Free energy of N=4 super Yang-Mills in Higgs phase and non-extremal D3-brane interactions

Abstract

We study the free energy of \N=4 super Yang-Mills theory in the Higgs phase with a mass scale M corresponding to non-zero v.e.v. of the scalar fields. At zero temperature this theory describes a system of parallel separated extremal D3-branes. Non-zero temperature corresponds to non-extremality in supergravity description. We interpret the supergravity interaction potential between a non-extremal D3-brane and a D3-brane probe as contribution of massive states to the free energy of N --> infinity SYM theory at strong 't Hooft coupling (N g^2_{YM} >> 1). Both low (M >> T) and high (T >> M) temperature regimes are considered. For low temperature we find that the structure of terms that appear in the free energy at strong and weak coupling is the same. The analysis of the high-temperature regime depends on a careful identification of the scalar field v.e.v. in terms of the distance between branes in the supergravity description and again predicts strong coupling terms similar to those found in the weak-coupling \N=4 SYM theory. We consider also the corrections to the strong coupling results by taking into account the leading \a'^3 R^4 string contribution to the supergravity effective action. This gives rise to the (N g^2_{YM})^{-3/2} corrections in the coefficient functions of 't Hooft coupling which multiply different terms in free energy.

21 pages, harvmac, references added

References in corpus (13)

• Gauge Theory Correlators from Non-Critical String Theory
• Wilson-Polyakov Loop at Finite Temperature in Large N Gauge Theory and Anti-de Sitter Supergravity
• Coupling Constant Dependence in the Thermodynamics of N=4 Supersymmetric Yang-Mills Theory
• Non-perturbative Effects in AdS5 * S5 String Theory and d=4 SUSY Yang-Mills
• Absorption by Branes and Schwinger Terms in the World Volume Theory
• Higher Order Graviton Scattering in M(atrix) Theory
• Comments on Higher Derivative Operators in Some SUSY Field Theories
• Possible Resolution of Black Hole Singularities from Large N Gauge Theory
• Long-distance interactions of branes: correspondence between supergravity and super Yang-Mills descriptions
• Supersymmetry and Higher Derivative Terms in the Effective Action of Yang-Mills Theories
• Probing Near Extremal Black Holes with D-branes
• Quantum Corrections to the QED Vacuum Energy
• Open superstring partition function in constant gauge field background at finite temperature

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