Towards Holography in the BV-BFV Setting

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.