Holographical description of BPS Wilson loops in flavored ABJM theory
Bin Chen
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Jun-Bao Wu
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Meng-Qi Zhu
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Open Access
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c The Authors.
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5 Yiheyuan Rd
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Beijing 100871
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P. R. China
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Institute of High Energy Physics, and Theoretical Physics Center for Science Facilities
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Peking University
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5 Yiheyuan Rd, Beijing 100871
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P. R. China
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Collaborative Innovation Center of Quantum Matter
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Center for High Energy Physics, Peking University
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Department of Physics, and State Key Laboratory of Nuclear Physics and Technology
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Via Bonomea
265, I 34136, Trieste
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Italy
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Chinese Academy of Sciences
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19B Yuquan Road, Beijing 100049
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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)