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arXiv · 2104.14710

Chern-Simons Invariants from Ensemble Averages

Meer Ashwinkumar·Matthew Dodelson·Abhiram Kidambi·Jacob M. Leedom·Masahito Yamazaki
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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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Meer Ashwinkumar, Matthew Dodelson, Abhiram Kidambi, Jacob M. Leedom, Masahito Yamazaki. 2021-04-30. Chern-Simons Invariants from Ensemble Averages. https://doi.org/10.1007/jhep08(2021)044

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