Handling Handles: Nonplanar Integrability in $\mathcal{N}=4$ Supersymmetric Yang-Mills Theory

Abstract

We propose an integrability setup for the computation of correlation functions of gauge-invariant operators in $\mathcal{N}=4$ supersymmetric Yang-Mills theory at higher orders in the large $N_{\text{c}}$ genus expansion and at any order in the 't Hooft coupling $g_{\text{YM}}^2{N}_{\text{c}}$. In this multi-step proposal, one polygonizes the string worldsheet in all possible ways, hexagonalizes all resulting polygons, and sprinkles mirror particles over all hexagon junctions to obtain the full correlator. We test our integrability-based conjecture against a non-planar four-point correlator of large half-BPS operators at one and two loops.

6 pages, 4 figures; v2: updated references, typos, minor improvements (published version)

References in corpus (14)

• Holography from Conformal Field Theory
• Dual Superconformal Symmetry from AdS5 x S5 Superstring Integrability
• Mellin amplitudes for $Ad{S}_5\times S^5$
• How to Succeed at Holographic Correlators Without Really Trying
• Loop Corrections to Supergravity on $Ad{S}_5\times S^5$
• Hexagonalization of Correlation Functions
• Structure Constants and Integrable Bootstrap in Planar N=4 SYM Theory
• Nonplanar Integrability
• Loop corrections for Kaluza-Klein AdS amplitudes
• Colour-dressed hexagon tessellations for correlation functions and non-planar corrections
• Hexagonalization of Correlation Functions II: Two-Particle Contributions
• NUTs and bolts beyond Lovelock
• Handling Handles. Part II. Stratification and Data Analysis
• Conical Twist Fields and Null Polygonal Wilson Loops

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