Abstract
In this paper, a minimal surface in q-deformed AdS5×S5 with a cusp boundary is studied in detail. This minimal surface is dual to a cusped Wilson loop in dual field theory. We find that the area of the minimal surface has both logarithmic squared divergence and logarithmic divergence. The logarithmic squared divergence cannot be removed by either Legendre transformation or the usual geometric subtraction. We further make an analytic continuation to the Minkowski signature, taking the limit such that the two edges of the cusp become light-like, and extract the anomalous dimension from the coefficient of the logarithmic divergence. This anomalous dimension goes back smoothly to the results in the undeformed case when we take the limit that the deformation parameter goes to zero.
Highlights
Integrability [1] and localization [2] make us be able to compute some important quantities in N = 4 super Yang-Mills theory as non-trivial functions of ’t Hooft coupling λ and the rank of the gauge group N 4
Cusp anomalous dimension f (λ) is among these interesting quantities and its value at finite λ in the planar limit can be computed using this powerful integrability method [6, 7]. This function appears as a cusp anomaly of a light-like Wilson loop [8, 9]. It appears as the coefficient in front of log S of the anomalous dimension of large spin twist-two operator[10, 11]
We find the area of the worldsheet has behavior different from both the case with circle as boundary and the holographic dual of cusped Wilson loops in the undeformed case
Summary
The energy E and spin S of these spinning strings will not have the relation E − S ∼ f (λ) log S in the large S limit Another interesting result [55] is that the open F-string solution with boundary a circle has finite area without peforming geometric substraction or Legendre transformation which was used for the undeformed case, though there are divergences in the action when the boundary is a straight line [52]. By continuation to the Minkowski signature and subtracting the logarithmic squared divergence by hand, we computed the cusp anomalous dimension for the deformed case We find that this result can be smoothly connected with the result in the undeformed case when we take the limit that the deformation parameter tends to zero.
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