The D⁶ R⁴ interaction as a Poincaré series, and a related shifted convolution sum

2022/09/30 by Kim Klinger-Logan, Stephen D. Miller, Klinger-Logan, Kim +3 · 1 citation
Physics and Astronomy · #Black Holes and Theoretical Physics #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Number Theory (math.NT) #Particle physics theoretical and experimental studies

paper · pdf · doi:10.48550/arxiv.2210.00047

openalex publication_date 2022/09/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We complete the program, initiated in a 2015 paper of Green, Miller, and Vanhove, of directly constructing the automorphic solution to the string theory D⁶ R⁴ differential equation (Δ-12)f=-E_3/2² for SL(2,\Z). The construction is via a type of Poincaré series, and requires explicitly evaluating a particular double integral. We also show how to use double Dirichlet series to formally 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 (and later proved rigorously by Fedosova, Klinger-Logan, and Radchenko using the Gross-Zagier Holomorphic Projection Lemma.).

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