Vector-Chiral Equivalence in Null Gauged WZNW Theory

TL;DR

This paper demonstrates a transformation linking vector and chiral gauged WZNW models for classical Lie groups, revealing a deep equivalence and its relation to duality in symmetric spaces.

Contribution

It introduces an explicit map between vector and chiral gauged WZNW models for classical Lie groups, highlighting their equivalence.

Findings

Vector and chiral gauged WZNW models are equivalent via a specific transformation.

The explicit map is provided for classical Lie groups $A_N$, $B_N$, $C_N$, $D_N$.

Connection established between this map and duality in Riemannian symmetric spaces.

Abstract

We consider the standard vector and chiral gauged WZNW models by their gauged maximal null subgroups and show that they can be mapped to each other by a special transformation. We give an explicit expression for the map in the case of the classical Lie groups $ A_N $, $ B_N $, $ C_N $, $ D_N $, and note its connection with the duality map for the Riemmanian globally symmetric spaces.