A modified c = 1 matrix model with new critical behavior

Abstract

By introducing a ∫ dt g (Tr Φ 2( t)) 2 term into the action of the c = 1 matrix model of two-dimensional quantum gravity, we find a new critical behavior for random surfaces. The planar limit of the path integral generates multiple spherical “bubbles” which touch one another at single points. At a special value of g, the sum over connected surfaces behaves as Δ 2log Δ, where Δ is the cosmological constant (the sum over surfaces of area A goes as A −3). For comparison, in the conventional c = 1 model the sum over planar surfaces behaves as Δ 2 log Δ .