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CFT Correlators and Mapping Class Group Averages.

Iordanis Romaidis1, Ingo Runkel2

  • 1School of Mathematics, University of Edinburgh, Mayfield Road, Edinburgh, EH9 3FD UK.

Communications in Mathematical Physics
|October 10, 2024
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This study establishes a bulk-boundary correspondence in 3D topological field theories, linking mapping class group averages to 2D rational conformal field theories (CFTs). Ising-type modular fusion categories are shown to satisfy key properties for this connection.

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Area of Science:

  • Theoretical Physics
  • High Energy Physics
  • Quantum Field Theory

Background:

  • Mapping class group averages are relevant to 3D gravity partition functions.
  • 3D topological field theories provide a framework for studying bulk-boundary correspondences.
  • 2D rational conformal field theories (CFTs) have rich mathematical structures.

Purpose of the Study:

  • To establish a bulk-boundary correspondence between mapping class group averages and 2D rational CFT correlators.
  • To investigate the properties of chiral mapping class group representations in this context.
  • To extend existing results to surfaces with or without field insertions.

Main Methods:

  • Utilizing 3D topological field theories.
  • Analyzing irreducible chiral mapping class group representations with a finiteness property.
  • Examining Ising-type modular fusion categories.

Main Results:

  • A bulk-boundary correspondence is established for specific 3D topological field theories.
  • Ising-type modular fusion categories are demonstrated to satisfy the required properties.
  • The results extend previous findings to surfaces with and without field insertions.

Conclusions:

  • The study successfully links 3D gravity partition functions to 2D rational CFTs through a bulk-boundary correspondence.
  • The findings highlight the role of Ising-type modular fusion categories in this framework.
  • The absence of invertible global symmetries in the considered examples is noted.