Higher d Eisenstein series and a duality-invariant distance measure

Creators: Benjamin, Nathan¹; Fitzpatrick, A. Liam²

1. California Institute of Technology
2. Boston University

Abstract

The Petersson inner product is a natural inner product on the space of modular invariant functions. We derive a formula, written as a convergent sum over elementary functions, for the inner product E_s(G, B) of the real analytic Eisenstein series and a general point in Narain moduli space. We also discuss the utility of the Petersson inner product as a distance measure on the space of 2d CFTs, and apply our procedure to evaluate this distance in various examples.

Copyright and License

© The Authors. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. Article funded by SCOAP3.

Acknowledgement

We are grateful to Cyuan-Han Chang, Scott Collier, Jim Halverson and Ami Katz for useful discussions, and to Cameron Cogburn for collaboration in the early stages of the project. We are also grateful to Boris Pioline for bringing to our attention the works [1, 6, 7] and to Eric Perlmutter for comments on a previous version of the paper. NB is supported by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award Number DE-SC0011632, and by the Sherman Fairchild Foundation. ALF is supported by the US Department of Energy Office of Science under Award Number DE-SC0015845, the Simons Collaboration on the Non-Perturbative Bootstrap, and a Sloan Foundation fellowship. ALF thanks the Aspen Center for Physics for hospitality while this work was completed.

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