Integrable Field Theories derived from 4D Self-dual Gravity
نویسنده
چکیده
We reformulate the self-dual Einstein equation as a trio of di erential form equations for simple two-forms. Using them, we can quickly show the equivalence of the theory and 2D sigma models valued in in nite-dimensional group, which was shown by Park and Husain earlier. We also derive other eld theories including the 2D Higgs bundle equation. This formulation elucidates the relation among those eld theories. e-mail: [email protected], [email protected]
منابع مشابه
Four Dimensional Integrable Theories
There exist many four dimensional integrable theories. They include self-dual gauge and gravity theories, all their extended supersymmetric generalisations, as well the full (non-self-dual) N=3 super Yang-Mills equations. We review the harmonic space formulation of the twistor transform for these theories which yields a method of producing explicit connections and metrics. This formulation uses...
متن کامل5 D ec 1 99 6 THE NONCRITICAL W ∞ STRING SECTOR OF THE MEMBRANE
The exact quantum integrability aspects of a sector of the membrane is investigated. It is found that spherical membranes (in the lightcone gauge) moving in flat target spacetime backgrounds admit a class of integrable solutions linked to SU (∞) SDYM equations (dimensionally reduced to one temporal dimension) which, in turn, are related to Plebanski 4D SD Gravitational equations. A further rota...
متن کاملHolomorphic Chern-Simons-Witten Theory: from 2D to 4D Conformal Field Theories
It is well known that rational 2D conformal field theories are connected with Chern-Simons theories defined on 3D real manifolds. We consider holomorphic analogues of Chern-Simons theories defined on 3D complex manifolds (six real dimensions) and describe 4D conformal field theories connected with them. All these models are integrable. We describe analogues of the Virasoro and affine Lie algebr...
متن کاملNonlinear Integrable Systems
W algebras arise in the study of various nonlinear integrable systems such as: self-dual gravity, the KP and Toda hierarchies, their quasi-classical (or dispersionless) limit, etc. Twistor theory provides a geometric background for these algebras. Present state of these topics is overviewed. A few ideas on possible deformations of self-dual gravity (including quantum deformations) are presented.
متن کاملIntegrable Deformations of Self Dual Gravity
A proposal for constructing a universal nonlinear Ŵ∞ algebra is made as the symmetry algebra of a rotational Killing-symmetry reduction of the nonlinear perturbations of Moyal-Integrable deformations of D = 4 Self Dual Gravity (IDSDG). This is attained upon the construction of a nonlinear bracket based on nonlinear gauge theories associated with infinite dimensional Lie algebras. A Quantization...
متن کامل