Holographical description of BPS Wilson loops in flavored ABJM theory

Journal of High Energy Physics, Dec 2014

Bin Chen, Jun-Bao Wu, Meng-Qi Zhu

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Holographical description of BPS Wilson loops in flavored ABJM theory

Bin Chen 0 2 3 4 5 6 7 Jun-Bao Wu 0 1 2 6 7 Meng-Qi Zhu 0 2 6 7 Open Access 0 2 6 7 c The Authors. 0 2 6 7 0 5 Yiheyuan Rd , Beijing 100871 , P. R. China 1 Institute of High Energy Physics, and Theoretical Physics Center for Science Facilities 2 Peking University , 5 Yiheyuan Rd, Beijing 100871 , P. R. China 3 Collaborative Innovation Center of Quantum Matter 4 Center for High Energy Physics, Peking University 5 Department of Physics, and State Key Laboratory of Nuclear Physics and Technology 6 Via Bonomea 265, I 34136, Trieste , Italy 7 Chinese Academy of Sciences , 19B Yuquan Road, Beijing 100049 , P. R. China As holographic description of BPS Wilson loops in N = 3 flavored ABJM theory with Nf = k = 1, BPS M2-branes in AdS4 N (1, 1) are studied in details. Two 1/3-BPS membrane configurations are found. One of them is dual to the 1/3-BPS Wilson loop of Gaiotto-Yin type. The regulated membrane action captures precisely the leading exponential behavior of the vacuum expectation values of 1/3-BPS Wilson loops in the strong coupling limit, which was computed before using supersymmetric localization technique. Moreover, there is no BPS membrane with more supersymmetries in the background, under quite natural assumption on the membrane worldvolume. This suggests that there is no Wilson loop preserving more than 1/3 supersymmetries in such flavored Simons Theories, 1/N Expansion 1 Introduction 2 Field theory results 3 Background and Killing spinors 4 BPS M2-branes 5 Conclusion and discussions A Spin connection of AdS4 N (1, 1) Introduction Supersymmetric Wilson loop is an important probe in studying supersymmetric quantum field theory and AdS/CFT correspondence. In the field theory, the computation of the vacuum expectation value(VEV) of such Bogomolnyi-Prasad-Sommerfield(BPS) Wilson loop often boils down to a matrix model, within recent developments of localization techniques [1]. This allows us to obtain exact results to all loops. On the other hand, if the supersymmetric field theory has a holographic dual, the BPS Wilson loop in certain representations could be dual to a fundamental string [2, 3] or even D-brane [4, 5] ending on the contour of the loop.1 This opens a new window to study the AdS/CFT correspondence and the string interactions. Among various studies on the BPS Wilson loop, the ones in three-dimensional(3d) supersymmetric Chern-Simons-matter theories are of particular interest. The gauge field in pure Chern-Simons theory is not dynamical, and the study of Wilson loops in this theory leads to important results on Jones polynomials for knots [7]. When the ChernSimons field is coupled to matter, the theory is no longer topological and displays more interesting dynamics. Moreover the Chern-Simons-matter theories could be the low energy effective action of membranes, and in the large N limit they may dual to M-theory on AdS4 M7 or the reduced type IIA string theory on AdS4 M6. In [8], Gaiotto and Yin Chern-Simons-matter theories. The constructions are similar to the one of half-BPS Wilson N = 2 supersymmetries, the Wilson loop is W = TrRP exp 1Recently, a novel and interesting method to obtain certain D-brane solutions dual to Wilson loops appeared in [6]. the following 1/3-BPS one W = TrRP exp chiral superfield in the adjoint representation of the gauge group. The BPS Wilson loop of similar structure in the Aharony-Bergman-Jafferis-Maldacena (ABJM) theory [9], which is of the multiple membranes, was constructed in [1012]. In this construction, the auxiliary choice of the matter content and the superpotential does not happen for the Wilson loop of Gaiotto-Yin (GY) type. The ABJM theory has a holographic description in terms of type IIA string theory on AdS4 CP 3 or M-theory on AdS4 S7/Zk. In the IIA string loop in the fundamental representation. This F-string solution was found to preserve half of the supersymmetries of the background [10, 12]. It can also be uplifted to an M2brane in AdS4 S7/Zk. The worldvolume of this M2-brane is AdS2 S1. The AdS2 part is inside AdS4 and S1 is inside S7/Zk and along the direction performing the Zk orbifolding. The presence of such half-BPS F1 or M2 brane suggests that there should be half-BPS Wilson loops in the ABJM theory. Eventually, the sought-after Wilson loop was constructed successfully in [13] by including the fermions in bi-fundamental representation into the construction. To incorporate the fermion, the connection in the GY-type Wilson loop has to be augmented to a superconnection, whose holonomy gives the Wilson loop wanted. By using localization [13, 14], the VEV of both 1/6- and 1/2-BPS Wilson loops can be computed as the correlation functions in the matrix models. It turned out that in the planar and strong coupling limits, the leading exponential behaviors of the VEVs are in perfect agreement with holographic results [15], which could be read from the regulated action of the dual macroscopic open string. Such novel construction (...truncated)


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Bin Chen, Jun-Bao Wu, Meng-Qi Zhu. Holographical description of BPS Wilson loops in flavored ABJM theory, Journal of High Energy Physics, 2014, pp. 143, Volume 2014, Issue 12, DOI: 10.1007/JHEP12(2014)143