Induced QCD at Large N

Abstract

We propose and study at large N a new lattice gauge model , in which the Yang-Mills interaction is induced by the heavy scalar field in adjoint representation. At any dimension of space and any $N$ the gauge fields can be integrated out yielding an effective field theory for the gauge invariant scalar field, corresponding to eigenvalues of the initial matrix field. This field develops the vacuum average, the fluctuations of which describe the elementary excitations of our gauge theory. At $N=\infty$ we find two phases of the model, with asymptotic freedom corresponding to the strong coupling phase (if there are no phase transitions at some critical $N$). We could not solve the model in this phase, but in the weak coupling phase we have derived exact nonlinear integral equations for the vacuum average and for the scalar excitation spectrum. Presumably the strong coupling equations can be derived by the same method.

20 pages

Cited by in corpus (85)

• Random Matrix Theory and Chiral Symmetry in QCD
• Integrability and Matrix Models
• A generalized ensemble of random matrices
• Generation of Matrix Models by W-operators
• BGWM as Second Constituent of Complex Matrix Model
• On the Large N Limit of the Itzykson-Zuber Integral
• Random matrix theory and symmetric spaces
• On some integrals over the U(N) unitary group and their large N limit
• Unitary Integrals and Related Matrix Models
• Updating QCD${}_2$
• Fermionic Matrix Models
• Area Law and Continuum Limit in "Induced QCD"
• The Itzykson-Zuber Integral for U(m|n)
• Generalized Penner models to all genera
• Free Variables and the Two Matrix Model
• Heavy Dynamical Fermions in Lattice QCD
• Induced QCD and Hidden Local ZN Symmetry
• Some Remarks About Induced QCD
• Chiral Random Matrix Model for Critical Statistics
• Exact solution of d=1 Kazakov-Migdal induced gauge theory
• Hermitian Matrix Model with Plaquette Interaction
• Statistical limits of dictionary learning: random matrix theory and the spectral replica method
• Two dimensional QCD is a one dimensional Kazakov-Migdal model
• Adjoint Fermion Matrix Models
• Coloring Random Triangulations
• The Problem of Large-N Phase Transition in Kazakov-Migdal Model of Induced QCD
• Toward an analytic determination of the deconfinement temperature in SU(2) L.G.T.
• Low Temperature Expansion of Matrix Models
• The Kazakov-Migdal Model as a High Temperature Lattice Gauge Theory
• Some Remarks About the Two-Matrix Penner Model and the Kazakov-Migdal Model
• Continuum Limits of ``Induced QCD": Lessons of the Gaussian Model at d=1 and Beyond
• Kazakov--Migdal Model with Logarithmic Potential and the Double Penner Matrix Model
• Phase Transitions in Induced QCD
• Coherent state operators, giant gravitons, and gauge-gravity correspondence
• Challenges of Matrix Models
• Coherent state excitations and string-added coherent states in gauge-gravity correspondence
• Generalized Drinfeld-Sokolov Hierarchies, Quantum Rings, and W-Gravity
• Compositeness Condition for Dynamically Induced Gauge Theories
• Strings, Matrix Models, and Meanders
• Variational Master Field for Large-N Interacting Matrix Models - Free Random Variables on Trial
• Adjoint non-Abelian Coulomb gas at large N
• Deconfinement Transition in Large N Lattice Gauge Theory
• Exact Results in Discretized Gauge Theories
• Orthogonality Relations and Supercharacter Formulas of U(m|n) Representations
• A Simple Model Inducing QCD
• A Study of the $N=2$ Kazakov-Migdal Model
• Kazakov-Migdal model on the Graph and Ihara Zeta Function
• Critical Behaviour of a Fermionic Random Matrix Model at Large-N
• Bosonic color-flavor transformation for the special unitary group
• The Spectrum of the Kazakov Migdal-Model
• The orthogonality relations for the supergroup $U(m|n)$
• Exactly Soluble QCD and Confinement of Quarks
• The Spatial String Tension in High Temperature Lattice Gauge Theories
• Induced QCD I: Theory
• The Color-Flavor Transformation and Lattice QCD
• Howe Duality for an Induced Model of Lattice U(N) Yang-Mills Theory
• Difficulties in Inducing a Gauge Theory at Large N
• Gross-Witten-Wadia Phase Transition in Induced QCD on the Graph
• Nonrelativistic Particle in Free Random Gauge Background
• D-dimensional Induced Gauge Theory as a Solvable Matrix Model
• Induced QCD Without Local Confinement
• Large N Matrix Hyperspheres and the Gauge-Gravity Correspondence
• Induced QCD II: Numerical results
• Symmetry and Observables in Induced QCD
• Vector Induced Lattice Gauge Theories
• From hermitian matrix model to lattice gauge theory
• Large-N Quenching in the Kazakov-Migdal Model
• Noncommutative probability, matrix models, and quantum orbifold geometry
• A Candidate For The QCD String Based On Non-Backtracking Random Walks
• Nonabelian Duality and Solvable Large N Lattice Systems
• Matrix Models of Induced Large-N QCD
• QED out of matter
• Developments in Random Matrix Theory
• The Spatial Dynamics in Kazakov--Migdal Model
• Large Representation Recurrences in Large N Random Unitary Matrix Models
• Solution of gauge theories induced by fundamental representation scalars
• Induced QCD from the Noncommutative Geometry of a Supermanifold
• Some Analytical Results in (2+1) dimensional L.G.T.
• New Approach to Induced QCD
• Eigenvalue Dynamics and the Matrix Chain
• The Color--Flavor Transformation of induced QCD
• Geometric QCD II: The Confining Twistor String and Meson Spectrum
• Itzykson-Zuber correlators from character expansion
• Taming lattice artifacts with Pauli--Villars fields
• Loop Equations for the d-dimensional One-Hermitian Matrix model