preprint · arXiv (Cornell University) · 2020
Averaging Over Narain Moduli Space
Maloney, Alexander, Witten, Edward
Cited by 0Open access
Abstract
Recent developments involving JT gravity in two dimensions indicate that under some conditions, a gravitational path integral is dual to an average over an ensemble of boundary theories, rather than to a specific boundary theory. For an example in one dimension more, one would like to compare a random ensemble of two-dimensional CFT's to Einstein gravity in three dimensions. But this is difficult. For a simpler problem, here we average over Narain's family of two-dimensional CFT's obtained by toroidal compactification. These theories are believed to be the most general ones with their central charges and abelian current algebra symmetries, so averaging over them means picking a random CFT with those properties. The average can be computed using the Siegel-Weil formula of number theory and has some properties suggestive of a bulk dual theory that would be an exotic theory of gravity in three dimensions. The bulk dual theory would be more like $U(1)^{2D}$ Chern-Simons theory than like Einstein gravity.
Cite this paper
Maloney, A., & Witten, E. (2020). Averaging Over Narain Moduli Space. arXiv (Cornell University). https://doi.org/10.48550/arxiv.2006.04855
Maloney, Alexander, and Edward Witten. “Averaging Over Narain Moduli Space.” arXiv (Cornell University), 2020, https://doi.org/10.48550/arxiv.2006.04855.
Maloney, Alexander, and Edward Witten. 2020. “Averaging Over Narain Moduli Space.” arXiv (Cornell University). https://doi.org/10.48550/arxiv.2006.04855.
Maloney, A. and Witten, E. (2020) ‘Averaging Over Narain Moduli Space’, arXiv (Cornell University). Available at: https://doi.org/10.48550/arxiv.2006.04855.
@misc{maloney2020averaging,
title = {{Averaging Over Narain Moduli Space}},
author = {Maloney, Alexander and Witten, Edward},
journal = {arXiv (Cornell University)},
year = {2020},
doi = {10.48550/arxiv.2006.04855}
}Made from the index record. Check names, capitalisation and page numbers against the paper. Need another style? AI for Research has over 10,000.