Averaging over moduli in deformed WZW models

Junkai Dong (Department of Physics, Cornell University, Ithaca, New York, USA) ; Thomas Hartman (Department of Physics, Cornell University, Ithaca, New York, USA) ; Yikun Jiang (Department of Physics, Cornell University, Ithaca, New York, USA)

WZW models live on a moduli space parameterized by current-current deformations. The moduli space defines an ensemble of conformal field theories, which generically have N abelian conserved currents and central charge c > N. We calculate the average partition function and show that it can be interpreted as a sum over 3-manifolds. This suggests that the ensemble-averaged theory has a holographic dual, generalizing recent results on Narain CFTs. The bulk theory, at the perturbative level, is identified as U(1)2N Chern-Simons theory coupled to additional matter fields. From a mathematical perspective, our principal result is a Siegel-Weil formula for the characters of an affine Lie algebra.

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      "value": "WZW models live on a moduli space parameterized by current-current deformations. The moduli space defines an ensemble of conformal field theories, which generically have N abelian conserved currents and central charge c > N. We calculate the average partition function and show that it can be interpreted as a sum over 3-manifolds. This suggests that the ensemble-averaged theory has a holographic dual, generalizing recent results on Narain CFTs. The bulk theory, at the perturbative level, is identified as U(1)2N  Chern-Simons theory coupled to additional matter fields. From a mathematical perspective, our principal result is a Siegel-Weil formula for the characters of an affine Lie algebra."
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Published on:
28 September 2021
Publisher:
Springer
Published in:
Journal of High Energy Physics , Volume 2021 (2021)
Issue 9
Pages 1-34
DOI:
https://doi.org/10.1007/JHEP09(2021)185
arXiv:
2105.12594
Copyrights:
The Author(s)
Licence:
CC-BY-4.0

Fulltext files: