BV analysis of Polyakov and Nambu-Goto theories with boundary

TL;DR

This paper compares the BV quantization of Polyakov and Nambu-Goto string theories on manifolds with boundary, highlighting the successful BV formulation for Polyakov and the issues with Nambu-Goto, and describes their reduced phase spaces.

Contribution

It demonstrates the BV quantization for Polyakov string theory with boundary and clarifies the limitations of Nambu-Goto theory, providing a unified phase space description.

Findings

BV data induces compatible BV-quantization for Polyakov theory

Nambu-Goto theory fails to meet regularity requirements

Reduced phase spaces are explicitly described and related

Abstract

The Batalin-Vilkovisky data for Polyakov string theory on a manifold with (non-null) boundary is shown to induce compatible Batalin--Fradkin--Vilkovisky data, thus allowing BV-quantisation on manifolds with boundary. On the other hand, the analogous formulation of Nambu--Goto string theory fails to satisfy the needed regularity requirements. As a byproduct, a concise description is given of the reduced phase spaces of both models and their relation, for any target $d$-dimensional Lorentzian manifold.