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Chern-Simons invariants from ensemble averages

Ashwinkumar, Meer·Dodelson, Matthew·Kidambi, Abhiram·Leedom, Jacob M.·Yamazaki, Masahito
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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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72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDSAdS-CFT CorrespondenceChern-Simons TheoriesConformal Field TheoryGauge-gravity correspondence

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Ashwinkumar, Meer, Dodelson, Matthew, Kidambi, Abhiram, Leedom, Jacob M., Yamazaki, Masahito. 2021-08-10. Chern-Simons invariants from ensemble averages. https://doi.org/10.1007/jhep08(2021)044

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