BPS Partition Functions for S-folds

Abstract

We derive a formula for the BPS partition functions of arbitrary S-fold theories. We first generalize the known result for the $\mathcal{N}=4$ $U(N)$ supersymmetric Yang-Mills theory to $SO$ and $Sp$ theories, and then we extend the formula to $\mathcal{N}=3$ theories. We confirm that the results for rank $1$ and $2$ are consistent to the supersymmetry enhancement from $\mathcal{N}=3$ to $\mathcal{N}=4$. We also derive the same formula from the quantization of D3-branes in ${\mathbf{S}}^5/{\mathbb{Z}}_k$.

28 pages; v2:minor corrections, a reference added, section 5 inserted; v3:S-fold action modified, minor corrections, a reference added, version accepted for publication for JHEP

References in corpus (2)

• The 4d Superconformal Index from q-deformed 2d Yang-Mills
• Supersymmetric states of N=4 Yang-Mills from giant gravitons