Symplectic Gravity Models in Four, Three and Two Dimensions

Abstract

A class of the $D=4$ gravity models describing a coupled system of $n$ Abelian vector fields and the symmetric $n\times n$ matrix generalizations of the dilaton and Kalb-Ramond fields is considered. It is shown that the Pecci-Quinn axion matrix can be entered and the resulting equations of motion possess the $Sp(2n,R)$ symmetry in four dimensions. The stationary case is studied. It is established that the theory allows a $\sigma$-model representation with a target space which is invariant under the $Sp[2(n+1),R]$ group of isometry transformations. The chiral matrix of the coset $Sp[2(n+1),R]/U(n+1)$ is constructed. A Kähler formalism based on the use of the Ernst $(n+1)\times (n+1)$ complex symmetric matrix is developed. The stationary axisymmetric case is considered. The Belinsky-Zakharov chiral matrix depending on the original field variables is obtained. The Kramer-Neugebauer transformation, which algebraically maps the original variables into the target space ones, is presented.

21 pages, RevTex, no figuries

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• Strong-Weak Coupling Duality in Three Dimensional String Theory
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• Matrix Dilaton-Axion for Heterotic String in Three Dimensions
• DUALITY SYMMETRY GROUP OF TWO DIMENSIONAL HETEROTIC STRING THEORY
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Cited by in corpus (2)

• Mathematical and physical aspects of complex symmetric operators
• Charging Symmetries and Linearizing Potentials for Gravity Models with Symplectic Symmetry