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W-infinity algebras, Hawking radiation, and information retention by stringy black holes

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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 (the singular regions of which 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-infinity generators in its vertex function. The latter correspond to delocalized, nonpropagating, 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 -> (stringy black hole)(star), where the black hole is viewed as a stringy state with a specific configuration of W-infinity charges that are conserved. Hawking radiation is then the reverse process, with conservation of the W-infinity 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 W1+8 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.

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