Supersymmetric theories on squashed five-sphere

TL;DR

This paper constructs supersymmetric theories on a squashed five-sphere with various amounts of supersymmetry, using dimensional reduction and Noether procedures, providing explicit actions for these theories.

Contribution

It introduces a method to formulate supersymmetric theories on squashed five-spheres with different supercharges, expanding the understanding of supersymmetry in curved backgrounds.

Findings

Supersymmetric theories on squashed five-spheres with 2, 4, 6, and 12 supercharges constructed.

Explicit supersymmetric Yang-Mills and Chern-Simons actions derived.

Framework enables further studies of supersymmetry in curved geometries.

Abstract

We construct supersymmetric theories on the SU(3)xU(1) symmetric squashed five-sphere with 2, 4, 6, and 12 supercharges. We first determine the Killing equation by dimensional reduction from 6d, and use Noether procedure to construct actions. The supersymmetric Yang-Mills action is straightforwardly obtained from the supersymmetric Chern-Simons action by using a supersymmetry preserving constant vector multiplet.