Quantum Non-abelian Toda Field Theories

TL;DR

This paper derives an explicit conformally invariant action for non-abelian Toda field theories, verifies conformal invariance conditions to all orders, and calculates the central charge consistent with earlier results.

Contribution

It provides the first explicit form of the conformally invariant action for non-abelian Toda theories and confirms their conformal invariance to all orders.

Findings

Explicit conformally invariant action derived

Conformal invariance conditions satisfied to all orders

Central charge matches previous calculations

Abstract

We derive an explicit, exactly conformally invariant form for the action for the non-abelian Toda field theory. We demonstrate that the conformal invariance conditions, expressed in terms of the $\beta$-functions of the theory, are satisfied to all orders, and we use our results to obtain a value for the central charge agreeing with previous calculations.