The zero-action hypothesis and high-temperature thermodynamics in the heterotic superstring theory

Details The zero-action hypothesis and high-temperature thermodynamics in the heterotic superstring theory The zero-action hypothesis and high-temperature thermodynamics in the heterotic superstring theory

Jul 2005

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2005cqgra..22.2835p&link_type=abstract

Classical and Quantum Gravity, Volume 22, Issue 14, pp. 2835-2847 (2005).

Physics

Scientific paper

The effective action S for the Einstein theory of gravity coupled to massless scalar fields phi, spinor fields ψ and gauge vector fields Fij describing radiation, so that FijFij = 0, vanishes identically after substitution from the classical equations of motion, thus allowing a perfect fluid for which the energy density ρ and pressure p = (γ - 1)ρ are related by values of the adiabatic index throughout the range 4/3 <= γ <= 2. In the heterotic superstring theory, four-point gravitational interactions generate a tree-level quadratic, higher-derivative contribution to the Lagrangian, after reduction to four dimensions, whose form, unchanged at one-loop level, is {\cal R}^2 = B(R^2 -R_{ij}R^{ij}) = {1 \over 6} B (\gamma-2)(\gamma-1) \kappa^4 \rho^2 , where the constant B ap 1 for a three-generation Calabi Yau manifold, and which thus constitutes a type of anomaly. The zero-action hypothesis requires the theory to be free of such anomalies, and thus predicts that the Universe started off in the state p = ρ discussed by Zel'dovich, characterized by the maximum value γ = 2 consistent with causality. Applying classical thermodynamics to a perfect fluid, we find that ρ, p and hence also the Helmholtz free-energy density f ≡ -p, scale with temperature as Tγ/γ-1, leading to the prediction that f ~ T2, which is exactly verified by the calculation of Atick and Witten, valid at genus-one in the high-temperature limit T Gt TH, after Euclideanizing the time coordinate, where TH is the Hagedorn temperature. The response of the action to the operators T, C and P is also discussed, T-invariance requiring γ = 2 and hence S = 0, and P-invariance requiring S = 0, showing that the zero-action hypothesis can be understood in terms of these discrete symmetries.

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