Gravity duals for the Coulomb branch of marginally deformed Script N = 4 Yang-Mills

Abstract

Supergravity backgrounds dual to a class of exactly marginal deformations of N = 4 supersymmetric Yang-Mills can be constructed through an SL(2, R) sequence of T-dualities and coordinate shifts. We apply this transformation to multicenter solutions and derive supergravity backgrounds describing the Coulomb branch of N = 1 theories at strong 't Hooft coupling as marginal deformations of N = 4 Yang-Mills. For concreteness we concentrate to cases with an SO(4) × SO(2) symmetry preserved by continuous distributions of D3-branes on a disc and on a three-dimensional spherical shell. We compute the expectation value of the Wilson loop operator and confirm the Coulombic behaviour of the heavy quark-antiquark potential in the conformal case. When the vev is turned on we find situations where a complete screening of the potential arises, as well as a confining regime where a linear or a logarithmic potential prevails depending on the ratio of the quark-antiquark separation to the typical vev scale. The spectra of massless excitations on these backgrounds are analyzed by turning the associated differential equations into Schrödinger problems. We find explicit solutions taking into account the entire tower of states related to the reduction of type-IIB supergravity to five dimensions, and hence we go beyond the s-wave approximation that has been considered before for the undeformed case. Arbitrary values of the deformation parameter give rise to the Heun differential equation and the related Inozemtsev integrable system, via a non-standard trigonometric limit as we explicitly demonstrate.

Velocity and chemical-potential dependence of the heavy-quark interaction inN=4SYM plasmas

“…I) and [25] (see Sec. V, where x played the role of an angular variable), we briefly review the results without entering into the intermediate computational details.…”

“…Independence of the Lagrangian from y and x leads to two first-order equations expressing the conservation of the ''energy'' and the momentum x conjugate to xy. Integrating these equations, one obtains [25] L sin 2 1 ÿ 2…”

“…Compared to[25], this function has been rescaled by a factor of f y u 5. The significance of the radius u v has been pointed out in[8] for one-quark configurations and in[21][22][23] for two-quark configurations.…”

Near BPS Wilson loop in β-deformed theories

“…Aspects of the supergravity duals of Wilson loops in the β-deformed SYM theory has been studied before [22,23] 1 . However the form of the field theory operators that are in dual with the supergravity configurations has not been identified.…”

On supersymmetry and other properties of a class of marginally deformed backgrounds

“…These Higgs expectation values correspond on the gravity side to multicenter distributions of branes. In [10] we employed a sequence of T-dualities and coordinates shifts on multicenter solutions to find gravity duals for the Coulomb branches of marginally deformed N = 4 Yang-Mills. In this note we will focus on the deformation of uniform continuous distributions of D3-branes on a disc and on a three-dimensional spherical shell preserving a global SO(4) × SO(2) symmetry group.…”