Conformal Algebra and Physical States in a NonCritical 3Brane on R × S^{3}
Abstract
A worldvolume model of a noncritical 3brane is quantized in a strong coupling phase in which fluctuations of the conformal mode become dominant. This phase, called the conformalmode dominant phase, is realized at very high energies far beyond the Planck mass scale. We separately treat the conformal mode and the traceless mode and quantize the conformal mode nonperturbatively, while the traceless mode is treated in a perturbative method that is renormalizable and asymptotically free. In the conformalmode dominant phase, the coupling of the traceless mode vanishes, and the worldvolume dynamics are described by a fourdimensional conformal field theory (CFT_{4}). We canonically quantize this model on R × S ^{3}, where the dynamical fields are expanded in spherical tensor harmonics on S ^{3}, which include both positivemetric and negativemetric modes. Conformal charges and a conformal algebra are constructed. They yield strong constraints on physical states. We find that all negativemetric modes are related to positivemetric modes through the charges, and thus negativemetric modes are themselves not independent physical modes. Physical states satisfying the conformal invariance conditions are given by particular combinations of positivemetric and negativemetric modes. An infinite number of such physical states are constructed. In the Appendices, we construct spherical vector and tensor harmonics on S ^{3} in practical forms using the Wigner D functions and the ClebschGordan coefficients and calculate the integrals of three and four products of these harmonics over S ^{3}.
 Publication:

Progress of Theoretical Physics
 Pub Date:
 December 2003
 DOI:
 10.1143/PTP.110.1169
 arXiv:
 arXiv:hepth/0307008
 Bibcode:
 2003PThPh.110.1169H
 Keywords:

 High Energy Physics  Theory
 EPrint:
 53 pages, published version