Chern-Simons invariants from ensemble averages
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Chern-Simons invariants from ensemble averages

  • Author(s): Ashwinkumar, Meer;
  • Dodelson, Matthew;
  • Kidambi, Abhiram;
  • Leedom, Jacob M;
  • Yamazaki, Masahito
  • et al.
Abstract

Abstract We discuss ensemble averages of two-dimensional conformal field theories associated with an arbitrary indefinite lattice with integral quadratic form Q. We provide evidence that the holographic dual after the ensemble average is the three-dimensional Abelian Chern-Simons theory with kinetic term determined by Q. The resulting partition function can be written as a modular form, expressed as a sum over the partition functions of Chern-Simons theories on lens spaces. For odd lattices, the dual bulk theory is a spin Chern-Simons theory, and we identify several novel phenomena in this case. We also discuss the holographic duality prior to averaging in terms of Maxwell-Chern-Simons theories.

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