Diffeomorphism algebra of two dimensional free massless scalar field with signature change

TL;DR

This paper investigates the effects of signature change in a two-dimensional scalar field model, revealing modifications in the energy spectrum and diffeomorphism algebra that differ from the standard Virasoro algebra, especially at low energies.

Contribution

It introduces a model of scalar fields with signature change and analyzes how this affects the energy spectrum and the algebra of conserved charges, highlighting deviations from the Virasoro algebra.

Findings

Energy spectrum depends on the signature change angle 

Diffeomorphism algebra differs from Virasoro at low energies

Central term in the algebra is modified and does not revert to the standard form

Abstract

We study a model of free massless scalar fields on a two dimensional cylinder with metric that admits a change of signature between Lorentzian and Euclidean type (ET), across the two timelike hypersurfaces (with respect to Lorentzian region). Considering a long strip-shaped region of the cylinder, denoted by an angle \theta, as the signature changed region it is shown that the energy spectrum depends on the angle \theta and in a sense differs from ordinary one for low energies. Morever diffeomorphism algebra of corresponding infinite conserved charges is different from '' Virasoro'' algebra and approaches to it at higher energies. The central term is also modified but does not approach to the ordinary one at higher energies.