Constraints in the BV formalism: Six-dimensional supersymmetry and its twists

Saberi, Ingmar und Williams, Brian R. (2022): Constraints in the BV formalism: Six-dimensional supersymmetry and its twists. In: Advances in Mathematics, Bd. 412, 108806

Abstract

We formulate the abelian six-dimensional N = (2, 0) theory perturbatively, in a generalization of the Batalin-Vilkovisky formalism. Using this description, we compute the holomor-phic and non-minimal twists at the perturbative level. This calculation hinges on the existence of an L infinity action of the su-persymmetry algebra on the abelian tensor multiplet, which we describe in detail. Our formulation appears naturally in the pure spinor superfield formalism, but understanding it re-quires developing a presymplectic generalization of the BV formalism, inspired by Dirac's theory of constraints. The holomorphic twist consists of symplectic-valued holomorphic bosons from the N = (1, 0) hypermultiplet, together with a de-generate holomorphic theory of holomorphic one-forms from the N = (1, 0) tensor multiplet, which can be seen to describe the infinitesimal intermediate Jacobian variety. We check that our formulation and our results match with known ones un-der various dimensional reductions, as well as comparing the holomorphic twist to Kodaira-Spencer theory. Matching our formalism to five-dimensional Yang-Mills theory after reduc-tion leads to some issues related to electric-magnetic duality;we offer some speculation on a nonperturbative resolution. (c) 2022 Published by Elsevier Inc.

• Dokumententyp: Zeitschriftenartikel
• Fakultät: Physik
• Themengebiete: 500 Naturwissenschaften und Mathematik > 530 Physik
• ISSN: 0001-8708
• Sprache: Englisch