Towards holography in the BV-BFV setting

Abstract

We show how the BV-BFV formalism provides natural solutions to descent equations, and discuss how it relates to the emergence of holographic counterparts of given gauge theories. Furthermore, by means of an AKSZ-type construction we reproduce the Chern-Simons to Wess-Zumino-Witten correspondence from infinitesimal local data, and show an analogous correspondence for BF theory. We discuss how holographic correspondences relate to choices of polarisation relevant for quantisation, proposing a semi-classical interpretation of the quantum holographic principle.

arXiv comment42 pages, Accepted manuscript. A comment on the Poisson Sigma model was added. Few stylistic improvements

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Cited by in corpus (16)

• Symplectic reduction of Yang-Mills theory with boundaries: from superselection sectors to edge modes, and back
• Presymplectic AKSZ formulation of Einstein gravity
• General Relativity and the AKSZ construction
• BV equivalence with boundary
• Presymplectic gauge PDEs and Lagrangian BV formalism beyond jet-bundles
• Quantum Chern-Simons theories on cylinders: BV-BFV partition functions
• The quasilocal degrees of freedom of Yang-Mills theory
• Gravity with torsion as deformed $BF$ theory
• A note on gluing via fiber products in the (classical) BV-BFV formalism
• BV analysis of Polyakov and Nambu-Goto theories with boundary
• Full S-matrices and Witten diagrams with (relative) L-infinity algebras
• Defects via Factorization Algebras
• The linear CS/WZW bulk/boundary system in AQFT
• Dimensional reduction of Courant sigma models and Lie theory of Poisson groupoids
• Out-of-time-order asymptotic observables are quasi-isomorphic to time-ordered amplitudes
• Quantizing Derived Mapping Stacks