Symplectic Gravity Models in Four, Three and Two Dimensions

Details Symplectic Gravity Models in Four, Three and Two Dimensions Symplectic Gravity Models in Four, Three and Two Dimensions

1996-10-28

arxiv.org/abs/hep-th/9610222v1

J.Math.Phys. 39 (1998) 5446-5457

Physics

High Energy Physics

High Energy Physics - Theory

21 pages, RevTex, no figuries

Scientific paper

10.1063/1.532583

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 K\"ahler 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.

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