Seiberg-Witten Theories on Ellipsoids

TL;DR

This paper derives conditions for supersymmetry in Seiberg-Witten theories on curved 4D ellipsoids and computes their partition functions, revealing a potential link to 2D Liouville or Toda theories.

Contribution

It introduces new Killing spinor equations for Seiberg-Witten theories on curved backgrounds and calculates their partition functions on ellipsoids, suggesting a novel correspondence with 2D conformal field theories.

Findings

Supersymmetry is preserved on ellipsoids with appropriate auxiliary fields.

Partition functions match structures of 2D Liouville or Toda correlators.

The results imply a deeper connection between 4D gauge theories and 2D CFTs.

Abstract

We present a set of equations for a 4D Killing spinor which guarantees the Seiberg-Witten theories on a curved background to be supersymmetric. The equations involve an SU(2) gauge field and some auxiliary fields in addition to the metric. Four-dimensional ellipsoids with U(1)xU(1) isometry are shown to admit a supersymmetry if these additional fields are chosen appropriately. We compute the partition function of general Seiberg-Witten theories on ellipsoids, and the result suggests a correspondence with 2D Liouville or Toda correlators with general coupling constant b.