Large $N$ and large representations of Schur line defect correlators

Abstract

We study the large $N$ and large representation limits of the Schur line defect correlators of the Wilson line operators transforming in the (anti)symmetric, hook and rectangular representations for $\mathcal{N}=4$ $U(N)$ super Yang-Mills theory. By means of the factorization property, the large $N$ correlators of the Wilson line operators in arbitrary representations can be exactly calculated in principle. In the large representation limit they turn out to be expressible in terms of certain infinite series such as Ramanujan's general theta functions and the $q$-analogues of multiple zeta values ($q$-MZVs). Several generating functions for combinatorial objects, including partitions with non-negative cranks and conjugacy classes of general linear groups over finite fields, emerge from the large $N$ correlators. Also we find conjectured properties of the automorphy and the hook-length expansion satisfied by the large $N$ correlators.

68 pages, 1 figure

References in corpus (15)

• Holographic Wilson Loops
• The 4d Superconformal Index from q-deformed 2d Yang-Mills
• Wilson Loops of Anti-symmetric Representation and D5-branes
• On gravitational description of Wilson lines
• Multiply wound Polyakov loops at strong coupling
• The Spectrum of Excitations of Holographic Wilson Loops
• Wilson loop correlators at strong coupling: from matrices to bubbling geometries
• Semi-classical open string corrections and symmetric Wilson loops
• $\mathcal{N}=2^{\ast }$ Schur indices
• Computing Wilson lines with dielectric branes
• Exact Stringy Microstates from Gauge Theories
• Exact $\mathcal{N}=2^{\ast }$ Schur line defect correlators
• A prediction for bubbling geometries
• Line defect Schur indices, Verlinde algebras and $U(1{)}_r$ fixed points
• Strings in Bubbling Geometries and Dual Wilson Loop Correlators

Cited by in corpus (9)

• Giant graviton expansions and ETW brane
• Excitations of bubbling geometries for line defects
• Orbifold ETW brane and half-indices
• M2-M5 giant graviton expansions
• ADHM Wilson line defect indices
• S-duality of boundary lines in $\mathcal{N}=4$ SYM theories and supersymmetric indices
• $\mathcal{N}=4$ line defect correlators of type BCD
• Interface line operators in $\mathcal{N}=4$ SYM theories and supersymmetric indices
• Schur Connections: Chord Counting, Line Operators, and Indices