Nonminimal couplings in twodimensional gravity: a quantum investigation
Abstract
We investigate the quantum effects of the nonminimal mattergravity couplings derived by Cangemi and Jackiw in the realm of a specific fermionic theory, namely the abelian Thirring model on a Riemann surface of genus zero and one. The structure and the strength of the new interactions are seen to be highly constrained, when the topology of the underlying manifold is taken into account. As a matter of fact, by requiring to have a welldefined action, we are led both to quantization rules for the coupling constants and to selection rules for the correlation functions. Explicit quantum computations are carried out in genus one (torus). In particular the twopoint function and the chiral condensate are carefully derived for this case. Finally the effective gravitational action, coming from integrating out the fermionic degrees of freedom, is presented. It is different from the standard Liouville one: a new nonlocal functional of the conformal factor arises and the central charge is improved, depending also on the Thirring coupling constant. This last feature opens the possibility of giving a new explicit representation of the minimal series in terms of a fermionic interacting model.
 Publication:

Nuclear Physics B
 Pub Date:
 February 1997
 DOI:
 10.1016/S05503213(97)002095
 arXiv:
 arXiv:hepth/9612025
 Bibcode:
 1997NuPhB.495..400G
 Keywords:

 High Energy Physics  Theory
 EPrint:
 Latex, 41 Pages