Super Yang-Mills on Branched Covers and Weighted Projective Spaces

Abstract

In this work we conjecture the Coulomb branch partition function, including flux and instanton contributions, for the $\mathcal{N}=2$ vector multiplet on weighted projective space ${\mathbb{CP}}_{\mathbf{N}}^2$ for equivariant Donaldson-Witten and ``Pestun-like'' theories. We claim that this partition function agrees with the one obtained from dimensional reduction of the 5d $\mathcal{N}=1$ vector multiplet on a certain branched cover of $S^5$. More precisely, the branch locus and indices have to be such that they match the singular locus and deficit angles in ${\mathbb{CP}}_{\mathbf{N}}^2$. Our conjecture is substantiated by checking that partition functions on spindles are similarly obtained from dimensional reduction of the 3d $\mathcal{N}=2$ vector multiplet on branched covers of $S^3$. This work paves the way for obtaining partition functions on more generic symplectic toric orbifolds.

22 pages; corrected statements about S1 action and base space

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Cited by in corpus (5)

• Holographic Generalised Gukov-Witten Defects
• Exact Results for SYM on $Y^{p,q}$ and $S^2\times S^2$ with Conical Singularities
• Supersymmetric localisation of $\mathcal{N}=(2,2)$ theories on a spindle
• Bubbling saddles of the gravitational index
• Large $N$ limits of supersymmetric quantum field theories: A pedagogical overview