Thermal flow in the gravitational O(n) model

We study the massless flow from the critical point (dilute loops) to the low-temperature phase (dense loops) of the O(n) loop gas model when the model is coupled to 2D gravity. The flow is generated by the gravitationally dressed thermal operator Φ1,3 coupled to the renormalized loop tension λ ∼ T − Tc. We find that the susceptibility as a function of the thermal coupling λ and the cosmological constant μ satisfies a simple transcendental equation. Talk delivered at the Fourth International Symposium ”Quantum Theory and Symmetries”, Varna, Bulgaria, 15-21 August 2005 1 [email protected] Associate member of INRNE – BAS, Sofia, Bulgaria