Toward tensor renormalization group study of three-dimensional non-Abelian gauge theory
Takaaki Kuwahara, Asato Tsuchiya
Abstract
Abstract We propose a method to represent the path integral over gauge fields as a tensor network. We introduce a trial action with variational parameters and generate gauge field configurations with the weight defined by the trial action. We construct initial tensors with indices labelling these gauge field configurations. We perform the tensor renormalization group (TRG) with the initial tensors and optimize the variational parameters. As a first step to the TRG study of non-Abelian gauge theory in more than two dimensions, we apply this method to three-dimensional pure SU(2) gauge theory. Our result for the free energy agrees with the analytical results in the weak and strong coupling regimes.
Topics & Concepts
PhysicsTensor (intrinsic definition)Mathematical physicsGauge theoryGauge (firearms)RenormalizationPath integral formulationBRST quantizationRenormalization groupIntroduction to gauge theoryQuantum gauge theoryAction (physics)Gauge groupSupersymmetric gauge theoryAbelian groupHamiltonian lattice gauge theoryGauge anomalyQuantum electrodynamicsGauge fixingQuantum mechanicsGauge bosonMathematicsPure mathematicsHistoryQuantumArchaeologyBlack Holes and Theoretical PhysicsParticle physics theoretical and experimental studiesCosmology and Gravitation Theories