Running Gauge Coupling and Quark-Antiquark Potential in Non-SUSY Gauge Theory at Finite Temperature from IIB SG/CFT correspondence

Abstract

We discuss the non-constant dilaton deformed ${\mathrm{AdS}}_5\times {\mathrm{S}}_5$ solutions of IIB supergravity where AdS sector is described by black hole. The investigation of running gauge coupling (exponent of dilaton) of non-SUSY gauge theory at finite temperature is presented for different regimes (high or low T, large radius expansion). Running gauge coupling shows power-like behavior on temperature with stable fixed point. The quark-antiquark potential at finite T is found and possibility of confinement is established. It is shown that non-constant dilaton affects the potential, sometimes reversing its behavior if we compare it with the constant dilaton case ($\mathcal{N}=4$ super Yang-Mills theory). Thermodynamics of obtained backgrounds is studied. In particular, next-to-leading term to free energy F is evaluated as $F=-\frac{{\tilde{V}}_3}{4{\pi }^2}(\frac{N^2(\pi T{)}^4}{2}+\frac{5c^2}{768g_{YM}^{6}N{{\alpha }^{\prime }}^6(\pi T{)}^4})$. Here ${\tilde{V}}_3$ is the volume of the space part in the boundary of AdS, c is the parameter coming from the non-constant dilaton and N is the number of the coincident D3-branes.

LaTeX file, 27 pages, misprints are corrected

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