Dissipation of the String Embedding Dimension in the Singlet Sector of a Matrix Model at Large $\alpha^\prime$

TL;DR

This paper studies a phase transition in a matrix model's singlet sector, showing how the continuum behavior shifts from a $c=1$ conformal matter phase to pure gravity, with implications for large $eta$ regimes.

Contribution

It introduces a generalized matrix model with variable eigenvalue number, revealing a continuous phase transition characterized by differing density of states and correlators.

Findings

Identification of a phase transition between $c=1$ and pure gravity phases.

Calculation of density of states and correlators showing distinct behaviors in each phase.

Overlap of scaling regions enabling a continuous flow between phases.

Abstract

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 character- ised by an extremely large Regge slope $\alpha^\prime$ which scales as $\beta^{2/5}$ causing the scaling regions of the two phases to overlap. In this way a continuous flow from one phase to the other is made poss- ible. 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 differ- ently in the two phases,a fact which demonstrates the phase transition. We comment on a possible relation between this transition and large \alpha^\prime$ semiclassical expansions in the continuum.