Gauge theory duals of black hole – black string transitions of gravitational theories on a circle (original) (raw)

Abstract

We study the black hole -black string phase transitions of gravitational theories compactified on a circle using the holographic duality conjecture. The gauge theory duals of these theories are maximally supersymmetric and strongly coupled 1 + 1 dimensional SU (N ) Yang-Mills theories compactified on a circle, in the large N limit. We perform the strongly coupled finite temperature gauge theory calculations on a lattice, using the recently developed exact lattice supersymmetry methods based on topological twisting and orbifolding. The spatial Polyakov line serves as relevant order parameter of the confinement -deconfinement phase transitions in the gauge theory duals.

Figures (3)

now with 6 as the angular coordinate on the (T-dual) spatial $1, again with 6~60+2n. The requirement that the supergravity solution and its perturbations are good, gives the condition Mss land t << 1 from requiring a’ and winding corrections to be small near the horizon. Below dimensionless temperatures t ~ 1/ VN, the above background is strongly effected by string winding modes near the horizon which wrap over the spatial circle. We then cannot analyse the IIB string theory behaviour simply using ITB supergravity. However, we may employ the trick of T-duality, acting on the spatial circle, to map the IIB solution to one in ITA theory which in fact can be described in IIA supergravity. One finds the following IIA solution after T-duality,

now with 6 as the angular coordinate on the (T-dual) spatial $1, again with 6~60+2n. The requirement that the supergravity solution and its perturbations are good, gives the condition Mss land t << 1 from requiring a’ and winding corrections to be small near the horizon. Below dimensionless temperatures t ~ 1/ VN, the above background is strongly effected by string winding modes near the horizon which wrap over the spatial circle. We then cannot analyse the IIB string theory behaviour simply using ITB supergravity. However, we may employ the trick of T-duality, acting on the spatial circle, to map the IIB solution to one in ITA theory which in fact can be described in IIA supergravity. One finds the following IIA solution after T-duality,

Figure 1. Spatial and temporal Polyakov lines (P; and P;) vs square root of the coupling (V/’) for maximally supersymmetric SU(3) Yang-Mills on a 2 x 8 lattice using different values of the infrared regulator m.

Figure 1. Spatial and temporal Polyakov lines (P; and P;) vs square root of the coupling (V/’) for maximally supersymmetric SU(3) Yang-Mills on a 2 x 8 lattice using different values of the infrared regulator m.

Figure 2. Spatial and temporal Polyakov lines (P, and P;) vs square root of the coupling (V’) for maximally supersymmetric SU(N) Yang-Mills with N = 2,3,4 on a 2 x 8 lattice using the value m = 0.10 for the infrared regulator.

Figure 2. Spatial and temporal Polyakov lines (P, and P;) vs square root of the coupling (V’) for maximally supersymmetric SU(N) Yang-Mills with N = 2,3,4 on a 2 x 8 lattice using the value m = 0.10 for the infrared regulator.

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