Tensor network approach to two-dimensional Yang–Mills theories
Masafumi Fukuma, Daisuke Kadoh, Nobuyuki Matsumoto
Abstract
Abstract We propose a novel tensor network representation for two-dimensional Yang–Mills theories with arbitrary compact gauge groups. In this method, tensor indices are given directly by group elements with no direct use of the character expansion. We apply the tensor renormalization group method to this tensor network for SU(2) and SU(3), and find that the free energy density and the energy density are accurately evaluated. We also show that the singular value decomposition of a tensor has a group-theoretic structure and can be associated with the character expansion.
Topics & Concepts
Tensor (intrinsic definition)PhysicsCharacter (mathematics)Stress–energy tensorMathematical physicsTensor contractionTensor densityGroup (periodic table)Gauge groupRepresentation (politics)Tensor fieldGauge theoryPure mathematicsExact solutions in general relativityMathematicsQuantum mechanicsGeometryLawPoliticsPolitical sciencePhysics of Superconductivity and MagnetismBlack Holes and Theoretical PhysicsParticle physics theoretical and experimental studies