Zeta-function regularization of holographic Wilson loops

Abstract

Using ζ-function regularization, we study the one-loop effective action of fundamental strings in AdS 5 ×S 5 dual to the latitude 1 4 -BPS Wilson loop in N = 4 Super-Yang-Mills theory. To avoid certain ambiguities inherent to string theory on curved backgrounds we subtract the effective action of the holographic 1 2 -BPS Wilson loop. We find agreement with the expected field theory result at first order in the small latitude angle expansion but discrepancies at higher order.

Toward precision holography in type IIA with Wilson loops

“…We see that the rescaled operator does not depend on θ 0 , meaning that these fluctuations contribute only with an anomaly [35],…”

“…The ζ-function regularization method is non-perturbative but does not seem to lead to the expected field theory answer as it stands. We have previously developed the ζ-function approach in [34] and applied it to the N = 4 context in [35] motivated by the goal of constructing a regularization that is explicitly diffeomorphic invariant. The key new ingredient in this work that introduces extra ambiguities with respect to our earlier efforts is the fact that some of the modes correspond to massless fermions.…”

“…In this section we follow our previous work [34,35] where we developed a regularization in the case of radial determinants that coincides with ζ-function regularization in various cases. There are various reasons to tackle the problem using these methods.…”

Quantum corrections to minimal surfaces with mixed three-form flux

“…The product over one-dimensional determinants was then performed in the zeta-function regularization scheme and it was shown to be in agreement with the gauge theory, up to a normalization factor which was later retrieved in [7]. Such an approach to the quantization of minimal surfaces has paved the way of several complementary lines of research [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25].…”

Note on generating functions and connected correlators of 1/2-BPS Wilson loops in $$ \mathcal{N} $$ = 4 SYM theory

“…The first 1/N correction for A k was extracted in [18] from the exact solution [13], but it is unclear whether a similar calculation is possible for higher orders in 1/N . Efforts to compute 1/ √ λ corrections as well as 1-loop effective actions on the gravitational side of the duality include [19][20][21][22][23][24][25][26][27][28][29][30].…”