We construct a generalized cusped Wilson loop operator in  = 6 super Chern-Simons-matter theories which is locally invariant under half of the supercharges. It depends on two parameters and interpolates smoothly between the 1/2 BPS line or circle and a pair of antiparallel lines, representing a natural generalization of the quark-antiquark potential in ABJ(M) theories. For particular choices of the parameters we obtain 1/6 BPS configurations that, mapped on S 2 by a conformal transformation, realize a three-dimensional analogue of the wedge DGRT Wilson loop of  = 4. The cusp couples, in addition to the gauge and scalar fields of the theory, also to the fermions in the bifundamental representation of the U(N) × U(M) gauge group and its expectation value is expressed as the holonomy of a suitable super-connection. We discuss the definition of these observables in terms of traces and the role of the boundary conditions of fermions along the loop. We perform a complete two-loop analysis, obtaining an explicit result for the generalized cusp at the second non-trivial order, from which we read off the interaction potential between heavy 1/2 BPS particles in the ABJ(M) model. Our results open the possibility to explore in the three-dimensional case the connection between localization properties and integrability, recently advocated in D = 4.

The generalized cusp in ABJ(M) $$ \mathcal{N} $$ = 6 Super Chern-Simons theories / Griguolo, Luca; Daniele, Marmiroli; Gabriele, Martelloni; Domenico, Seminara. - In: JOURNAL OF HIGH ENERGY PHYSICS. - ISSN 1029-8479. - 2013:5(2013). [10.1007/JHEP05(2013)113]

The generalized cusp in ABJ(M) $$ \mathcal{N} $$ = 6 Super Chern-Simons theories

GRIGUOLO, Luca;
2013-01-01

Abstract

We construct a generalized cusped Wilson loop operator in  = 6 super Chern-Simons-matter theories which is locally invariant under half of the supercharges. It depends on two parameters and interpolates smoothly between the 1/2 BPS line or circle and a pair of antiparallel lines, representing a natural generalization of the quark-antiquark potential in ABJ(M) theories. For particular choices of the parameters we obtain 1/6 BPS configurations that, mapped on S 2 by a conformal transformation, realize a three-dimensional analogue of the wedge DGRT Wilson loop of  = 4. The cusp couples, in addition to the gauge and scalar fields of the theory, also to the fermions in the bifundamental representation of the U(N) × U(M) gauge group and its expectation value is expressed as the holonomy of a suitable super-connection. We discuss the definition of these observables in terms of traces and the role of the boundary conditions of fermions along the loop. We perform a complete two-loop analysis, obtaining an explicit result for the generalized cusp at the second non-trivial order, from which we read off the interaction potential between heavy 1/2 BPS particles in the ABJ(M) model. Our results open the possibility to explore in the three-dimensional case the connection between localization properties and integrability, recently advocated in D = 4.
2013
The generalized cusp in ABJ(M) $$ \mathcal{N} $$ = 6 Super Chern-Simons theories / Griguolo, Luca; Daniele, Marmiroli; Gabriele, Martelloni; Domenico, Seminara. - In: JOURNAL OF HIGH ENERGY PHYSICS. - ISSN 1029-8479. - 2013:5(2013). [10.1007/JHEP05(2013)113]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11381/2708296
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