Generalized Gauss map and the geometry of strings

Journal Article · Fri Feb 15 04:00:00 EST 1991 · Annals of Physics (New York); (United States)

DOI:https://doi.org/10.1016/0003-4916(91)90227-Y· OSTI ID:5614788

Viswanathan, K S; Parthasarathy, R ^[1]; Kay, D

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1. Simon Fraser Univ., Burnaby, British Columbia (Canada)

A two-dimensional (Euclidean) string world sheet conformally immersed in R{sup n} is described in terms of the Grassmannian {sigma}-model G{sub 2,n}, through the generalized Gauss map. In order for the Gauss map to reproduce the work sheet, certain integrability conditions must be satisfied by the {sigma}-model fields. The geometrical properties of the surface, relevant to string theories, such as the Nambu-Goto action and the one involving the extrinsic geometry of the surface are expressed in terms of the Grassmannian fields. One-loop effects are evaluated for the action involving the extrinsic geometry in R{sup 3} incorporating the integrability conditions. In R{sup 4} the relation between self-intersection number of the immersed surfaces and the instanons of the Grassmannian is briefly discussed. A generalization of Kenmotsu equation and the representation theorem in R{sup 4} is presented.

• OSTI ID: 5614788
• Journal Information: Annals of Physics (New York); (United States), Journal Name: Annals of Physics (New York); (United States) Vol. 206:1; ISSN APNYA; ISSN 0003-4916
• Country of Publication: United States
• Language: English

Related Subjects

662110* -- General Theory of Particles & Fields-- Theory of Fields & Strings-- (1992-)
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
BOSON-EXCHANGE MODELS
COMPOSITE MODELS
CONFORMAL MAPPING
EXTENDED PARTICLE MODEL
FIELD THEORIES
GEOMETRY
INSTANTONS
MAPPING
MATHEMATICAL MODELS
MATHEMATICAL SPACE
MATHEMATICS
PARTICLE MODELS
PERIPHERAL MODELS
QUANTUM CHROMODYNAMICS
QUANTUM FIELD THEORY
QUARK MODEL
QUASI PARTICLES
SIGMA MODEL
SPACE
STRING MODELS
TOPOLOGICAL MAPPING
TRANSFORMATIONS