Abstract
We investigate the exact results for circular 1/4 and 1/2 BPS Wilson loops in the d = 3 mathcal = 4 super Chern-Simons-matter theory that could be obtained by orbifolding Aharony-Bergman-Jafferis-Maldacena (ABJM) theory. The partition function of the mathcal = 4 orbifold ABJM theory has been computed previously in the literature. In this paper, we re-derive it using a slightly different method. We calculate the vacuum expectation values of the circular 1/4 BPS Wilson loops in fundamental representation and of circular 1/2 BPS Wilson loops in arbitrary representations. We use both the saddle point approach and Fermi gas approach. The results for Wilson loops are in accord with the available gravity results.
Highlights
In the N = 4 orbifold ABJM theory with gauge group U (N )2r, there are 2r linearly independent 1/2 BPS Wilson loops that preserve the same supersymmetries, but there are not so many 1/2 BPS branes in M-theory in AdS4×S7/(Zr×Zrk) spacetime
We review some results in ABJM theory
We have calculated the vacuum expectation values of the circular BPS Wilson loops in arbitrary representations in the N = 4 orbifold ABJM theory
Summary
The computation of the partition function of the N = 4 orbifold ABJM theory can be localized to the matrix model [17]3. When r = 1 it is reduced to the ABJM matrix model (2.1) It can be written as canonical ensemble partition function of an N -particle Fermi gas with one-particle density matrix [23]. From the results of ABJM theory we have nprt(μ) = Crμ2 + nr0, Nrpt(μ) = Crμ2 + Br, Jrpt(μ). This is in accordance with the result in [30], and here we re-derive it in a different way.
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