Correlation functions of the energy momentum tensor on spaces of constant curvature
Sep, 199969 pages
Published in:
- Nucl.Phys.B 571 (2000) 287-357
e-Print:
- hep-th/9909043 [hep-th]
Report number:
- DAMTP-1999-114,
- SWAT-240,
- CERN-TH-99-274,
- DAMTP-99-114
Citations per year
Abstract:
An analysis of one and two point functions of the energy momentum tensor on homogeneous spaces of constant curvature is undertaken. The possibility of proving a -theorem in this framework is discussed, in particular in relation to the coefficients , which appear in the energy momentum tensor trace on general curved backgrounds in four dimensions. Ward identities relating the correlation functions are derived and explicit expressions are obtained for free scalar, spinor field theories in general dimensions and also free vector fields in dimension four. A natural geometric formalism which is independent of any choice of coordinates is used and the role of conformal symmetries on such constant curvature spaces is analysed. The results are shown to be constrained by the operator product expansion. For negative curvature the spectral representation, involving unitary positive energy representations of , for two point functions of vector currents is derived in detail and extended to the energy momentum tensor by analogy. It is demonstrated that, at non coincident points, the two point functions are not related to in any direct fashion and there is no straightforward demonstration obtainable in this framework of irreversibility under renormalisation group flow of any function of the couplings for four dimensional field theories which reduces to at fixed points.Note:
- 72 pages, plain TeX file using harvmac, final revision for publication
- 11.10.-z
- 11.25.Hf
- 11.10.Kk
- 04.62.+v
- tensor: energy-momentum
- correlation function
- Ward identity
- field theory: scalar
- field theory: spinor
- field theory: vector
References(50)
Figures(0)