scholarly journals THE EXTENSION STRUCTURE OF 2D MASSIVE CURRENT ALGEBRAS

1992 ◽  
Vol 07 (35) ◽  
pp. 3309-3318 ◽  
Author(s):  
J. LAARTZ
Keyword(s):  
Sigma Models ◽  
Current Algebra ◽  
Second Step ◽  
Two Dimensional ◽  
Split Extension ◽  
Nonlinear Sigma Models ◽  
Current Algebras

The extension structure of the two-dimensional current algebra of nonlinear sigma models is analyzed by introducing Kostant Sternberg (L, M) systems. It is found that the algebra obeys a two-step extension by Abelian ideals. The second step is a non-split extension of a representation of the quotient of the algebra by the first step of the extension. The cocycle which appears is analyzed.

Four-Loop-OrderβFunction for Two-Dimensional Nonlinear Sigma Models

1986 ◽  
Vol 57 (12) ◽  
pp. 1383-1385 ◽  
Author(s):  
Werner Bernreuther ◽  
Franz J. Wegner
Keyword(s):  
Sigma Models ◽  
Two Dimensional ◽  
Nonlinear Sigma Models

scholarly journals Algebra of Nonlocal Charges in Supersymmetric Nonlinear Sigma Models

1997 ◽  
Vol 12 (02) ◽  
pp. 419-436 ◽  
Author(s):  
L. E. Saltini ◽  
A. Zadra
Keyword(s):  
Sigma Models ◽  
Sigma Model ◽  
Graphic Method ◽  
Two Dimensional ◽  
Conserved Charges ◽  
Classical Algebra ◽  
Dirac Brackets ◽  
Yangian Algebra ◽  
Graphic Methods ◽  
Nonlinear Sigma Models

We propose a graphic method to derive the classical algebra (Dirac brackets) of nonlocal conserved charges in the two-dimensional supersymmetric nonlinear O(N) sigma model. As in the purely bosonic theory we find a cubic Yangian algebra. We also consider the extension of graphic methods to other integrable theories.

NEW N=2 MATTER COUPLINGS IN SUPERSPACE

1988 ◽  
Vol 03 (03) ◽  
pp. 703-719 ◽  
Author(s):  
S.V. KETOV
Keyword(s):  
Sigma Models ◽  
Dimensional Reduction ◽  
Two Dimensional ◽  
Kähler Metrics ◽  
Kahler Metrics ◽  
Four Dimensions ◽  
Yang Mills ◽  
Quaternionic Kähler ◽  
Nonlinear Sigma Models

The generalized N=2 tensor multiplets are defined and the corresponding interacting models are constructed in N=2 superspace in four dimensions. The couplings with the N=2 Yang-Mills fields are given too. The two-dimensional nonlinear N=4 supersymmetric sigma models obtained via dimensional reduction are known to be finite. The construction gives rise to a variety of explicitly constructed quaternionic-Kähler metrics. Some two-dimensional N=4 supersymmetric sigma models with nonvanishing torsion turn out to be equivalent to the ordinary N=4 hyper-Kähler nonlinear sigma models without torsion.

The gravitational field about a spinning particle

2000 ◽  
Vol 78 (10) ◽  
pp. 947-957 ◽  
Author(s):  
D.G.C. McKeon
Keyword(s):  
Gravitational Field ◽  
Sigma Models ◽  
Effective Action ◽  
Infrared Divergence ◽  
Two Dimensional ◽  
Spinning Particle ◽  
One Dimensional ◽  
The One ◽  
Infrared Divergences ◽  
Nonlinear Sigma Models

We consider the action for N = 1 and N = 2 spinning particles in the presence of a background gravitational field. The action for the gravitational field induced by one-loop effects is examined to lowest order in the metric. This is the one-dimensional analogue of calculations performed in two-dimensional nonlinear sigma models. The inherent infrared divergences are quite severe, and it is found that the effective action depends crucially on how they are treated, as is the case in two-dimensional nonlinear sigma models. Using one approach, an intractable infrared divergence arises, while with another technique, the effective action vanishes. A calculational technique introduced by Onofri is employed. A novel N = 4 spinning particle is considered briefly.PACS No.: 12.60Jv

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