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The Virasoro fusion kernel and Ruijsenaars' hypergeometric function.

Julien Roussillon1

  • 1Department of Mathematics, KTH Royal Institute of Technology, 100 44 Stockholm, Sweden.

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PubMed
Summary
This summary is machine-generated.

The Virasoro fusion kernel is proven to be a hypergeometric function. This finding connects quantum field theory with integrable systems, revealing new mathematical structures.

Keywords:
2d conformal field theoryIntegrability

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Area of Science:

  • Mathematical Physics
  • Quantum Field Theory
  • Integrable Systems

Background:

  • The Virasoro algebra is central to conformal field theory.
  • Ruijsenaars' hypergeometric functions are significant in the study of integrable systems.
  • Understanding the relationship between these mathematical objects is an ongoing challenge.

Purpose of the Study:

  • To establish a precise connection between the Virasoro fusion kernel and Ruijsenaars' hypergeometric functions.
  • To demonstrate that the Virasoro fusion kernel is a joint eigenfunction of specific difference operators.
  • To explore the implications of this connection for quantum relativistic integrable systems.

Main Methods:

  • Proving the Virasoro fusion kernel as a joint eigenfunction of four difference operators.
  • Renormalizing the Virasoro fusion kernel.
  • Mapping difference operators to quantum relativistic hyperbolic Calogero-Moser Hamiltonians.

Main Results:

  • The Virasoro fusion kernel is shown to be equal to Ruijsenaars' hypergeometric function, up to normalization.
  • A renormalized version of the kernel is identified.
  • The difference operators are shown to correspond to quantum relativistic hyperbolic Calogero-Moser Hamiltonians.

Conclusions:

  • The study establishes a direct equivalence between the Virasoro fusion kernel and Ruijsenaars' hypergeometric function.
  • This provides a new perspective on the mathematical structures underlying quantum field theory and integrable systems.
  • The findings open avenues for further research into the interplay between these fields.