Higher d Eisenstein series and a duality-invariant distance measure

Benjamin, Nathan; Fitzpatrick, A. Liam

doi:10.1007/jhep04(2024)142

Title: Higher d Eisenstein series and a duality-invariant distance measure

Journal Article · 26 April 2024 · Journal of High Energy Physics (Online)

DOI: https://doi.org/10.1007/jhep04(2024)142 · OSTI ID:2479638

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California Institute of Technology (CalTech), Pasadena, CA (United States)
Boston University, MA (United States)

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 ($$τ$$, $$\overline{τ}$$) 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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Research Organization:: California Institute of Technology (CalTech), Pasadena, CA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), High Energy Physics (HEP)

Grant/Contract Number:: SC0011632; SC0015845

OSTI ID:: 2479638

Journal Information:: Journal of High Energy Physics (Online), Journal Name: Journal of High Energy Physics (Online) Journal Issue: 4 Vol. 2024; ISSN 1029-8479

Publisher:: Springer NatureCopyright Statement

Country of Publication:: United States

Language:: English

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