Explicit solution for p - q duality in two-dimensional quantum gravity

By using Sato's infinite dimensional Grassmannian theory of the KP hierarchy, we study the global structure of the theory space of 2D quantum gravity coupled to various minimal conformal fields labeled by a pair of integers (p, q). After giving a rigorous proof of the equivalence of Douglas's equation and the Schwinger-Dyson equation (W-constrainton a τ function), we establish thep-q duality of the (p, q) quantum gravity at Green's function level. As an application, we discuss the metamorphosis of operators under unitarity-preserving renormalization group flows.

quantum gravity
dimension: 2
duality
Dyson-Schwinger equation
Kadomtsev-Petviashvili equation
renormalization group
field theory: conformal

References(18)

Figures(0)

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