# Flavor deformations and supersymmetry enhancement in $4d$ $\mathcal{N}=2$ theories

### Submission summary

 As Contributors: Usman Naseer · Charles Thull Arxiv Link: https://arxiv.org/abs/2110.09329v3 (pdf) Date accepted: 2022-06-01 Date submitted: 2022-05-17 11:14 Submitted by: Naseer, Usman Submitted to: SciPost Physics Academic field: Physics Specialties: High-Energy Physics - Theory Approach: Theoretical

### Abstract

We study $\mathcal{N}=2$ theories on four-dimensional manifolds that admit a Killing vector $v$ with isolated fixed points. It is possible to deform these theories by coupling position-dependent background fields to the flavor current multiplet. The partition function of the deformed theory only depends on the value of the background scalar fields at the fixed points of $v$. For a single adjoint hypermultiplet, the partition function becomes independent of the supergravity as well as the flavor background if the scalars attain special values at the fixed points. For these special values, supersymmetry at the fixed points enhances from the Donaldson-Witten twist to the Marcus twist or the Vafa-Witten twist of $\mathcal{N}=4$ SYM. Our results explain the recently observed squashing independence of $\mathcal{N}=2^*$ theory on the squashed sphere and provide a new squashing independent point. Interpreted through the AGT-correspondence, this implies the $b$-independence of torus one-point functions of certain local operators in Liouville/Toda CFT. The position-dependent deformations imply relations between correlators of partially integrated operators in any $\mathcal{N}=2$ SCFT with flavor symmetries.

###### Current status:
Publication decision taken: accept

Editorial decision: For Journal SciPost Physics: Publish
(status: Editorial decision fixed and (if required) accepted by authors)

We thank the referees for their careful reading of the manuscript and their suggestions. We have incorporated all their suggestions in the new manuscript and the list of changes is given.

### List of changes

1. Fixed various punctuations typos in eqs. (3.4), (3.19), (4.3), (4.11) as pointed out by referee 2
2. Highlighted in equation (3.11) the special values for $m_x$ as well as the definition of $m^*_{\varepsilon_x,\varepsilon'_x}$.
3. Replaced $\varepsilon_y$ in eqs. (2.18) and (3.10) by $\varespilon_y$ in eq. (2.18), (3.10).
4. Fixed typos pointed out by referee 1 in eq. 3.21 and on page 19.