Quantum Conserved Currents in Supersymmetric Toda Theories

TL;DR

This paper constructs and analyzes quantum conserved currents in supersymmetric Toda theories based on specific superalgebras, establishing their quantum integrability and real particle masses despite non-hermitian Lagrangians.

Contribution

It introduces superspace Miura transformations for these theories and demonstrates quantum integrability through conserved higher-spin currents and real mass spectra.

Findings

Constructed superspace Miura transformations.

Proved quantum integrability of the models.

Confirmed real masses and soliton solutions.

Abstract

We consider $N=1$ supersymmetric Toda theories which admit a fermionic untwisted affine extension, i.e. the systems based on the $A(n,n)$, $D(n+1,n)$ and $B(n,n)$ superalgebras. We construct the superspace Miura trasformations which allow to determine the W-supercurrents of the conformal theories and we compute their renormalized expressions. The analysis of the renormalization and conservation of higher-spin currents is then performed for the corresponding supersymmetric massive theories. We establish the quantum integrability of these models and show that although their Lagrangian is not hermitian, the masses of the fundamental particles are real, a property which is maintained by one-loop corrections. The spectrum is actually much richer, since the theories admit solitons. The existence of quantum conserved higher-spin charges implies that elastic, factorized S-matrices can be constructed.