Abstract
In this work, we study the line and loop operators in three-dimensional mathcal{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-Simons- matter 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/ϵ expansion.
Highlights
ABJM theory and γ-deformationWe start with the ABJM theory whose Lagrangian is shown in the appendix A
Reduces the path integral computing the vacuum expectation value (VEV) of the circular half-BPS Wilson loop in SYM4 to a finite-dimensional integral [4]
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
Summary
We start with the ABJM theory whose Lagrangian is shown in the appendix A. The ABJM theory is a N = 6 supersymmetric Chern-Simons-matter theory with gauge group U(N ) × U(N ) and the Chern-Simons levels k and −k, respectively. The gauge sector consists of two gauge fields Aμ and Bμ associated with the first and the second U(N ). Where the antisymmetric product of the two charge vectors qA and qB is given by qA ∧ qB = qTACqB,. The U(1) charges of the fields are given by the table below:. F φ1 φ2 φ3 φ4 ψ1 ψ2 ψ3 ψ4 q1 − + + − − + + − q2 + − + − + − + − q3 + + − − + + − − This replacement should be performed on every product appearing in the Lagrangian. The γ-deformed ABJM action in our convention is presented in the appendix A
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