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.
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Cabo-Bizet, A. Factorising the 3D topologically twisted index. J. High Energ. Phys. 2017, 115 (2017). https://doi.org/10.1007/JHEP04(2017)115
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DOI: https://doi.org/10.1007/JHEP04(2017)115