ABJ Wilson loops and Seiberg duality
113B04 - 113B04
Progress of Theoretical and Experimental Physics
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We study supersymmetric Wilson loops in the N=6 supersymmetric U(N1)k×U(N2)−k Chern–Simons-matter (CSM) theory, the ABJ theory, at finite N1 , N2 , and k . This generalizes our previous study on the ABJ partition function. First computing the Wilson loops in the U(N1)×U(N2) lens space matrix model exactly, we perform an analytic continuation, N2 to −N2 , to obtain the Wilson loops in the ABJ theory that is given in terms of a formal series and is only valid in perturbation theory. Via a Sommerfeld–Watson-type transform, we provide a nonperturbative completion that renders the formal series well defined at all couplings. This is given by min(N1,N2) -dimensional integrals that generalize the “mirror description” of the partition function of the ABJM theory. Using our results, we find the maps between the Wilson loops in the original and Seiberg dual theories and prove the duality. In our approach we can explicitly see how the perturbative and nonperturbative contributions to the Wilson loops are exchanged under the duality. The duality maps are further supported by a heuristic yet very useful argument based on the brane configuration as well as an alternative derivation based on that of Kapustin and Willett (arXiv:1302.2164 [hep-th]).
AuthorsShinji, H; Keita, N; Masaki, S
- College Publications