Implications of Conformal Invariance for Quantum Field Theories in $d>2$
Abstract
Recently obtained results for two and three point functions for quasiprimary operators in conformally invariant theories in arbitrary dimensions {\absit d} are described. As a consequence the three point function for the energy momentum tensor has three linearly independent forms for general {\absit d} compatible with conformal invariance. The corresponding coefficients may be regarded as possible generalisations of the Virasoro central charge to {\absit d} larger than 2. Ward identities which link two linear combinations of the coefficients to terms appearing in the energy momentum tensor trace anomaly on curved space are discussed. The requirement of positivity for expectation values of the energy density is also shown to lead to positivity conditions which are simple for a particular choice of the three coefficients. Renormalisation group like equations which express the constraints of broken conformal invariance for quantum field theories away from critical points are postulated and applied to two point functions.\hfill\break Talk presented at the XXVII Ahrenshoop International Symposium.
 Publication:

arXiv eprints
 Pub Date:
 December 1993
 arXiv:
 arXiv:hepth/9312176
 Bibcode:
 1993hep.th...12176O
 Keywords:

 High Energy Physics  Theory
 EPrint:
 14pages, Damtp 93/67