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Loop Operators in Three-Dimensional $\mathcal{N}=2$ Fishnet Theories

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.