M5 brane on $R^{1,2} \times S^3$

TL;DR

This paper analyzes the supersymmetry structure of M5 branes on a specific curved background, deriving on-shell closure and connecting to super Yang-Mills theory via dimensional reduction, with new insights into graviphoton contributions.

Contribution

It provides a detailed derivation of supersymmetry variations for M5 branes on curved spaces and introduces an additional graviphoton term related to the Hopf bundle twisting.

Findings

On-shell closure on Lie derivatives achieved for M5 brane supersymmetry variations.

Dimensional reduction yields super Yang-Mills theory on R^{1,2} x S^2 with 8 supersymmetries.

Additional graviphoton term associated with Hopf bundle twisting identified.

Abstract

We deconstruct 16 rigid supersymmetry variations for M5 brane on $\mb{R}^{1,2}\times (S^3/{\mb{Z}_k})$ and obtain on-shell closure on Lie derivatives. Dimensional reduction on the Hopf fiber by taking $k\rightarrow \infty$ gives sYM on ${\mb{R}}^{1,2} \times S^2$ with 8 rigid supersymmetries. We reproduce the result in arXiv:0908.3263 but we also derive an additional graviphoton term which is associated with the twisting of the Hopf bundle.