Four Loop Order Beta Function of Nonlinear Models in Symmetric Spaces
198916 pages
Published in:
- Nucl.Phys.B 316 (1989) 663-678
- Published: 1989
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Abstract: (Elsevier)
The beta-function for the grassmannian nonlinear σ-model of symmetry U (N) U (p) ∗ U (N−p) has been calculated directly in four-loop order in d =2+ ε dimensions. Using isomorphisms and information from 1 N expansions I obtain the four-loop β-function for a large class of manifolds. Consequences are: (i) the degeneracy of the exponent ν for chiral models on the group manifolds SU( N ) and SO( N ) in three-loop order is lifted in four-loop order; (ii) the conductivity exponent at the mobility edge for the orthogonal case acquires a negative correction; (iii) the β-function bends over in the symplectic (i.e. spin-orbit coupling) case which suggests a nontrivial mobility edge fixed-point in d = 2 dimensions.- FIELD THEORETICAL MODEL: SIGMA
- NONLINEAR
- MODEL: GRASSMANN
- RENORMALIZATION: BETA FUNCTION
- EXPANSION 1/N
- SYMMETRY: SU(N)
- SYMMETRY: SO(N)
- PERTURBATION THEORY: HIGHER-ORDER
- FIELD THEORY: CRITICAL PHENOMENA
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