On Loop Equations In KdV Exactly Solvable String Theory

Details On Loop Equations In KdV Exactly Solvable String Theory On Loop Equations In KdV Exactly Solvable String Theory

1991-11-30

arxiv.org/abs/hep-th/9111064v1

Mod.Phys.Lett.A7:1263-1272,1992

Physics

High Energy Physics

High Energy Physics - Theory

13 pages

Scientific paper

10.1142/S0217732392003748

The non-perturbative behaviour of macroscopic loop amplitudes in the exactly solvable string theories based on the KdV hierarchies is considered. Loop equations are presented for the real non-perturbative solutions living on the spectral half-line, allowed by the most general string equation $[\tilde{P},Q]=Q$, where $\tilde{P}$ generates scale transformations. In general the end of the half-line (the `wall') is a non-perturbative parameter whose r\^ole is that of boundary cosmological constant. The properties are compared with the perturbative behaviour and solutions of $[P,Q]=1$. Detailed arguments are given for the $(2,2m-1)$ models while generalisation to the other $(p,q)$ minimal models and $c=1$ is briefly addressed.

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