Dual Computations of Non-abelian Yang-Mills on the Lattice

Abstract

In the past several decades there have been a number of proposals for computing with dual forms of non-abelian Yang-Mills theories on the lattice. Motivated by the gauge-invariant, geometric picture offered by dual models and successful applications of duality in the U(1) case, we revisit the question of whether it is practical to perform numerical computation using non-abelian dual models. Specifically, we consider three-dimensional SU(2) pure Yang-Mills as an accessible yet non-trivial case in which the gauge group is non-abelian. Using methods developed recently in the context of spin foam quantum gravity, we derive an algorithm for efficiently computing the dual amplitude and describe Metropolis moves for sampling the dual ensemble. We relate our algorithms to prior work in non-abelian dual computations of Hari Dass and his collaborators, addressing several problems that have been left open. We report results of spin expectation value computations over a range of lattice sizes and couplings that are in agreement with our conventional lattice computations. We conclude with an outlook on further development of dual methods and their application to problems of current interest.

arXiv commentv1: 18 pages, 7 figures, v2: Many changes to appendix, minor changes throughout, references and figures added, v3: minor corrections, 22 pages

References in corpus (20)

• Spin Foam Models
• A numerical study of confinement in compact QED
• Spin Foam Models of Riemannian Quantum Gravity
• A spin foam model for pure gauge theory coupled to quantum gravity
• The dual of pure non-Abelian lattice gauge theory as a spin foam model
• Dual of 3-dimensional pure SU(2) Lattice Gauge Theory and the Ponzano-Regge Model
• Scaling analysis of the magnetic monopole mass and condensate in the pure U(1) lattice gauge theory
• Investigating Confinement in Dually Transformed U(1) Lattice Gauge Theory
• A numerical study of a confined $Q\bar{Q}$ system in compact U(1) lattice gauge theory in 4D
• An efficient algorithm for the Riemannian 10j symbols
• q-Deformed spin foam models of quantum gravity
• Yang-Mills Theory in Three Dimensions as Quantum Gravity Theory
• Flux tubes and their interaction in U(1) lattice gauge theory
• Duals of nonabelian gauge theories in $D$ dimensions
• Analytic derivation of dual gluons and monopoles from SU(2) lattice Yang-Mills theory. II. Spin foam representation
• Current Status of the Numerical Simulations of d=3 SU(2) Lattice Gauge Theory in the Dual Formulation
• Exact duality transformations for sigma models and gauge theories
• Quasi-local Update Algorithms for Numerical Simulations of d=3 SU(2) LGT in the Dual Formulation
• Field Strength and Monopoles in Dual U(1) Lattice Gauge Theory
• U(1) Lattice Gauge theory and its Dual

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