Constraints in the BV formalism: sixdimensional supersymmetry and its twists
Abstract
We formulate the abelian sixdimensional $\mathcal{N}=(2,0)$ theory perturbatively, in a generalization of the BatalinVilkovisky formalism. Using this description, we compute the holomorphic and nonminimal twists at the perturbative level. This calculation hinges on the existence of an $L_\infty$ action of the supersymmetry algebra on the abelian tensor multiplet, which we describe in detail. Our formulation appears naturally in the pure spinor superfield formalism, but understanding it requires developing a presymplectic generalization of the BV formalism, inspired by Dirac's theory of constraints. The holomorphic twist consists of symplecticvalued holomorphic bosons from the $\mathcal{N}=(1,0)$ hypermultiplet, together with a degenerate holomorphic theory of holomorphic coclosed oneforms from the $\mathcal{N}=(1,0)$ tensor multiplet, which can be interpreted as representing the intermediate Jacobian. We check that our formulation and our results match with known ones under various dimensional reductions, as well as comparing the holomorphic twist to KodairaSpencer theory. Matching our formalism to fivedimensional YangMills theory after reduction leads to some issues related to electricmagnetic duality; we offer some speculation on a nonperturbative resolution.
 Publication:

arXiv eprints
 Pub Date:
 September 2020
 DOI:
 10.48550/arXiv.2009.07116
 arXiv:
 arXiv:2009.07116
 Bibcode:
 2020arXiv200907116S
 Keywords:

 Mathematical Physics;
 High Energy Physics  Theory;
 Mathematics  Algebraic Topology
 EPrint:
 v2: updated grant information. 82 pages, seven figures. Comments appreciated!