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 S3. 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 two-loop, 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 cT 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.
Highlights
AdS/CFT correspondence [1,2,3], since they possess string or M-theory duals, or weakly coupled higher-spin fields in AdS4 [4]
From a general point of view, progress on the non-perturbative dynamics of SCFTs has been favoured by two powerful tools, the conformal bootstrap and supersymmetric localization
The situation becomes even more interesting since, due to the enhanced supersymmetry the correlation functions of dimension-one topological operators can be related to the ones of the stress-energy tensor in a particular kinematic configuration
Summary
Inside the complexification of the su(3), we can select the su(1, 1)( sl(2)) subalgebra generated by su(1, 1). These generators obey the following commutation relations [R0, R±] = ±R± [R+, R−] = −2R0. The topological twist can be performed by taking a suitable diagonal sum of the original spacetime conformal algebra defined in (C.1) with the su(1, 1) given in (3.4). We shall denote this twisted conformal algebra on the line with su(1, 1). The twisted generators L±, L0 and the charges Q1 and Q2 span a superalgebra, which possesses a central extension given by. Where M is the u(1) generator defined in (C.4)
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