Heriot-Watt Mathematics Report Series
HWM99-16, May 1999

The Wrong Kind of Gravity

W Janke and D Johnston

Abstract

The KPZ formula shows that coupling spin models to 2D quantum gravity dresses the conformal weights to get new critical exponents, where the relation between the original and dressed weights depends only on the central charge of the matter. At the discrete level the coupling to 2D gravity is effected by putting the spin models on annealed ensembles of planar random graphs or their dual triangulations, where the connectivity fluctuates on the same time-scale as the spins.

Since the sole determining factor in the dressing is the central charge, one could contemplate putting a spin model on an ensemble, either quenched or annealed, of 2D gravity graphs with the ``wrong'' central charge. We might then expect to see the critical exponents appropriate to the central charge used in generating the graphs. In such cases the KPZ formula could be interpreted as giving a continuous line of critical exponents which depend on the central charge of the graphs. We note that rational exponents other than the KPZ values can be generated using this procedure for the Ising, tricritical Ising and 3-state Potts models.

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Full text: http://www.ma.hw.ac.uk/~des/wrong2.ps.gz

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