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Defects in N=1 minimal models and RG flows

Matthias R. Gaberdiel, Lasse Merkens

TL;DR

The paper develops a defect-based framework to constrain RG flows among ${\cal N}=1$ superconformal minimal models, first using a bosonic SU(2) coset description of the subalgebra and then elevating the discussion to the full superconformal theory. By identifying defects that commute with the perturbations, it derives RG invariants from defect quantum dimensions and twisted Hilbert-space spin content, which must match between UV and IR. The main results yield explicit flow patterns ${\cal SM}(p,q)\to{\cal SM}(p,q')$ with $q'=sp-I$ (and their SUSY counterparts ${\cal SM}(p,sp+I)\to{\cal SM}(p,sp-I)$), along with the perturbing fields and preserved defect sets that implement these flows. The approach reproduces known unitary flows and provides a principled, extensible method for analyzing a broad class of ${\cal N}=1$ minimal models and potential generalizations to higher supersymmetry in string-theoretic contexts.

Abstract

Utilising the symmetry constraints of suitable topological defects, the possible RG flows of N=1 superconformal minimal models are studied. We first employ a coset description that only captures the bosonic subalgebra, and then generalise the discussion to the actual superconformal models.

Defects in N=1 minimal models and RG flows

TL;DR

The paper develops a defect-based framework to constrain RG flows among superconformal minimal models, first using a bosonic SU(2) coset description of the subalgebra and then elevating the discussion to the full superconformal theory. By identifying defects that commute with the perturbations, it derives RG invariants from defect quantum dimensions and twisted Hilbert-space spin content, which must match between UV and IR. The main results yield explicit flow patterns with (and their SUSY counterparts ), along with the perturbing fields and preserved defect sets that implement these flows. The approach reproduces known unitary flows and provides a principled, extensible method for analyzing a broad class of minimal models and potential generalizations to higher supersymmetry in string-theoretic contexts.

Abstract

Utilising the symmetry constraints of suitable topological defects, the possible RG flows of N=1 superconformal minimal models are studied. We first employ a coset description that only captures the bosonic subalgebra, and then generalise the discussion to the actual superconformal models.
Paper Structure (31 sections, 107 equations, 2 tables)

This paper contains 31 sections, 107 equations, 2 tables.

Table of Contents

  1. Introduction
  2. ${\cal N}=1$ minimal models and their coset description
  3. The ${\cal N}=1$ minimal models
  4. Coset description
  5. The $S$-matrix and the fusion rules
  6. Symmetries
  7. The case $u=\frac{|q-p|}{2}$ odd
  8. The case $u=\frac{|q-p|}{2}$ even
  9. Relevant deformations
  10. The defects of the bosonic coset theory
  11. Simple defects and their symmetries
  12. The worldsheet fermion number defect
  13. RG flows of ${\cal N}=1$ minimal models
  14. Renormalisation group invariants
  15. The spin content of the twisted Hilbert space
  16. ...and 16 more sections