$W_\infty$ Algebras, Hawking Radiation and Information Retention by Stringy Black Holes

TL;DR

This paper proposes that quantum $W$-symmetries, specifically $W_$ algebras, encode information retention in stringy black holes during Hawking radiation, challenging the traditional view of information loss.

Contribution

It introduces a framework where $W_$ symmetries and associated topological states preserve information in stringy black holes through Hawking radiation.

Findings

$W_$ charges are conserved during black hole interactions.

Hawking radiation spectrum is governed by $W_{1+}$ algebra matrix elements.

Classical horizon area remains conserved under a gauged $W_{1+}$ algebra.

Abstract

We have argued previously, based on the analysis of two-dimensional stringy black holes, that information in stringy versions of four-dimensional Schwarzschild black holes (whose singular regions are represented by appropriate Wess-Zumino-Witten models) is retained by quantum $W$-symmetries when the horizon area is not preserved due to Hawking radiation. It is key that the exactly-marginal conformal world-sheet operator representing a massless stringy particle interacting with the black hole requires a contribution from $W_\infty$ generators in its vertex function. The latter correspond to delocalised, non-propagating, string excitations that guarantee the transfer of information between the string black hole and external particles. When infalling matter crosses the horizon, these topological states are excited via a process: (Stringy black hole) + infalling matter $\rightarrow $ (Stringy black hole)$^\star$, where the black hole is viewed as a stringy state with a specific configuration of $W_\infty$ charges that are conserved. Hawking radiation is then the reverse process, with conservation of the $W_\infty$ charges retaining information. The Hawking radiation spectrum near the horizon of a Schwarzschild or Kerr black hole is specified by matrix elements of higher-order currents that form a phase-space $W_{1+\infty}$ algebra. We show that an appropriate gauging of this algebra preserves the horizon two-dimensional area classically, as expected because the latter is a conserved Noether charge.