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String-theoretic unitary S-matrix at the threshold of black-hole production

G. Veneziano

TL;DR

The paper presents an explicitly unitary S-matrix formulation for string-theoretic, trans-Planckian collisions, valid over a broad region of energy and impact parameter, and analyzes the approach to black-hole production thresholds. It shows that near the threshold the final-state structure exhibits precursors of BH evaporation, including an anti-scaling behavior of inclusive spectra and a Poisson-distributed population of cut gravi-reggeons, with diffractive excitations maintaining coherence. By connecting the string/black-hole correspondence and the Hawking/Hagedorn transition, the work suggests a smooth transition to BH-like thermality while preserving unitarity, and it identifies a key scale M_* = M_s/g_s that governs the energy window. These insights have implications for information retrieval in high-energy quantum gravity scenarios and for potential collider signatures in models with large extra dimensions, providing a quantitative framework tying string dynamics to BH physics.

Abstract

Previous results on trans-Planckian collisions in superstring theory are rewritten in terms of an explicitly unitary S-matrix whose range of validity covers a large region of the energy/impact-parameter plane. Amusingly, as part of this region's border is approached, properties of the final state start resembling those expected from the evaporation of a black-hole even well below its production threshold. More specifically, we conjecture that, in an energy window extending up such a threshold, inclusive cross sections satisfy a peculiar "anti-scaling" behaviour seemingly preparing for a smooth transition to black-hole physics.

String-theoretic unitary S-matrix at the threshold of black-hole production

TL;DR

The paper presents an explicitly unitary S-matrix formulation for string-theoretic, trans-Planckian collisions, valid over a broad region of energy and impact parameter, and analyzes the approach to black-hole production thresholds. It shows that near the threshold the final-state structure exhibits precursors of BH evaporation, including an anti-scaling behavior of inclusive spectra and a Poisson-distributed population of cut gravi-reggeons, with diffractive excitations maintaining coherence. By connecting the string/black-hole correspondence and the Hawking/Hagedorn transition, the work suggests a smooth transition to BH-like thermality while preserving unitarity, and it identifies a key scale M_* = M_s/g_s that governs the energy window. These insights have implications for information retrieval in high-energy quantum gravity scenarios and for potential collider signatures in models with large extra dimensions, providing a quantitative framework tying string dynamics to BH physics.

Abstract

Previous results on trans-Planckian collisions in superstring theory are rewritten in terms of an explicitly unitary S-matrix whose range of validity covers a large region of the energy/impact-parameter plane. Amusingly, as part of this region's border is approached, properties of the final state start resembling those expected from the evaporation of a black-hole even well below its production threshold. More specifically, we conjecture that, in an energy window extending up such a threshold, inclusive cross sections satisfy a peculiar "anti-scaling" behaviour seemingly preparing for a smooth transition to black-hole physics.

Paper Structure

This paper contains 5 sections, 37 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Three regimes in super-Planckian collisions
  3. Explicitly unitary S-matrix in Regions I and III
  4. Properties of the final state in the energy window
  5. Implications for the information paradox

Figures (4)

  • Figure 1: Phase diagram of trans-Planckian scattering showing three different kinematic regions and two different paths towards the regime of large BH production.
  • Figure 2: Further subdivision of the phase diagram of Fig. 1 for $D=4$.
  • Figure 3: Further subdivision of the phase diagram of Fig. 1 for $D=6$. A qualitatively similar behaviour holds for any $D>4$.
  • Figure 4: Energy dependence of $\langle M \rangle_{\rm DE}$ and $\langle E \rangle_{\rm CGR}$ in the energy window $M_s/g_s < E < M_s/g_s^2$ showing in particular the anti-scaling behaviour of the latter. The two curves cross at the energy $M_s g_s^{-4/3}$ corresponding to closing the rapidity gap between the two DE states.