Gauged Nonlinear Sigma Model and Boundary Diffeomorphism Algebra

TL;DR

This paper explores a Chern-Simons gauged nonlinear sigma model with boundary, revealing how bulk diffeomorphism invariance leads to a boundary theory with an enlarged Virasoro algebra and explicit solutions for Gauss's law.

Contribution

It demonstrates the reduction of the bulk theory to a boundary nonlinear sigma model on Hermitian symmetric space and computes the boundary diffeomorphism algebra.

Findings

Gauss's law explicitly solvable on Hermitian symmetric space

Bulk theory reduces to boundary nonlinear sigma model

Boundary diffeomorphism algebra forms an enlarged Virasoro algebra

Abstract

We consider Chern-Simons gauged nonlinear sigma model with boundary which has a manifest bulk diffeomorphism invariance. We find that the Gauss's law can be solved explicitly when the nonlinear sigma model is defined on the Hermitian symmetric space, and the original bulk theory completely reduces to a boundary nonlinear sigma model with the target space of Hermitian symmetric space. We also study the symplectic structure, compute the diffeomorphism algebra on the boundary, and find an (enlarged) Virasoro algebra with classical central term.