In string theory, elementary particles are represented by vibrational modes of a string. Strings interact by various joining and splitting processes, and the probabilities that certain scattering processes occur are given by string scattering amplitudes. When computing a low-energy expansion of these string scattering amplitudes, coefficient functions arise that are automorphic functions appearing as solutions to various differential equations and whose expressions involve combinations of Eisenstein series on an arithmetic quotient of the exceptional group E_8. The first few solutions to these differential equations are known on SL_2(R). We describe work toward a spectral solution in the SL_3(R) case. This project was initiated at the Rethinking Number Theory 3 workshop and is in collaboration with Maryam Khaqan, Kim Klinger-Logan, Manish Pandey, and Runqiu Xu.
Spectral Theory of Automorphic Forms Applied to String Scattering Amplitudes
Holley Friedlander, Dickinson College
Authors: Maryam Khaqan, Kim Klinger-Logan, Manish Pandey, Runqiu Xu
2023 AWM Research Symposium
Number Theory at Primarily Undergraduate Institutions [Organized by Bella Tobin and Leah Sturman]