Doubled Conformal Compactification

We use Weyl transformations between the Minkowski spacetime and dS/AdS spacetime to show that one cannot well define the electrodynamics globally on the ordinary conformal compactification of the Minkowski spacetime (or dS/AdS spacetime), where the electromagnetic field has a sign factor (and thus is discountinuous) at the light cone. This problem is intuitively and clearly shown by the Penrose diagrams, from which one may find the remedy without too much difficulty. We use the Minkowski and dS spacetimes together to cover the compactified space, which in fact leads to the doubled conformal compactification. On this doubled conformal compactification, we obtain the globally well-defined electrodynamics.Comment: 14 pages, 4 figure

Nonlinear W^∞\hat{W}_{\infty} Current Algebra in the SL(2,R)/U(1) Coset Model

Previously we have established that the second Hamiltonian structure of the KP hierarchy is a nonlinear deformation, called $\hat{W}_{\infty}$, of the linear, centerless $W_{\infty}$ algebra. In this letter we present a free-field realization for all generators of $\hat{W}_{\infty}$ in terms of two scalars as well as an elegant generating function for the $\hat{W}_{\infty}$ currents in the classical conformal $SL(2,R)/U(1)$ coset model. After quantization, a quantum deformation of $\hat{W}_{\infty}$ appears as the hidden current algebra in this model. The $\hat{W}_{\infty}$ current algebra results in an infinite set of commuting conserved charges, which might give rise to $W$-hair for the 2d black hole arising in the corresponding string theory at level $k=9/4$.Comment: 11