# Bootstrapping Mixed MN Correlators in 3D

### Submission summary

 As Contributors: Stefanos Robert Kousvos · Andreas Stergiou Arxiv Link: https://arxiv.org/abs/2112.03919v3 (pdf) Date accepted: 2022-06-10 Date submitted: 2022-06-01 14:56 Submitted by: Kousvos, Stefanos Robert Submitted to: SciPost Physics Academic field: Physics Specialties: High-Energy Physics - Theory Approaches: Theoretical, Computational

### Abstract

The recent emergence of the modern conformal bootstrap method for the study of conformal field theories (CFTs) has enabled the revisiting of old problems in classical critical phenomena described by three-dimensional CFTs. The study of such CFTs with $O(m)^n \rtimes S_n$ global symmetry, also known as MN models, is pursued in this work. Systems of mixed correlators involving scalar operators in two different representations of the global symmetry group are considered. Isolated allowed regions are found in parameter space for various values of $m$ and $n$. These "islands" can be separated into two qualitative groups: those close to the unitarity bound and those further away. As a by-product of our analysis generic tensor structures required to bootstrap any $G^n \rtimes S_n$ theory with $G$ arbitrary are worked out.

Published as SciPost Phys. 12, 206 (2022)

We have incorporated a few more changes to clarify some of the additional issues raised by the referees. These are listed below.

### List of changes

1) We added an additional sentence at the end of paragraph 2 on page 3 to clarify why we are interested in the $\Delta_X$ - $\Delta_\phi$ plane of parameter space.

2) At the top of page 4 we added some information and some additional references regarding experimentally relevant symmetries.

3) Page 3: in depth -> in-depth.

4) We added a paragraph at the bottom of page 15.

5) We expanded the paragraph on page 22 in order to specify precisely what we have explicitly checked. The main purpose of this is for the reader to know what has and has not been checked.