Exact Scattering in the SU(n) Supersymmetric Principal Chiral Model

TL;DR

This paper proposes an exact factorizable S-matrix for the SU(n) supersymmetric principal chiral model, confirming its spectrum and mass-gap through perturbative and TBA calculations, with no additional CDD factors.

Contribution

It introduces a complete, exact S-matrix for the SU(n) supersymmetric principal chiral model, incorporating supersymmetries and confirming the spectrum and mass-gap.

Findings

The S-matrix matches perturbative and TBA results.

No additional CDD factors are needed in the S-matrix.

An exact expression for the mass-gap is derived.

Abstract

The complete spectrum of states in the supersymmetric principal chiral model based on SU(n) is conjectured, and an exact factorizable S-matrix is proposed to describe scattering amongst these states. The SU(n)_L*SU(n)_R symmetry of the lagrangian is manifest in the S-matrix construction. The supersymmetries, on the other hand, are incorporated in the guise of spin-1/2 charges acting on a set of RSOS kinks associated with su(n) at level n. To test the proposed S-matrix, calculations of the change in the ground-state energy in the presence of a coupling to a background charge are carried out. The results derived from the lagrangian using perturbation theory and from the S-matrix using the TBA are found to be in complete agreement for a variety of background charges which pick out, in turn, the highest weight states in each of the fundamental representations of SU(n). In particular, these methods rule out the possibility of additional CDD factors in the S-matrix. Comparison of the expressions found for the free-energy also yields an exact result for the mass-gap in these models: m/Lambda_{MS-bar}=(n/pi)sin(pi/n).