Chern-Simons Invariants from Ensemble Averages

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...

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Bibliographic Details
Published in:arXiv.org 2021-06
Main Authors: Meer Ashwinkumar, Dodelson, Matthew, Kidambi, Abhiram, Leedom, Jacob M, Yamazaki, Masahito
Format: Article
Language:English
Subjects:
Field theory (physics)
Holography
Lattices
Partitions (mathematics)
Quadratic forms
Quantum theory
Online Access:Get full text
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.2104.14710