Exact Matrix Elements in Supersymmetric Theories

TL;DR

This paper calculates exact form factors in N=1 Super Sinh-Gordon model, solving coupled equations and exploring analytic continuations to study related supersymmetric models and a fermionic c-theorem.

Contribution

It provides the first exact determination of form factors for trace operators in supersymmetric theories by solving unitarity and crossing equations.

Findings

Exact form factors for N=1 Super Sinh-Gordon model obtained.

Analytic continuation links to Roaming Series and minimal supersymmetric models.

A fermionic c-theorem and sum-rule are established.

Abstract

The lowest representatives of the Form Factors relative to the trace operators of N=1 Super Sinh-Gordon Model are exactly calculated. The novelty of their determination consists in solving a coupled set of unitarity and crossing equations. Analytic continuations of the Form Factors as functions of the coupling constant allows the study of interesting models in a uniform way, among these the latest model of the Roaming Series and the minimal supersymmetric models as investigated by Schoutens. A fermionic version of the $c$-theorem is also proved and the corresponding sum-rule derived.