Solving the strongly coupled 2D gravity III: String susceptibility and topological N-point functions

TL;DR

This paper explores two-dimensional gravity in the strong coupling regime, revealing new features and a novel cosmological term that influence string susceptibility and topological N-point functions, diverging from traditional weak-coupling results.

Contribution

It introduces a new cosmological operator in strong coupling 2D gravity and derives its effects on string susceptibility and topological functions, extending previous operator approaches.

Findings

String susceptibility is real, unlike KPZ continuation.

Strongly coupled models are solvable up to sixth order using ward identities.

Gravity and matter quantum numbers are entangled differently than in weak coupling.

Abstract

We spell out the derivation of novel features, put forward earlier in a letter, of two dimensional gravity in the strong coupling regime, at $C_L=7$, 13, 19. Within the operator approach previously developed, they neatly follow from the appearence of a new cosmological term/marginal operator, different from the standard weak-coupling one, that determines the world sheet interaction. The corresponding string susceptibility is obtained and found real contrary to the continuation of the KPZ formula. Strongly coupled (topological like) models--only involving zero-mode degrees of freedom--are solved up to sixth order, using the ward identities which follow from the dependence upon the new cosmological constant. They are technically similar to the weakly coupled ones, which reproduce the matrix model results, but gravity and matter quantum numbers are entangled differently.