 Award ID(s):
 1820651
 NSFPAR ID:
 10311699
 Date Published:
 Journal Name:
 Journal of High Energy Physics
 Volume:
 2019
 Issue:
 8
 ISSN:
 10298479
 Format(s):
 Medium: X
 Sponsoring Org:
 National Science Foundation
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null (Ed.)A bstract The 1/2BPS Wilson loop in $$ \mathcal{N} $$ N = 4 supersymmetric YangMills theory is an important and wellstudied example of conformal defect. In particular, much work has been done for the correlation functions of operator insertions on the Wilson loop in the fundamental representation. In this paper, we extend such analyses to Wilson loops in the largerank symmetric and antisymmetric representations, which correspond to probe D3 and D5 branes with AdS 2 × S 2 and AdS 2 × S 4 worldvolume geometries, ending at the AdS 5 boundary along a onedimensional contour. We first compute the correlation functions of protected scalar insertions from supersymmetric localization, and obtain a representation in terms of multiple integrals that are similar to the eigenvalue integrals of the random matrix, but with important differences. Using ideas from the Fermi Gas formalism and the Clustering method, we evaluate their large N limit exactly as a function of the ’t Hooft coupling. The results are given by simple integrals of polynomials that resemble the Q functions of the Quantum Spectral Curve, with integration measures depending on the number of insertions. Next, we study the correlation functions of fluctuations on the probe D3 and D5 branes in AdS. We compute a selection of three and fourpoint functions from perturbation theory on the Dbranes, and show that they agree with the results of localization when restricted to supersymmetric kinematics. We also explain how the difference of the internal geometries of the D3 and D5 branes manifests itself in the localization computation.more » « less

A bstract We compute 1 /λ corrections to the fourpoint functions of halfBPS operators in SU( N ) $$ \mathcal{N} $$ N = 4 superYangMills theory at large N and large ’t Hooft coupling λ = $$ {g}_{\mathrm{YM}}^2N $$ g YM 2 N using two methods. Firstly, we relate integrals of these correlators to derivatives of the mass deformed S 4 free energy, which was computed at leading order in large N and to all orders in 1 /λ using supersymmetric localization. Secondly, we use AdS/CFT to relate these 1 /λ corrections to higher derivative corrections to supergravity for scattering amplitudes of KaluzaKlein scalars in IIB string theory on AdS 5 × S 5 , which in the flat space limit are known from worldsheet calculations. These two methods match at the order corresponding to the tree level R 4 interaction in string theory, which provides a precise check of AdS/CFT beyond supergravity, and allow us to derive the holographic correlators to tree level D 4 R 4 order. Combined with constraints from [1], our results can be used to derive CFT data to oneloop D 4 R 4 order. Finally, we use AdS/CFT to fix these correlators in the limit where N is taken to be large while g YM is kept fixed. In this limit, we present a conjecture for the small mass limit of the S 4 partition function that includes all instanton corrections and is written in terms of the same Eisenstein series that appear in the study of string theory scattering amplitudes.more » « less

A bstract We study the large charge sector of the defect CFT defined by the halfBPS Wilson loop in planar N = 4 supersymmetric YangMills theory. Specifically, we consider correlation functions of two large charge insertions and several light insertions in the doublescaling limit where the ’t Hooft coupling λ and the large charge J are sent to infinity, with the ratio J/ $$ \sqrt{\lambda } $$ λ held fixed. They are holographically dual to the expectation values of light vertex operators on a classical string solution with large angular momentum, which we evaluate in the leading large J limit. We also compute the twopoint function of large charge insertions by evaluating the onshell string action, supplemented by the boundary terms that generalize the one introduced by Drukker, Gross and Ooguri for the Wilson loop without insertions. For a special class of correlation functions, we reproduce the string results from field theory by using supersymmetric localization. The results are given by correlation functions in an “emergent” matrix model whose matrix size is proportional to J and whose spectral curve coincides with that of the classical string. Similar matrix models appeared in the study of extremal correlators in rank1 $$ \mathcal{N} $$ N = 2 superconformal field theories, but our results hold also for nonextremal cases.more » « less

A bstract We study the fourpoint function of the lowestlying halfBPS operators in the $$ \mathcal{N} $$ N = 4 SU( N ) superYangMills theory and its relation to the flatspace fourgraviton amplitude in type IIB superstring theory. We work in a large N expansion in which the complexified YangMills coupling τ is fixed. In this expansion, nonperturbative instanton contributions are present, and the SL(2 , ℤ) duality invariance of correlation functions is manifest. Our results are based on a detailed analysis of the sphere partition function of the massdeformed SYM theory, which was previously computed using supersymmetric localization. This partition function determines a certain integrated correlator in the undeformed $$ \mathcal{N} $$ N = 4 SYM theory, which in turn constrains the fourpoint correlator at separated points. In a normalization where the twopoint functions are proportional to N 2 − 1 and are independent of τ and $$ \overline{\tau} $$ τ ¯ , we find that the terms of order $$ \sqrt{N} $$ N and $$ 1/\sqrt{N} $$ 1 / N in the large N expansion of the fourpoint correlator are proportional to the nonholomorphic Eisenstein series $$ E\left(\frac{3}{2},\tau, \overline{\tau}\right) $$ E 3 2 τ τ ¯ and $$ E\left(\frac{5}{2},\tau, \overline{\tau}\right) $$ E 5 2 τ τ ¯ , respectively. In the flat space limit, these terms match the corresponding terms in the type IIB Smatrix arising from R 4 and D 4 R 4 contact interactions, which, for the R 4 case, represents a check of AdS/CFT at finite string coupling. Furthermore, we present striking evidence that these results generalize so that, at order $$ {N}^{\frac{1}{2}m} $$ N 1 2 − m with integer m ≥ 0, the expansion of the integrated correlator we study is a linear sum of nonholomorphic Eisenstein series with halfinteger index, which are manifestly SL(2 , ℤ) invariant.more » « less

Abstract The emerging study of fractons, a new type of quasi‐particle with restricted mobility, has motivated the construction of several classes of interesting continuum quantum field theories with novel properties. One such class consists of
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