Flavor deformations and supersymmetry enhancement in 4d N = 2 theories

We study 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 N = 4 SYM. Our results explain the recently observed squashing independence of 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 N = 2 SCFT with flavor symmetries.

Automated summary

This study focuses on N = 2 theories in four-dimensional manifolds with a Killing vector v that has isolated fixed points. By coupling position-dependent background fields to the flavor current multiplet, these theories can be deformed. The partition function of the deformed theory only depends on the value of the background scalar fields at the fixed points of v. When the scalars attain special values at the fixed points, the partition function becomes independent of supergravity and flavor background. These findings explain the observed squashing independence of N = 2* theory on the squashed sphere, providing a new squashing independent point. Through the AGT correspondence, this implies the b-independence of torus one-point functions of certain local operators in Liouville/Toda CFT.