Wilson Surface One-Point Functions: A Case Study

Abstract

We compute holographic one-point functions for Wilson surfaces in the case of a toroidal surface operator. Compared to the cases of a planar or spherical surface operator, these one-point functions exhibit a more intricate dependence on the shape and position of both the surface and the local operators. Averaging over the moduli space of membranes dual to the surface operator plays a key role in the computations. We obtain both analytical and numerical results. The case of a cylindrical surface operator is also studied.

Figures (8)

• Figure 1: $f_1(\frac{y_1}{r},\frac{y_2}{r})$
• Figure 2: $f_2(\frac{y_1}{r},\frac{y_2}{r})$
• Figure 3: $p_1(\frac{y_1}{r},\frac{y_2}{r})$
• Figure 4: $p_2(\frac{y_1}{r},\frac{y_2}{r})$
• Figure 5: $q_1(\frac{y_1}{r},\frac{y_2}{r})$