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arXiv · 2308.11715

Higher $d$ Eisenstein Series and a Duality-Invariant Distance Measure

Nathan Benjamin·A. Liam Fitzpatrick
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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 $E_s(\tau, \bar{\tau})$ 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.

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Nathan Benjamin, A. Liam Fitzpatrick. 2023-08-22. Higher $d$ Eisenstein Series and a Duality-Invariant Distance Measure. https://arxiv.org/abs/2308.11715

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