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Large N Partition Functions, Holography, and Black Holes.

Nikolay Bobev1, Junho Hong1, Valentin Reys1

  • 1Instituut voor Theoretische Fysica, KU Leuven, Celestijnenlaan 200D, B-3001 Leuven, Belgium.

Physical Review Letters
|August 8, 2022
PubMed
Summary

We derived a closed-form expression for the ABJM theory

Area of Science:

  • Theoretical Physics
  • String Theory
  • Quantum Field Theory

Background:

  • The ABJM theory is a key model in M-theory, describing multiple M2-branes.
  • Understanding its properties is crucial for advancements in string theory and quantum gravity.

Purpose of the Study:

  • To derive a simple closed-form expression for the topologically twisted index of the ABJM theory.
  • To obtain analytic expressions for this index in the 't Hooft limit.

Main Methods:

  • The study utilizes a fixed k and all-orders 1/N expansion.
  • It also employs an all-orders 1/sqrt[λ] expansion in the 't Hooft limit.

Main Results:

  • A simple closed-form expression for the topologically twisted index of the ABJM theory was found.

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  • Analytic expressions for the index at fixed genus in the 't Hooft limit were obtained.

    • Conclusions:

    • The findings have significant implications for holographic duality.
    • This work advances the microscopic entropy counting of supersymmetric static AdS_{4} black holes.
    • Generalizations to other superconformal field theories (SCFTs) are also considered.