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We constructed a conformal field theory partition function. This reveals two special states interpreted as strings in AdS3, with all others representing black hole microstates.

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Area of Science:

  • Theoretical Physics
  • Quantum Field Theory
  • String Theory

Background:

  • Conformal field theories (CFTs) are crucial in understanding critical phenomena and quantum gravity.
  • The Virasoro algebra governs 2D CFTs, with its primary fields and spectral gaps being key characteristics.
  • Modular invariance and unitarity are fundamental properties for consistent quantum field theories.

Purpose of the Study:

  • To construct a unitary, modular-invariant torus partition function for a 2D CFT.
  • To analyze the spectral gap of Virasoro primary states and identify special states.
  • To explore the physical interpretation of these states within the AdS/CFT correspondence.

Main Methods:

  • Construction of a torus partition function for a 2D CFT.
  • Analysis of the Virasoro primary spectral gap.
  • Identification and characterization of specific quantum states based on their spin and scaling properties.

Main Results:

  • A unitary, modular-invariant torus partition function was successfully constructed.
  • A Virasoro primary spectral gap of Δ_{*}=[(c-1)/12] above the vacuum was identified.
  • Two specific states (O_{*}) with spin scaling linearly with the central charge (c) were found.

Conclusions:

  • The identified special states (O_{*}) can be interpreted as strongly coupled strings in Anti-de Sitter space in three dimensions (AdS3).
  • All other quantum states in this model represent black hole microstates.
  • This work provides insights into the microstate structure of quantum black holes and string theory in AdS3.