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1. Large charges on the Wilson loop in $$ \mathcal{N} $$ = 4 SYM: matrix model and classical string

   https://doi.org/10.1007/JHEP03(2022)020  

   Giombi, Simone ; Komatsu, Shota ; Offertaler, Bendeguz ( March 2022 , Journal of High Energy Physics)

   A bstract We study the large charge sector of the defect CFT defined by the half-BPS Wilson loop in planar N = 4 supersymmetric Yang-Mills theory. Specifically, we consider correlation functions of two large charge insertions and several light insertions in the double-scaling 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 two-point function of large charge insertions by evaluating the on-shell 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 rank-1 $$ \mathcal{N}more »$$ N = 2 superconformal field theories, but our results hold also for non-extremal cases.« less
2. $$ \mathcal{N} $$ = 4 Super-Yang-Mills correlators at strong coupling from string theory and localization

   https://doi.org/10.1007/JHEP12(2019)119  

   Binder, Damon J. ; Chester, Shai M. ; Pufu, Silviu S. ; Wang, Yifan ( December 2019 , Journal of High Energy Physics)

   A bstract We compute 1 /λ corrections to the four-point functions of half-BPS operators in SU( N ) $$ \mathcal{N} $$ N = 4 super-Yang-Mills 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 Kaluza-Klein 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 one-loop D 4 R 4 order. Finally, we use AdS/CFT to fix these correlators in themore »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.« less
3. Chern-Simons theory from M5-branes and calibrated M2-branes

   https://doi.org/10.1007/JHEP08(2019)165  

   Mezei, Márk ; Pufu, Silviu S. ; Wang, Yifan ( August 2019 , Journal of High Energy Physics)

   A bstract We study a sector of the 5d maximally supersymmetric Yang-Mills theory on S 5 consisting of 1 / 8-BPS Wilson loop operators contained within a great S 3 inside S 5 . We conjecture that these observables are described by a 3d Chern Simons theory on S 3 , analytically continued to a pure imaginary Chern-Simons level. Therefore, the expectation values of these 5d Wilson loops compute knot invariants. We verify this conjecture in the weakly-coupled regime from explicit Feynman diagram computations. At strong coupling, these Wilson loop operators lift to 1 / 8-BPS surface operators in the 6d (2 , 0) theory on S 1 × S 5 . Using AdS/CFT, we show that these surface operators are dual to M2-branes subject to certain calibration conditions required in order to preserve supersymmetry. We compute the renormalized action of a large class of calibrated M2-branes and obtain a perfect match with the field theory prediction. Finally, we present a derivation of the 3d Chern-Simons theory from 5d super-Yang-Mills theory using supersymmetric localization, modulo a subtle issue that we discuss.
4. Janus on the brane

   https://doi.org/10.1007/JHEP07(2020)243  

   Gutperle, Michael ; Uhlemann, Christoph F. ( July 2020 , Journal of High Energy Physics)

   Abstract We present a non-supersymmetric deformation of probe branes describing conformal defects of codimension two in AdS/CFT. The worldvolume of the probe branes is deformed from AdS p × S 1 embedded in an AdS p +2 × ℳ D  −  p  − 2 background to an embedding of Janus form, which uses an AdS p− 1 slicing of AdS p and in which the brane bends along the slicing coordinate. In field theory terms this realizes conformal interfaces on codimension- two defects. We discuss these “Janus on the brane” solutions for AdS 3 × S 1 D3-branes in the AdS 5 × S 5 solution of Type IIB, realizing interfaces on surface defects in $$ \mathcal{N} $$ N = 4 SYM, and show that similar solutions exist for probe branes in AdS p +2 × S 9 −p vacua of M-theory and in the AdS 6 × S 4 solution of massive Type IIA.
5. Modular invariance in superstring theory from $$ \mathcal{N} $$ = 4 super-Yang-Mills

   https://doi.org/10.1007/JHEP11(2020)016  

   Chester, Shai M. ; Green, Michael B. ; Pufu, Silviu S. ; Wang, Yifan ; Wen, Congkao ( November 2020 , Journal of High Energy Physics)

   A bstract We study the four-point function of the lowest-lying half-BPS operators in the $$ \mathcal{N} $$ N = 4 SU( N ) super-Yang-Mills theory and its relation to the flat-space four-graviton amplitude in type IIB superstring theory. We work in a large- N expansion in which the complexified Yang-Mills coupling τ is fixed. In this expansion, non-perturbative 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 mass-deformed 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 four-point correlator at separated points. In a normalization where the two-point 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 four-point correlator are proportional to the non-holomorphic Eisenstein series $$ E\left(\frac{3}{2},\tau, \overline{\tau}\right) $$ E 3 2 τ τ ¯ and $$more »E\left(\frac{5}{2},\tau, \overline{\tau}\right) $$ E 5 2 τ τ ¯ , respectively. In the flat space limit, these terms match the corresponding terms in the type IIB S-matrix arising from R 4 and D 4 R 4 contact inter-actions, 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 non-holomorphic Eisenstein series with half-integer index, which are manifestly SL(2 , ℤ) invariant.« less