Modular anomaly equation for Schur index of $$ \mathcal{N} $$ = 4 super-Yang-Mills
Min-xin Huang
Abstract
A bstract We propose a novel modular anomaly equation for the unflavored Schur index in the $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = 4 SU( N ) super-Yang-Mills theory. The vanishing conditions overdetermine the modular ambiguity ansatz from the equation, thus together they are sufficient to recursively compute the exact Schur indices for all SU( N ) gauge groups. Using the representations as MacMahon’s generalized sum-of-divisors functions and Jacobi forms, we then prove our proposal as well as elucidate a general formula conjectured by Pan and Peelaers.
Topics & Concepts
AnsatzPhysicsAnomaly (physics)Mathematical physicsGauge theorySupersymmetric gauge theoryFunctional equationPure mathematicsYang–Mills theoryYang–Mills existence and mass gapMathematicsQuantum mechanicsDifferential equationBlack Holes and Theoretical PhysicsQuantum Chromodynamics and Particle InteractionsNoncommutative and Quantum Gravity Theories