Loop operators in three-dimensional N $$ \mathcal{N} $$ = 2 fishnet theories
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Springer
Received: April 24, Revised: June 7, Accepted: June 9, Published: July 29,
2020 2020 2020 2020
Jun-bao Wu,a,b Jia Tianb and Bin Chenb,c,d a
Center for Joint Quantum Studies and Department of Physics, School of Science, Tianjin University, 135 Yaguan Road, Tianjin 300350, P.R. China b Center for High Energy Physics, Peking University, 5 Yiheyuan Rd, Beijing 100871, P.R. China c Department of Physics and State Key Laboratory of Nuclear Physics and Technology, Peking University, 5 Yiheyuan Rd, Beijing 100871, P.R. China d Collaborative Innovation Center of Quantum Matter, 5 Yiheyuan Rd, Beijing 100871, P.R. China
E-mail: [email protected], [email protected], [email protected] Abstract: In this work, we study the line and loop operators in three-dimensional N = 2 fishnet theories in detail. We construct the straight line and circular loop operators which are at least classically half-BPS. We develop a new regularization scheme at frame −1 which is suitable for the study of the fermionic BPS loops in general super-Chern-Simonsmatter theories. We initialize the perturbative computation for the vacuum expectation values of the circular BPS loop operators based on this scheme. We construct the cusped line operators as well, and compute the vacuum expectation values of these cusped line operators up to two-loop order. We find that the universal cusp anomalous dimension vanishes, if we put aside the fact that the generalized potential has a double pole in the 1/ expansion. Keywords: Wilson, ’t Hooft and Polyakov loops, Chern-Simons Theories ArXiv ePrint: 2004.07592
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP07(2020)215
JHEP07(2020)215
Loop operators in three-dimensional N = 2 fishnet theories
Contents 1
2 Three-dimensional N = 2 fishnet theories 2.1 ABJM theory and γ-deformation 2.2 Double scaling limit and fishnet theory
4 4 5
3 BPS line/loop operators 3.1 Line operators along timelike straight line 3.2 Circular loop operators 3.3 N = 2 notations
7 7 8 9
4 Perturbative computations 4.1 Regularization scheme for fermionic loop operators at framing −1 4.2 The vacuum expectation values of circular loop operators
10 11 13
5 Line operator with a cusp 5.1 The construction 5.2 Perturbative calculations
15 15 16
6 Conclusion and discussions
20
A The Lagrangian of ABJM theory and its γ-deformation
22
B The propagators of the scalars and fermions
23
1
Introduction
Wilson loop operators play an important role in the study of dynamics of gauge theory. The vacuum expectation value (VEV) of the Wilson loop provides the criteria for color confinement [1]. In supersymmetric gauge theory, it is natural to consider the Wilson loop operators preserving part of the supersymmetries, which have better ultraviolet behavior. The first kind of BPS Wilson loop operator was constructed [2, 3] in four-dimensional N = 4 super Yang-Mills (SYM4 ) theory. The obtained Maldacena-Wilson loop has a simple holographic description in terms of classical open string solution
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