Modular properties of 6d (DELL) systems

• Published in: The journal of high energy physics Vol. 2017; no. 11; pp. 1 - 34
• Main Authors: Aminov, G., Mironov, A., Morozov, A.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.11.2017; Springer Nature B.V; SpringerOpen
• Subjects: Anomalies in Field and String Theories; Classical and Quantum Gravitation; Elementary Particles; High energy physics; Integrable Hierarchies; Invariance; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; String Theory; Supersymmetric Gauge Theory; Supersymmetry and Duality; Yang-Mills theory; Anomalies in Field and String Theories; Integrable Hierarchies; Supersymmetry and Duality; Supersymmetric Gauge Theory
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP11(2017)023

A bstract If super-Yang-Mills theory possesses the exact conformal invariance, there is an additional modular invariance under the change of the complex bare charge . The low-energy Seiberg-Witten prepotential ℱ( a ), however, is not explicitly invariant, because the flat moduli also change a  − →  a D  = ∂ℱ/∂ a . In result, the prepotential is not a modular form and depends also on the anomalous Eisenstein series E 2 . This dependence is usually described by the universal MNW modular anomaly equation. We demonstrate that, in the 6 d SU( N ) theory with two independent modular parameters τ and τ ^ , the modular anomaly equation changes, because the modular transform of τ is accompanied by an ( N -dependent!) shift of τ ^ and vice versa. This is a new peculiarity of double-elliptic systems, which deserves further investigation.