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arXiv · 2012.11613

The topological line of ABJ(M) theory

Nicola Gorini·Luca Griguolo·Luigi Guerrini·Silvia Penati·Domenico Seminara·Paolo Soresina
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Abstract

We construct the one-dimensional topological sector of $\mathcal N = 6$ ABJ(M) theory and study its relation with the mass-deformed partition function on $S^3$. Supersymmetric localization provides an exact representation of this partition function as a matrix integral, which interpolates between weak and strong coupling regimes. It has been proposed that correlation functions of dimension-one topological operators should be computed through suitable derivatives with respect to the masses, but a precise proof is still lacking. We present non-trivial evidence for this relation by computing the two-point function at twoloop, successfully matching the matrix model expansion at weak coupling and finite ranks. As a by-product we obtain the two-loop explicit expression for the central charge $c_T$ of ABJ(M) theory. Three- and four-point functions up to one-loop confirm the relation as well. Our result points towards the possibility to localize the one-dimensional topological sector of ABJ(M) and may also be useful in the bootstrap program for 3d SCFTs.

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Nicola Gorini, Luca Griguolo, Luigi Guerrini, Silvia Penati, Domenico Seminara, Paolo Soresina. 2020-12-21. The topological line of ABJ(M) theory. https://doi.org/10.1007/jhep06(2021)091

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