be obtained in the context of the AKSZ sigma models and we now show how (see also [28,31] for related discussions).…”

“…Moreover, we show that in certain limits these conditions reproduce known results, for example integrability conditions for Dirac structures, such as the ones found in Refs. [29][30][31] and additional ones derived in Ref. [8].…”

“…in [28] and [31] and they can be solved in many ways, as we will explore below. The second consistency condition that has to be satisfied reads as…”