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

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Abstract

We construct a generalized cusped Wilson loop operator in \( \mathcal{N} \) = 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 \( \mathcal{N} \) = 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.

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Authors and Affiliations

  1. Dipartimento di Fisica, Università di Parma and INFN Gruppo Collegato di Parma, Viale G.P. Usberti 7/A, 43100, Parma, Italy

    Luca Griguolo & Daniele Marmiroli

  2. Dipartimento di Fisica e Astronomia, Università di Firenze and INFN Sezione di Firenze, Via G. Sansone 1, 50019, Sesto Fiorentino, Italy

    Gabriele Martelloni & Domenico Seminara

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  1. Luca Griguolo
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  2. Daniele Marmiroli
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  3. Gabriele Martelloni
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  4. Domenico Seminara
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Correspondence to Domenico Seminara.

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Griguolo, L., Marmiroli, D., Martelloni, G. et al. The generalized cusp in ABJ(M) \( \mathcal{N} \) = 6 Super Chern-Simons theories. J. High Energ. Phys. 2013, 113 (2013). https://doi.org/10.1007/JHEP05(2013)113

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