Publication: Gravity duals for the Coulomb branch of marginally deformed N=4 Yang-Mills
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2006-03
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Int School Advanced Studies
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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 Schr¨odinger 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.
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© SISSA 2006. K. S. thanks N. Brambilla for a useful correspondence. K. S. and D. Z. acknowledge the financial support provided through the European Community’s program “Constituents, Fundamental Forces and Symmetries of the Universe” with contract MRTN-CT-2004- 005104, the INTAS contract 03-51-6346 “Strings, branes and higher-spin gauge fields”, as well as the Greek Ministry of Education programs ΠYΘAΓOPAΣ with contract 89194 and EΠAN with code-number B.545. K. S. also thanks CERN and the University of Neuchâtel for hospitality and financial support during part of this research. In addition, D. Z. acknowledges the financial support provided through the Research Committee of the University of Patras for a “K. Karatheodory” fellowship under contract number 3022. Parts of this research were presented by K. S. in the RTN meeting “Constituents, Fundamental Forces and Symmetries of the Universe”, in Corfu, Greece, 20-26 September 2005.