Topological Rigid String Theory and Two Dimensional QCD

Abstract

We present a string theory that reproduces the large-$N$ expansion of two dimensional Yang-Mills gauge theory on arbitrary surfaces. First, a new class of topological sigma models is introduced, with path integrals localized to the moduli space of harmonic maps. The Lagrangian of these harmonic topological sigma models is of fourth order in worldsheet derivatives. Then we gauge worldsheet diffeomorphisms by introducing the induced worldsheet metric. This leads to a topological string theory, whose Lagrangian coincides in the bose sector with the rigid string Lagrangian discussed some time ago by Polyakov and others as a candidate for QCD string theory. The path integral of this topological rigid string theory is localized to the moduli spaces of minimal-area maps, and calculates their Euler numbers. The dependence of the large-$N$ QCD partition functions on the target area emerges from measuring the volume of the moduli spaces, and can be reproduced by adding a Nambu-Goto term (improved by fermionic terms) to the Lagrangian of the topological rigid string.

55 pages, phyzzx, no figures. (One subsection added, on "Comparison to Previous Results"; final version to appear in Nucl. Phys. B.)

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Cited by in corpus (24)

• Membranes at Quantum Criticality
• Infinite N phase transitions in continuum Wilson loop operators
• Gauge/string duality for QCD conformal operators
• Six-Dimensional Tensionless Strings In The Large N Limit
• A Worldsheet Description of Large N_c Quantum Field Theory
• Tensor Models, Kronecker coefficients and Permutation Centralizer Algebras
• Strings from Feynman Graph counting : without large N
• Aspects of Gauge Theory on Commutative and Noncommutative Tori
• Perturbative and non-perturbative aspects of the two-dimensional string/Yang-Mills correspondence
• Thermodynamics of Noncritical M-Theory and the Topological A-Model
• Permutation symmetry in large N Matrix Quantum Mechanics and Partition Algebras
• String Theoretical Interpretation for Finite N Yang-Mills Theory in Two-Dimensions
• Decomposition and the Gross-Taylor string theory
• New rigid string instantons in $R^4$
• A String Theory for Two Dimensional Yang-Mills Theory I
• Hidden symmetries and Large N factorisation for permutation invariant matrix observables
• QCD strings with spinning quarks
• Rigid string instantons are pseudo-holomorphic curves
• String Duals of Two-Dimensional Yang-Mills and Symmetric Product Orbifolds
• Strings in Bimetric Spacetimes
• Duality of large N Yang-Mills Theory on $T^2\times R^n$
• Instantons, Fluxons and Open Gauge String Theory
• T-duality of large N QCD
• Lattice defect networks in 2d Yang-Mills