Multi-trace Correlators from Permutations as Moduli Space

Abstract

We study the $n$-point functions of scalar multi-trace operators in the $U(N_c)$ gauge theory with adjacent scalars, such as $\mathcal{N}=4$ super Yang-Mills, at tree-level by using finite group methods. We derive a set of formulae of the general $n$-point functions, valid for general $n$ and to all orders of $1/N_c$. In one formula, the sum over Feynman graphs becomes a topological partition function on ${\Sigma }_{0,n}$ with a discrete gauge group, which resembles closed string interactions. In another formula, a new skeleton reduction of Feynman graphs generates connected ribbon graphs, which resembles open string interaction. We define the moduli space ${\mathcal{M}}_{g,n}^{\mathrm{gauge}}$ from the space of skeleton-reduced graphs in the connected $n$-point function of gauge theory. This moduli space is a proper subset of ${\mathcal{M}}_{g,n}$ stratified by the genus, and its top component gives a simple triangulation of ${\Sigma }_{g,n}$.

76 pages, many figures, 1.6MB, v2: added Mathematica files and subsections. Typo corrected, v3: references added

References in corpus (24)

• Diagonal multi-matrix correlators and BPS operators in N=4 SYM
• Structure Constants and Integrable Bootstrap in Planar N=4 SYM Theory
• D-branes and K-theory in 2D topological field theory
• Quantum Spectral Curve and Structure Constants in N=4 SYM: Cusps in the Ladder Limit
• Handling Handles: Nonplanar Integrability in $\mathcal{N}=4$ Supersymmetric Yang-Mills Theory
• Colour-dressed hexagon tessellations for correlation functions and non-planar corrections
• Operator Mixing in Large $N$ Superconformal Field Theories on ${\mathbb{S}}^4$ and Correlators with Wilson loops
• From Matrix Models and quantum fields to Hurwitz space and the absolute Galois group
• Structure Constants of Defect Changing Operators on the 1/2 BPS Wilson Loop
• On the worldsheet theories of strings dual to free large N gauge theories
• Wave functions and correlation functions for GKP strings from integrability
• Handling Handles. Part II. Stratification and Data Analysis
• Comments on worldsheet theories dual to free large N gauge theories
• Minimal surfaces in AdS and the eight-gluon scattering amplitude at strong coupling
• What is the Simplest Gauge-String Duality?
• Lectures notes on compact Riemann surfaces
• The space-time operator product expansion in string theory duals of field theories
• Strebel Differentials With Integral Lengths And Argyres-Douglas Singularities
• Exciting LLM Geometries
• BPS operators in $\mathcal{N}=4$ $SO(N)$ super Yang-Mills theory: plethysms, dominoes and words
• Flavour singlets in gauge theory as Permutations
• Topological String Correlators from Matrix Models
• Restricted Schurs and correlators for SO(N) and Sp(N)
• Large Strebel graphs and $(3,2)$ Liouville CFT

Cited by in corpus (1)

• Three-point Functions in $\mathcal{N}=4$ SYM at Finite $N_c$ and Background Independence