Classical BV Theories on Manifolds with Boundary
Abstract
In this paper we extend the classical BV framework to gauge theories on spacetime manifolds with boundary. In particular, we connect the BV construction in the bulk with the BFV construction on the boundary and we develop its extension to strata of higher codimension in the case of manifolds with corners. We present several examples including electrodynamics, YangMills theory and topological field theories coming from the AKSZ construction, in particular, the ChernSimons theory, the BF theory, and the Poisson sigma model. This paper is the first step towards developing the perturbative quantization of such theories on manifolds with boundary in a way consistent with gluing.
 Publication:

Communications in Mathematical Physics
 Pub Date:
 December 2014
 DOI:
 10.1007/s0022001421453
 arXiv:
 arXiv:1201.0290
 Bibcode:
 2014CMaPh.332..535C
 Keywords:

 Mathematical Physics;
 High Energy Physics  Theory
 EPrint:
 The second version has many typos corrected, references added. Some typos are probably still there, in particular, signs in examples. In the third version more typoes are corrected and the exposition is slightly changed