Conformal Algebra and Physical States in Non-critical 3-brane on R*S^3

TL;DR

This paper studies a high-energy phase of a non-critical 3-brane model, quantizing conformal modes non-perturbatively and analyzing the conformal algebra to identify physical states constrained by conformal invariance.

Contribution

It introduces a non-perturbative quantization of conformal modes in a non-critical 3-brane and constructs the conformal algebra to determine physical states.

Findings

All negative-metric modes are related to positive-metric modes via conformal charges.

An infinite set of physical states satisfying conformal invariance are constructed.

The model describes a four-dimensional conformal field theory at high energy.

Abstract

A world-volume model of non-critical 3-brane is quantized in a strong coupling phase where fluctuations of the conformal mode become dominant. This phase, called the conformal-mode dominant phase, is realized at the very high energy far beyond the Planck mass scale. We separately treat the conformal mode and the traceless mode and quantize the conformal mode "non-perturbatively", while the traceless mode is treated in the perturbation which is renormalizable and asymptotically free. In the conformal-mode dominant phase, the coupling of the traceless mode vanishes and the world-volume dynamics is described as a four dimensional conformal field theory (CFT_4). We canonically quantize this model on R*S^3 where the dynamical metric fields are expanded using spherical tensor harmonics on S^3. Conformal charges and conformal algebra are constructed. They give strong constraints on physical states. We find that all negative-metric modes are related to positive-metric modes through the charges so that they are not independent physical modes themselves. An infinite number of physical states satisfying the conformal invariance conditions are constructed. In appendix, we construct spherical vector, tensor harmonics on S^3 in the useable form using Wigner D-functions and Clebsch-Gordan coefficients and calculate integrals of their products.