The one-dimensional Fermi gas of matrix eigenvalues of the Marinari-Parisi model at positive values of the cosmological constant is generalised. The number of matrix eigenvalues (i.e. gas particles) is varied while keeping the effective potential fixed. This model exhibits a transition from a phase whose continuum behaviour is that of c = 1 conformal matter coupled to gravity to the well-known pure gravity phase of the original model. The former phase is characterised by an extremely large Regge slope α′ which scales as β 2 5 causing the scaling regions of the two phases to overlap. In this way a continuous flow from one phase to the other is made possible. This phase transition occurs in the singlet sector of the matrix model. The density of states and the two puncture correlator at non-zero momenta are calculated on the sphere and are found to behave very differently in the two phases, a fact which demonstrates the phase transition. We comment on a possible relation between this transition and large α′ semiclassical expansions in the continuum.
Bibliographical noteFunding Information:
Supported in part by the Henri Gutwirth Fund. 2 Bitnet: PHR74JF@Technion.bitnet * In case of higher multicriticalities k ~ 3, the particles are subject to long-range two-body
ASJC Scopus subject areas
- Nuclear and High Energy Physics