C theorem and spectral representation
Aug, 1990
55 pages
Published in:
- Nucl.Phys.B 352 (1991) 616-670
- Published: 1991
Report number:
- RU-90-43,
- UB-ECM-PF-11-90
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Abstract: (Elsevier)
Zamolodchikov's c -theorem is reformulated by using the spectral representation for the two-point function of the stress tensor. This approach makes explicit the unitarity constraints on the field theory and implements a nice physical picture of the renormalization group flow. An attempt is made to generalize the theorem above two space-time dimensions. There are two candidate c -functions, the spectral densities for spin-zero and spin-two intermediate states. The latter one is ruled out by means of examples. The spin-zero density can satisfy a generalized c -theorem, if the corresponding “central charge” is well defined at the fixed points. A meaningful charge is obtained by defining the theory on curved hyperbolic space. However, its limit to flat space needs some assumptions which seem to hold for free theories only. As a by-product, the trace anomaly in four dimensions is related to the spectral densities.- field theory: conformal
- dimension: 2-4
- renormalization group: c-function
- tensor: energy-momentum
- two-point function
- spectral representation
- space-time
- anomaly: conformal
- unitarity
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