Construction and classification of novel BPS Wilson loops in quiver Chern–Simons-matter theories

Abstract

In this paper we construct and classify novel Drukker-Trancanelli (DT) type BPS Wilson loops along infinite straight lines and circles in N = 2, 3 quiver superconformal Chern-Simons-matter theories, Aharony-Bergman-Jafferis-Maldacena (ABJM) theory, and N = 4 orbifold ABJM theory. Generally we have four classes of Wilson loops, and all of them preserve the same supersymmetries as the BPS Gaiotto-Yin (GY) type Wilson loops. There are several free complex parameters in the DT type BPS Wilson loops, and for two classes of Wilson loops in ABJM theory and N = 4 orbifold ABJM theory there are supersymmetry enhancements at special values of the parameters. We check that the differences of the DT type and GY type Wilson loops are Q-exact with Q being some supercharges preserved by both the DT type and GY type Wilson loops. The results would be useful to calculate vacuum expectation values of the DT type Wilson loops in matrix models if they are still BPS quantum mechanically. * ouyangh@ihep.ac.cn † wujb@ihep.ac.cn ‡ jjzhang@ihep.ac.cn1 Introduction BPS (Bogomol'nyi-Prasad-Sommerfield) Wilson loops are important nonlocal objects in supersymmetric gauge theories, and in AdS/CFT correspondence [1-3] they are dual to probe F-strings/membranes in string/M theory [4-7], when they are in fundamental representation of the gauge group. BPS Wilson loops in three-dimensional quiver superconformal Chern-Simons-matter (CSM) theories are more complex than those in four-dimensional super Yang-Mills theories. One can use only bosonic fields and Note that the two equations are consistent, since they are complex conjugates of each other. In this case we haveThe Wilson loop is global SU (3) R-symmetry invariant. Whenᾱ 2 = 0, it is just Wilson loop that was constructed in [9].So for general parameters the Wilson loop with (4.26) is 1/6 BPS, and the preserved supersymmetries are (4.19). When there is also (4.33), the Wilson loop is enhanced to 1/2 BPS, and the preserved supersymmetries are (4.34). Class IIIn the second solution the calculation is parallel to that of the first one. We havē α 1,2 = β 1,2 = 0, (4.36)

Supersymmetric mixed boundary conditions in AdS2 and DCFT1 marginal deformations

“…We concentrated on a specific set of fluctuations, for the string worldsheet dual to Wilson loops in ABJM theories, consisting in massless scalar and fermionic fields. Our motivation was to identify boundary conditions that could correspond to the interpolating Wilson loop family found in [17,18] and reviewed in section 2. We interpreted the boundary conditions for the fluctuations as exact marginal deformations of the DCFT 1 defined by the loop.…”

“…The Q-exactness (2.16) for the circular loop case cannot be shown as simply as above due to a boundary term at 2π that we disregard for the straight line. Nevertheless, the statement (2.16) remains true for the circle since the steps in [12] apply straightforwardly as shown in [17,18]. We review them below.…”

“…A natural question then arises: whether mixing boundary conditions could give rise to Wilson loops that interpolate between the 1/2 and the 1/6 BPS ones. Interestingly, such a supersymmetric family of interpolating Wilson loops was found in [17,18]. Although it is natural to expect that the dual interpretation of them should be given in terms of some type of mixing boundary conditions, the precise details are not fully obvious and the role of supersymmetry have not been discussed yet in the literature.…”

“…The aim of this paper is to propose certain mixing boundary in AdS 2 corresponding to the interpolating Wilson loops described in [17,18]. There are two important restrictions that will guide us to make a proposal.…”

The quantum 1/2 BPS Wilson loop in N = 4 $$ \mathcal{N}=4 $$ Chern-Simons-matter theories

“…These operators were defined in [2][3][4][5][6] and we review their construction in section 2 along with a quick glimpse at the structure of the N = 4 CS models [7,8].…”