Conceptual Unification of Elementary Particles, Black Holes, Quantum De Sitter and Anti-De Sitter String States

Abstract

We provide a conceptual unified description of the quantum properties of black holes (BH), elementary particles, de Sitter (dS) and Anti de Sitter (AdS) string states.The conducting line of argument is the classical-quantum (de Broglie, Compton) duality here extended to the quantum gravity (string) regime (wave-particle-string duality). The semiclassical (QFT) and quantum (string) gravity regimes are respectively characterized and related: sizes, masses, accelerations and temperatures. The Hawking temperature, elementary particle and string temperatures are shown to be the same concept in different energy regimes and turn out the precise classical-quantum duals of each other; similarly, this result holds for the BH decay rate, heavy particle and string decay rates; BH evaporation ends as quantum string decay into pure (non mixed) radiation. Microscopic density of states and entropies in the two (semiclassical and quantum) gravity regimes are derived and related, an unifying formula for BH, dS and AdS states is provided in the two regimes. A string phase transition towards the dS string temperature (which is shown to be the precise quantum dual of the semiclassical (Hawking-Gibbons) dS temperature) is found and characterized; such phase transition does not occurs in AdS alone. High string masses (temperatures) show a further (square root temperature behaviour) sector in AdS. From the string mass spectrum and string density of states in curved backgrounds, quantum properties of the backgrounds themselves are extracted and the quantum mass spectrum of BH, dS and AdS radii obtained. Contents

Semiclassical (Quantum Field Theory) and Quantum (String) De Sitter Regimes: New Results

“…This is also the same behaviour of the microscopic density of states and entropy of strings with the spin modes included [14]. As pointed out in [13], this string behaviour is universal: this logarithmic singularity in the entropy (or pole singularity in the specific heat) holds in any number of dimensions, its origin is gravitational interaction in the presence of temperature, as Jeans's instability at finite temperature but with a more complex structure.…”

“…As pointed out in [13], this string behaviour is universal, it holds in any number of dimensions, and is similar to the Jeans's instability at finite temperature but with a more complex structure.…”

“…When m → M s the string becomes "classical " reflecting the classical properties of the background, m becomes M cl , (with α ′ instead of G/c 2 ), thus the string becomes the " background " [13]. Conversely, and interestingly enough, string back reaction supports this …”

“…(18) and Eq. (19), m s is the fundamental string mass and M s the characteristic string mass in de Sitter space time [7]- [9], [10], [13] …”

“…(56) s plus negative corrections in an expansion in powers of (R sem /R s ) [10]. The two phases: semiclassical and stringy are dual of each other in the precise sense of the classical-quantum duality [10], [12], [13].…”