Factorising the 3D Topologically Twisted Index

Abstract

We explore the path integration -- upon the contour of hermitian (non-auxliary) field configurations -- of topologically twisted $\mathcal{N}=2$ Chern-Simons-matter theory (TTCSM) on ${\mathbb{S}}_2$ times a segment. In this way, we obtain the formula for the 3D topologically twisted index, first as a convolution of TTCSM on ${\mathbb{S}}_2$ times halves of ${\mathbb{S}}_1$, second as TTCSM on ${\mathbb{S}}_2$ times ${\mathbb{S}}_1$ -- with a puncture --, and third as TTCSM on ${\mathbb{S}}_2\times {\mathbb{S}}_1$. In contradistinction to the first two cases, in the third case, the vector multiplet auxiliary field $D$ is constrained to be anti-hermitian.

v2:typos corrected and improved presentation of section 3; v3: matches the published version

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Cited by in corpus (10)

• An extremization principle for the entropy of rotating BPS black holes in AdS${}_5$
• Holographic microstate counting for AdS${}_4$ black holes in massive IIA supergravity
• Coulomb Branch Operators and Mirror Symmetry in Three Dimensions
• Microstate Counting of $Ad{S}_4$ Hyperbolic Black Hole Entropy via the Topologically Twisted Index
• N=2 gauge theories on the hemisphere $H{S}^4$
• Boundaries, Vermas, and Factorisation
• Localization of 4d $\mathcal{N}=1$ theories on ${\mathbb{D}}^2\times {\mathbb{T}}^2$
• Blocks and Vortices in the 3d ADHM Quiver Gauge Theory
• Black hole microstates and supersymmetric localization
• Gluing I: Integrals and Symmetries