Adventures in thermal duality. I. Extracting closed-form solutions for finite-temperature effective potentials in string theory

Abstract

Thermal duality, which relates the physics of closed strings at temperature T to the physics at the inverse temperature 1/T , is one of the most intriguing features of string thermodynamics. Unfortunately, the classical definitions of thermodynamic quantities such as entropy and specific heat are not invariant under the thermal duality symmetry. In this paper, we investigate whether there might nevertheless exist special solutions for the string effective potential such that the duality symmetry will be preserved for all thermodynamic quantities. Imposing this as a constraint, we derive a series of unique functional forms for the complete temperature-dependence of the required string effective potentials. Moreover, we demonstrate that these solutions successfully capture the leading temperature behavior of a variety of actual one-loop effective potentials for duality-covariant finite-temperature string ground states. This leads us to conjecture that our solutions might actually represent the exact effective potentials when contributions from all orders of perturbation theory are included. *

Partition functions, the Bekenstein bound and temperature inversion in anti-de Sitter space and its conformal boundary

“…Various authors [28][29][30] have consequently speculated that there should be a temperature inversion symmetry in string theory, with T −→ α ′ /T . It should be noted, however, that the temperature inversion we consider, where T −→ l 2 /(4π 2 T ), is distinct from the type of temperature inversion envisaged in string theory.…”

S-brane to thermal non-singular string cosmology

“…In these extreme situations, purely stringy phenomena occur, which do not admit conventional field theory descriptions [5]. String oscillators and winding states become relevant around the Hagedorn temperature T H , before the onset of curvature singularities, and drive a phase transition towards a non-trivial thermal vacuum [2,3,[6][7][8][9][10][11][12][13].…”

Three Duality Symmetries between Photons and Cosmic String Loops, and Macro and Micro Black Holes

“…In [1,2,5,9] there may be found the relations between the different thermodynamic quantities. Figure 1.…”

“…Thermal duality relates high-energy and low-energy states of corresponding dual systems in such a way that the thermal properties of a state of one of them at some temperature T are related to the properties of a state of the other system at temperature 1/T [1][2][3][4][5][6]. This sets a symmetry between T and T −1 states in the physical features of some couples of physical systems, and relates their respective thermodynamic functions.…”

“…For instance, in string theory it is known that the T duality between the behaviour of superstrings at long and short length scales, expressed in terms of energy as E(l) = E(l 2 c /l), which l 2 c a characteristic length, implies a thermal duality symmetry of some of their thermodynamic functions for temperatures T and T 2 c /T , with T c a characteristic temperature [1,2,4].…”