Evaporation of Microscopic Black Holes in String Theory and the Bound on Species

TL;DR

This work analyzes how the black hole bound on the number of particle species is realized in string theory with D-brane compactifications. It shows that KK modes saturate the bound in large-volume/low-string-scale setups, while the exponentially rising Regge tower does not lead to a breakdown of semi-classical BHs because the effective number of emitted string resonances is limited to N_eff ≈ 1/g_s^2, linking the Planck and string scales. The results unify geometric relations between M_4, M_s, and compactification volumes with species counting and provide constraints on moduli masses in TeV-scale string scenarios. Overall, the paper argues for a consistent picture in which BH physics and stringy spectra cohere through the bound on the number of species, with measurable implications for micro BHs and moduli phenomenology.

Abstract

We address the question how string compactifications with D-branes are consistent with the black hole bound, which arises in any theory with number of particle species to which the black holes can evaporate. For the Kaluza-Klein particles, both longitudinal and transversal to the D-branes, it is relatively easy to see that the black hole bound is saturated, and the geometric relations can be understood in the language of species-counting. We next address the question of the black hole evaporation into the higher string states and discover, that contrary to the naive intuition, the exponentially growing number of Regge states does not preclude the existence of semi-classical black holes of sub-stringy size. Our analysis indicates that the effective number of string resonances to which such micro black holes evaporate is not exponentially large but is bounded by N = 1/g_s^2, which suggests the interpretation of the well-known relation between the Planck and string scales as the saturation of the black hole bound on the species number. In addition, we also discuss some other issues in D-brane compactifications with a low string scale of order TeV, such as the masses of light moduli fields.