The $D^6 R^4$ interaction as a Poincar\'e series, and a related shifted convolution sum

Klinger-Logan, Kim; Miller, Stephen D.; Radchenko, Danylo

Document type :

Pré-publication ou Document de travail: Autre communication scientifique (congrès sans actes - poster - séminaire...)

Title :

The $D^6 R^4$ interaction as a Poincar\'e series, and a related shifted convolution sum

Author(s) :

Klinger-Logan, Kim [Auteur]
Miller, Stephen D. [Auteur]
Radchenko, Danylo [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]

Publication date :

2022-09-30

HAL domain(s) :

Mathématiques [math]/Théorie des nombres [math.NT]
Mathématiques [math]/Physique mathématique [math-ph]

English abstract : [en]

We complete the program, initiated in a 2015 paper of Green, Miller, and Vanhove, of directly constructing the automorphic solution to the string theory $D^6 R^4$ differential equation $(\Delta-12)f=-E_{3/2}^2$ for ...
Show more >We complete the program, initiated in a 2015 paper of Green, Miller, and Vanhove, of directly constructing the automorphic solution to the string theory $D^6 R^4$ differential equation $(\Delta-12)f=-E_{3/2}^2$ for $SL(2,\mathbb{Z})$. The construction is via a type of Poincar\'e series, and requires explicitly evaluating a particular double integral. We also show how to derive the predicted vanishing of one type of term appearing in $f$'s Fourier expansion, confirming a conjecture made by Chester, Green, Pufu, Wang, and Wen motivated by Yang-Mills theory.Show less >

Language :

Anglais

Comment :

15 pages

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