Character Expansions, Itzykson-Zuber Integrals, and the QCD Partition Function

Abstract

A combinatorial formula to generate U(N) character expansions is presented. It is shown that the resulting character expansion formulas greatly simplify a number of problems where integrals over the group manifolds need to be calculated. Several examples are given, including direct and very quick calculations of the Itzykson-Zuber integral and the finite volume effective partition function of QCD in the sector with a given topological charge.

14 pages, REVTEX

References in corpus (1)

• On Finite-Volume Gauge Theory Partition Functions

Cited by in corpus (49)

• Performance Analysis of MIMO-MRC in Double-Correlated Rayleigh Environments
• Symmetry of matrix-valued stochastic processes and noncolliding diffusion particle systems
• Factorization of Correlation Functions and the Replica Limit of the Toda Lattice Equation
• The Large N 't Hooft Limit of Coset Minimal Models
• Environmental dependence in the ellipsoidal collapse model
• Replica Limit of the Toda Lattice Equation
• Singular value statistics of matrix products with truncated unitary matrices
• Capacity and Character Expansions: Moment generating function and other exact results for MIMO correlated channels
• On some integrals over the U(N) unitary group and their large N limit
• Systematic approach to statistics of conductance and shot-noise in chaotic cavities
• Matrix Models for Random Partitions
• Eigenvalue Density of Correlated Complex Random Wishart Matrices
• Generalizations of some integrals over the unitary group
• On absolute moments of characteristic polynomials of a certain class of complex random matrices
• A few remarks on Colour-Flavour Transformations,truncations of random unitary matrices, Berezin reproducing kernels and Selberg type integrals
• QCD3 and the Replica Method
• Invariant Integration over the Unitary Group
• Strong-Weak Chern-Simons-Matter Dualities from a Lattice Construction
• Supersymmetric Quenching of the Toda Lattice Equation
• On matrix model partition functions for QCD with chemical potential
• Character Expansions for the Orthogonal and Symplectic Groups
• Dashen's Phenomenon in Gauge Theories with Spontaneously Broken Chiral Symmetries
• Dropping the independence: singular values for products of two coupled random matrices
• Mesoscopic QCD and the Theta Vacua
• Partition Functions in Statistical Mechanics, Symmetric Functions, and Group Representations
• Commutative families in $W_{\infty }$, integrable many-body systems and hypergeometric $\tau$-functions
• Cauchy formula and the character ring
• Simple maps, Hurwitz numbers, and Topological Recursion
• Chiral symmetry breaking with no bilinear condensate revisited
• Commutative families in DIM algebra, integrable many-body systems and $q,t$ matrix models
• Virasoro Constraints and Flavor-Topology Duality in QCD
• Matrix models for classical groups and Toeplitz$\pm$Hankel minors with applications to Chern-Simons theory and fermionic models
• Maximum Entropy MIMO Wireless Channel Models
• Two $\beta$-ensemble realization of $\beta$-deformed WLZZ models
• Character expansion method for supergroups and extended superversions of the Leutwyler-Smilga and Berezin-Karpelevich integrals
• Limiting Statistics of the Largest and Smallest Eigenvalues in the Correlated Wishart Model
• SU(N) polynomial integrals and some applications
• A Bayesian Framework for Collaborative Multi-Source Signal Detection
• Invariant and Group Theoretical Integrations over the U(n) Group
• Bosonic color-flavor transformation for the special unitary group
• Analysis of the QCD Kondo phase using random matrices
• Grassmannian Integrals as Matrix Models for Non-Compact Yangian Invariants
• Unitary matrix integral for QCD with real quarks and the GOE-GUE crossover
• Grassmannian Integrals in Minkowski Signature, Amplitudes, and Integrability
• On discrete surfaces: Enumerative geometry, matrix models and universality classes via topological recursion
• Generalised unitary group integrals of Ingham-Siegel and Fisher-Hartwig type
• Finite $N$ unitary matrix model
• Itzykson-Zuber correlators from character expansion
• On the Integrable Structure of Super Yang-Mills Scattering Amplitudes