RG domain wall for the N=1 minimal superconformal models

TL;DR

The paper addresses the UV–IR mapping in $N=1$ minimal superconformal models using Gaiotto's RG domain wall framework. It specializes the domain-wall construction to the flow ${ m SM}_{k+2} o{ m SM}_{k}$ via a current-algebra coset approach and computes explicit mixing coefficients for several operator classes, including NS and Ramond fields and their descendants. The main result is a complete agreement with leading and next-to-leading order perturbative calculations, with the $k$-dependence controlled by modular data $S^{(k)}$. This work extends the RG domain wall program to supersymmetric coset CFTs, clarifies the role of modular matrices in SUSY contexts, and provides a nonperturbative handle on UV–IR maps beyond the unitary minimal models.

Abstract

We specify Gaiotto's proposal for the RG domain wall between some coset CFT models to the case of two minimal N=1 SCFT models $SM_p$ and $SM_{p-2}$ related by the RG flow initiated by the top component of the Neveu-Schwarz superfield $Φ_{1,3}$ . We explicitly calculate the mixing coefficients for several classes of fields and compare the results with the already known in literature results obtained through perturbative analysis. Our results exactly match with both leading and next to leading order perturbative calculations.