Classical BV Theories on Manifolds with Boundary

By Alberto S. Cattaneo, P. Mnev, N. Reshetikhin. 2011

162 citations recorded by the source corpus.

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, Yang-Mills theory and topological field theories coming from the AKSZ construction, in particular, the Chern-Simons 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.

Subfields: Mathematical Physics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/fb395f4c4cec742101a7924a81bb88e190b486fc

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In Mathematical Physics

1. D. Gaitsgory
2. E. Frenkel
3. V. Drinfeld
4. E. Witten
5. D. Arinkin
6. T. Mochizuki
7. R. Bezrukavnikov
8. Y. Sakellaridis

In Nuclear and High Energy Physics

1. D. Gaitsgory

In Statistical and Nonlinear Physics

1. D. Gaitsgory
2. J. Francis

Citations in the corpus

• Sheaves of categories and the notion of 1-affineness (2013, methodology): “undary conditions, which is requiredin most applications to quantum field theories(see e.g. the workofCattaneoFelder on the Poisson sigma model [8, 9], and the recent work of Cattaneo-Mnev-Reshetikhin [10, 11]). We provide many examples of Lagrangian and symplectic structures that can be recovered in”