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Super Quantum Airy Structures.

Vincent Bouchard1, Paweł Ciosmak2, Leszek Hadasz3

  • 1Department of Mathematical and Statistical Sciences, University of Alberta, 632 CAB, Edmonton, AB T6G 2G1 Canada.

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We introduce super quantum Airy structures, a new supersymmetric generalization. These structures yield unique free energies satisfying a generalized topological recursion, with applications in superalgebras and vertex operator superalgebras.

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Area of Science:

  • Mathematical Physics
  • Quantum Field Theory
  • Supersymmetry

Background:

  • Quantum Airy structures are a key concept in mathematical physics.
  • Supersymmetry offers a powerful framework for generalizing existing theories.

Purpose of the Study:

  • To introduce and define super quantum Airy structures.
  • To explore their mathematical properties and connections to topological recursion.
  • To classify and provide examples of these novel structures.

Main Methods:

  • Development of a supersymmetric generalization of quantum Airy structures.
  • Proof of the unique assignment of free energies.
  • Demonstration of a supersymmetric topological recursion relation.

Main Results:

  • Introduction of super quantum Airy structures and their unique free energies.
  • Establishment of a supersymmetric topological recursion.
  • Analysis of gauge transformations, classical limits, fermionic variables, and graphical representations.
  • Classification and examples of finite-dimensional (superalgebras, super Frobenius algebras) and infinite-dimensional (vertex operator superalgebras) structures.

Conclusions:

  • Super quantum Airy structures provide a robust supersymmetric framework.
  • The established topological recursion offers new tools for studying these systems.
  • The presented examples highlight the broad applicability of these structures in theoretical physics.