String corrections to circular Wilson loop and anomalies

Abstract

We study string quantum corrections to the ratio of latitude and circular Wilson loops in N = 4 super-Yang-Mills theory at strong coupling. Conformal gauge for the corresponding minimal surface in AdS 5 × S 5 is singular and we show that an IR anomaly associated with the divergence in the conformal factor removes previously reported discrepancy with the exact field-theory result. We also carefully check conformal anomaly cancellation and recalculate fluctuation determinants by directly evaluating phaseshifts for all the fluctuation modes.

Toward precision holography in type IIA with Wilson loops

“…The situation is not completely satisfactory but sheds light on deficiencies and advantages of the various methods used to tackle questions of precision holography with Wilson loops. For example, some of the puzzles we face were confronted in the realm of N = 4 SYM and paved the way leading to perfect matching with the field theory answer in [11]. There the computations of the determinants was mapped from the disk to the cylinder.…”

“…First, one would obviously like to go beyond the small θ 0 limit and obtain and expression that is valid in the whole range of θ 0 . Second, by construction, our regularization is diffeomorphic invariant and works directly on the disk; other approaches [8,9,11] rely on mapping the problem from the disk to the cylinder. Although these latter methods have proven to be quite effective it is conceptually satisfying to deal with the problem directly on the disk.…”

“…At the moment we can track the discrepancy between the two methods to an ambiguity in the treatment of the m = 0 fermionic modes, we will return to this question elsewhere. It seems that a more expeditious way to get at the exact answer might follow the approach of [11,36] who mapped the spectral problems from the disk to the cylinder with the incorporation of an explicit diffeomorphic invariant cutoff; we hope to report on such explorations in an upcoming publication.…”

“…This discrepancy motivated much work [4][5][6][7] that largely confirmed the original discrepancy. A recent revival of this line of effort took place in [8,9] which considered, on the gravity side, the one-loop effective actions corresponding to the ratio of the expectation values of the [10] and recently a precise match has been described, for the N = 4 SYM case, [11] after imposing a diffeomorphism preserving cutoff.…”

Wilson loops and integrability

“…Wilson loop, for which some of the potential ambiguities of the string one-loop calculation drop out. The mismatch between the localization result and the string correction observed there [52,53] could recently be resolved [54,55,56].…”