Studies of the two-dimensional nonlinear sigma-model

Thesis/Dissertation · Thu Dec 31 23:00:00 EST 1987

OSTI ID:5115256

Buscher, T H

We consider various geometric characteristics of the classical bosonic two-dimensional nonlinear sigma-model and its supersymmetric extensions, and the conditions under which these characteristics are preserved in the quantum theory. We show that the one-loop counterterms for a class of N = 2 supersymmetric nonliner sigma-models with Wess-Zumino-Witten (W-Z-W) term in two dimensions, calculated with the N = 1 superspace normal-coordinate background-field method, agree with the results of an N = 2 superspace calculation and possess both supersymmetries of the classical action when the fields are on shell. We investigate the effect of duality transformation on the classical geometries of bosonic, N = 1 and N = 2 supersymmetric models with W-Z-W term, whose target-manifold metric and torsion are invariant under the Lie action of a family of commuting vector fields. For such models initially without torsion, we identify the torsion which appears after duality as the field strength of the gauge connection in a Kaluza-Klein interpretation of the initial geometry. We show that duality preserves quantum conformal invariance at order ({alpha}{prime}){sup 0}, where {alpha}{prime} is the string-tension parameter, provided the classical geometric effect of duality is augmented to include an action (a shift) on the dilaton field. We interpret the combined transformations as the order-({alpha}{prime}){sup 0} part of a quantum duality symmetry of the string background field equations. We give a path-integral implementation of the duality transformation, and find that the dilaton shift results from a functional jacobian. We construct a new class of N = 2 supersymmetric models with W-Z-W term, providing examples of an interesting new class of Kaehler-like manifold with two complex structures, parallel with respect to the natural sigma-model connections with (opposite) torsion, but which do not commute.

• Research Organization: State Univ. of New York, Stony Brook, NY (USA)
• OSTI ID: 5115256
• Country of Publication: United States
• Language: English

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