An exact string representation of 3d SU(2) lattice Yang--Mills theory

Abstract

We show that 3d SU(2) lattice Yang--Mills theory can be cast in the form of an exact string representation. The derivation starts from the exact dual (or spin foam) representation of the lattice gauge theory. We prove that every dual configuration (or spin foam) can be equivalently described as a self--avoiding worldsheet of strings on a framing of the lattice. Using this correspondence, we translate the partition function into a sum over closed worldsheets that are weighted with explicit amplitudes. The expectation value of two Polyakov loops with spin j becomes a sum over worldsheets that are bounded by 2j strings along a framing of the loops.

arXiv comment12 pages, 7 figures

References in corpus (9)

• Large N Field Theories, String Theory and Gravity
• Spin Foam Models
• Confining Strings
• Dual of 3-dimensional pure SU(2) Lattice Gauge Theory and the Ponzano-Regge Model
• Dual Computations of Non-abelian Yang-Mills on the Lattice
• Yang-Mills Theory in Three Dimensions as Quantum Gravity Theory
• Two-dimensional QCD and strings
• Dual representation of Polyakov loop in 3d SU(2) lattice Yang-Mills theory
• String Theory: The Early Years

Cited by in corpus (3)

• A Dual Algorithm for Non-abelian Yang-Mills coupled to Dynamical Fermions
• A Gauge-Independent Mechanism for Confinement and Mass Gap: Part I -- The General Framework
• Dual representation of Polyakov loop in 3d SU(2) lattice Yang-Mills theory