Titre :

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

Auteur(s) :

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

Date de publication :

2022-09-30

Discipline(s) HAL :

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

Résumé en anglais : [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 ...
Lire la suite >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.Lire moins >

Langue :

Anglais

Commentaire :

15 pages

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL

Date de dépôt :

2025-01-24T15:35:46Z