Classical Structure and Renormalization
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In this chapter we define the general bosonic Non-Linear Sigma-Model (NLSM) action (without a scalar potential) and discuss its symmetries and quantization. The two-dimensional (2d) NLSM are distinguished by their renormalizability and the existence of a Wess-Zumino-Novikov-Witten (WZNW) term of second order in the spacetime derivatives. The covariant background field method and on-shell renormalization are developed, and the three-loop Renormalization Group (RG) β-functions of the general two-dimensional NLSM are derived. The 2d WZNW model and the 2d Freedman-Townsend NLSM are defined, and their perturbative RG β-functions are calculated. We also briefly consider classical duality transformations in NLSM, gauging NLSM isometries, and the Skyrme model of pions and nucleons in four dimensions.
KeywordsRenormalization Group Classical Structure Feynman Graph Skyrme Model Spacetime Derivative
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