Toward precision holography with supersymmetric Wilson loops

Abstract

We consider certain 1/4 BPS Wilson loop operators in SU(N) ${\cal N}=4$ supersymmetric Yang-Mills theory, whose expectation value can be computed exactly via supersymmetric localization. Holographically, these operators are mapped to fundamental strings in AdS5 x S5. The string on-shell action reproduces the large N and large coupling limit of the gauge theory expectation value and, according to the AdS/CFT correspondence, there should also be a precise match between subleading corrections to these limits. We perform a test of such match at next-to-leading order in string theory, by deriving the spectrum of quantum fluctuations around the classical string solution and by computing the corresponding 1-loop effective action. We discuss in detail the supermultiplet structure of the fluctuations. To remove a possible source of ambiguity in the ghost zero mode measure, we compare the 1/4 BPS configuration with the 1/2 BPS one, dual to a circular Wilson loop. We find a discrepancy between the string theory result and the gauge theory prediction, confirming a previous result in the literature. We are able to track the modes from which this discrepancy originates, as well as the modes that by themselves would give the expected result.Comment: 5 pages; v2: 43 pages, long version fixing a mistake and altering the conclusion

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

“…Before commenting upon the possible origin of our discrepancy, we want to mention that the same finite remnant was found in [385] soon after our paper [4]. Although conceptually similar to ours, the work of [385] has some technical differences that are interesting to highlight.…”

“…The classical string surface dual to latitude loops was first presented in [383] and discussed in details in [298,384,385]. Here it is rederived using a strategy described at the end of one makes the following ansatz for the classical configuration…”

Toward precision holography in type IIA with Wilson loops

“…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.…”

“…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.…”

Minimal area surfaces in AdSn+1 and Wilson loops

“…There is a large amount of work on the subject, see for example [6][7][8][9][10] and, in particular [11][12][13][14][15][16][17][18][19][20] for the circular Wilson loop, the most studied case. The main interest of this problem is its integrability properties [21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36].…”