One-loop effective action of the holographic antisymmetric Wilson loop

Abstract

We systematically study the spectrum of excitations and the one-loop determinant of holographic Wilson loop operators in antisymmetric representations of N = 4 supersymmetric YangMills theory. Holographically, these operators are described by D5-branes carrying electric flux and wrapping an S 4 ⊂ S 5 in the AdS 5 × S 5 bulk background. We derive the dynamics of both bosonic and fermionic excitations for such D5-branes. A particularly important configuration in this class is the D5-brane with AdS 2 × S 4 worldvolume and k units of electric flux, which is dual to the circular Wilson loop in the totally antisymmetric representation of rank k. For this Wilson loop, we obtain the spectrum, show explicitly that it is supersymmetric and calculate the one-loop effective action using heat kernel techniques.

Quantum corrections to minimal surfaces with mixed three-form flux

“…Indeed, the extension under the presence of NS-NS flux of the minimal surface termed "quark-antiquark potential" in the context of the AdS 5 /CFT 4 correspondence, which subtends two parallel lines at the boundary of Euclidean AdS 3 , can be shown to adhere to the boundary in one of the two limits in which the R-R flux vanishes (that is, q = 1 or q = −1, depending on the conventions). 10 Similarly, the class of minimal surfaces subtending two concentric circumferences at the boundary of Euclidean AdS 3 considered in [26] displays a range of parameters for which the confinement of the world-sheet to the boundary in the limit of pure NS-NS flux again occurs. We may proceed analogously in these generalized cases, although the study of quadratic perturbation around those solutions and their associated functional determinants is considerably more involved.…”

“…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].…”

Phase transition of anti-symmetric Wilson loops in N = 4 $$ \mathcal{N}=4 $$ SYM

“…A similar matching was found between Wilson loops in the symmetric representations and D3-branes on the bulk side. However, a mismatch at the subleading order in the 1/N expansion was reported for both symmetric and antisymmetric representations [12][13][14][15] (see also [16] for a review of the status of this problem). Recently, the first 1/N correction of Wilson loops was computed for both symmetric [17] and anti-symmetric [18] representations, but the mismatch still remains as an issue.…”