Perturbative computation of string one-loop corrections to Wilson loop minimal surfaces in AdS 5 × S 5

Abstract

Abstract:We revisit the computation of the 1-loop string correction to the "latitude" minimal surface in AdS 5 × S 5 representing 1/4 BPS Wilson loop in planar N =4 SYM theory previously addressed in arXiv:1512.00841 and arXiv:1601.04708. We resolve the problem of matching with the subleading term in the strong coupling expansion of the exact gauge theory result (derived previously from localization) using a different method to compute determinants of 2d string fluctuation operators. We apply perturbation theory in a small parameter (angle of the latitude) corresponding to an expansion near the AdS 2 minimal surface representing 1/2 BPS circular Wilson loop. This allows us to compute the corrections to the heat kernels and zeta-functions of the operators in terms of the known heat kernels on AdS 2 . We apply the same method also to two other examples of Wilson loop surfaces: generalized cusp and k-wound circle.

Non-supersymmetric Wilson loop in $$ \mathcal{N} $$ = 4 SYM and defect 1d CFT

“…Let us now recall that the direct computation of the determinants in the string 1-loop partition function for the circular WML gives (after using (4.1) and separating out the linear divergence) [39][40][41] (see also [49][50][51])…”

Toward precision holography in type IIA with Wilson loops

“…More precisely, we will use perturbation theory valid in the limit when the induced world-sheet geometry can be considered as a small deformation of AdS 2 govern by the deformation parameter θ 0 . This approach has been successfully applied the holographic perturbative computation of a ratio of Wilson loops expectation values [10]. Namely, we will expand around the parameter α = θ 2 0 , where the near AdS 2 geometry corresponds to the latitude in S 2 ⊂ S 5 parametrized by angle θ 0 .…”

“…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.…”

Perturbative and Non-perturbative Approaches to String Sigma-Models in AdS/CFT

“…The motivation behind the correspondence (1.1) arose from the investigation of a stack of N parallel Dirichlet branes (D3-branes), 3d objects sweeping out a (1+3)-dimensional volume, separated by a distance d and embedded in type IIB string theory in R 1,9 . D-branes can be viewed in two equivalent ways, fundamentally…”

“…This served as a basis for the so-called Y-system [105] (an infinite set of non-linear functional equations) and its successor FiNLIE (acronym for ''finite system of non-linear integral equations"). The state-of-theart in elegance and computational efficiency in solving the spectral problem seems to be achieved in the form of a set of Riemann-Hilbert equations that defines the quantum spectral curve (QSC) approach (or Pµ-system) [115,116], where the so-called Q functions are 9 The integrability of the string in the AdS5 × S 5 background has been mostly studied in the supercoset description [78] (e.g. in [85]) than in the pure spinor version.…”