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1. All-loop-orders relation between Regge limits of $$ \mathcal{N} $$ = 4 SYM and $$ \mathcal{N} $$ = 8 supergravity four-point amplitudes

   https://doi.org/10.1007/JHEP02(2021)044  

   Naculich, Stephen G. (February 2021, Journal of High Energy Physics)

   null (Ed.)

   A bstract We examine in detail the structure of the Regge limit of the (nonplanar) $$ \mathcal{N} $$ N = 4 SYM four-point amplitude. We begin by developing a basis of color factors C ik suitable for the Regge limit of the amplitude at any loop order, and then calculate explicitly the coefficients of the amplitude in that basis through three-loop order using the Regge limit of the full amplitude previously calculated by Henn and Mistlberger. We compute these coefficients exactly at one loop, through $$ \mathcal{O}\left({\upepsilon}^2\right) $$ O ϵ 2 at two loops, and through $$ \mathcal{O}\left({\upepsilon}^0\right) $$ O ϵ 0 at three loops, verifying that the IR-divergent pieces are consistent with (the Regge limit of) the expected infrared divergence structure, including a contribution from the three-loop correction to the dipole formula. We also verify consistency with the IR-finite NLL and NNLL predictions of Caron-Huot et al. Finally we use these results to motivate the conjecture of an all-orders relation between one of the coefficients and the Regge limit of the $$ \mathcal{N} $$ N = 8 supergravity four-point amplitude. 

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2. Far beyond the planar limit in strongly-coupled $$ \mathcal{N} $$ = 4 SYM

   https://doi.org/10.1007/JHEP01(2021)103  

   Chester, Shai M.; Pufu, Silviu S. (January 2021, Journal of High Energy Physics)

   A bstract When the SU( N ) $$ \mathcal{N} $$ N = 4 super-Yang-Mills (SYM) theory with complexified gauge coupling τ is placed on a round four-sphere and deformed by an $$ \mathcal{N} $$ N = 2-preserving mass parameter m , its free energy F ( m, τ, $$ \overline{\tau} $$ τ ¯ ) can be computed exactly using supersymmetric localization. In this work, we derive a new exact relation between the fourth derivative $$ {\partial}_m^4F\left(m,\tau, \overline{\tau}\right)\left|{{}_m}_{=0}\right. $$ ∂ m 4 F m τ τ ¯ m = 0 of the sphere free energy and the integrated stress-tensor multiplet four-point function in the $$ \mathcal{N} $$ N = 4 SYM theory. We then apply this exact relation, along with various other constraints derived in previous work (coming from analytic bootstrap, the mixed derivative $$ {\partial}_{\tau }{\partial}_{\overline{\tau}}{\partial}_m^2F\left(m,\tau, \overline{\tau}\right)\left|{{}_m}_{=0}\right. $$ ∂ τ ∂ τ ¯ ∂ m 2 F m τ τ ¯ m = 0 , and type IIB superstring theory scattering amplitudes) to determine various perturbative terms in the large N and large ’t Hooft coupling λ expansion of the $$ \mathcal{N} $$ N = 4 SYM correlator at separated points. In particular, we determine the leading large- λ term in the $$ \mathcal{N} $$ N = 4 SYM correlation function at order 1 /N 8 . This is three orders beyond the planar limit. 

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3. Higher order RG flow on the Wilson line in $$ \mathcal{N} $$ = 4 SYM

   https://doi.org/10.1007/JHEP01(2022)056  

   Beccaria, M.; Giombi, S.; Tseytlin, A. A. (January 2022, Journal of High Energy Physics)

   A bstract Extending earlier work, we find the two-loop term in the beta-function for the scalar coupling ζ in a generalized Wilson loop operator of the $$ \mathcal{N} $$ N = 4 SYM theory, working in the planar weak-coupling expansion. The beta-function for ζ has fixed points at ζ = ±1 and ζ = 0, corresponding respectively to the supersymmetric Wilson-Maldacena loop and to the standard Wilson loop without scalar coupling. As a consequence of our result for the beta-function, we obtain a prediction for the two-loop term in the anomalous dimension of the scalar field inserted on the standard Wilson loop. We also find a subset of higher-loop contributions (with highest powers of ζ at each order in ‘t Hooft coupling λ ) coming from the scalar ladder graphs determining the corresponding terms in the five-loop beta-function. We discuss the related structure of the circular Wilson loop expectation value commenting, in particular, on consistency with a 1d defect version of the F-theorem. We also compute (to two loops in the planar ladder model approximation) the two-point correlators of scalars inserted on the Wilson line. 

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4. The $$ \mathcal{N} $$ = 2 prepotential and the sphere free energy

   https://doi.org/10.1007/JHEP06(2022)045  

   Zan, Bernardo; Freedman, Daniel Z.; Pufu, Silviu S. (June 2022, Journal of High Energy Physics)

   A bstract We study the mass-deformed sphere free energy of three-dimensional $$ \mathcal{N} $$ N = 2 superconformal field theories with holographic duals. Building on previous observations, we conjecture a proportionality relation between the sphere free energy on the boundary and the prepotential of the four-dimensional $$ \mathcal{N} $$ N = 2 supergravity theory in the bulk. We verify this formula by explicit computation in several examples of supergravity theories with vector multiplets and hypermultiplets. 

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5. Flowing to $$ \mathcal{N} $$ = 3 Chern-Simons-matter theory

   https://doi.org/10.1007/JHEP03(2020)100  

   Guarino, Adolfo; Tarrío, Javier; Varela, Oscar (March 2020, Journal of High Energy Physics)

   null (Ed.)

   A bstract New renormalisation group flows of three-dimensional Chern-Simons theories with a single gauge group SU( N ) and adjoint matter are found holographically. These RG flows have an infrared fixed point given by a CFT with $$ \mathcal{N} $$ N = 3 supersymmetry and SU(2) flavour symmetry. The ultraviolet fixed point is again described by a CFT with either $$ \mathcal{N} $$ N = 2 and SU(3) symmetry or $$ \mathcal{N} $$ N = 1 and G 2 symmetry. The gauge/gravity duals of these RG flows are constructed as domain-wall solutions of a gauged supergravity model in four dimensions that enjoys an embedding into massive IIA supergravity. A concrete RG flow that brings a mass deformation of the $$ \mathcal{N} $$ N = 2 CFT into the $$ \mathcal{N} $$ N = 3 CFT at low energies is described in detail. 

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