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Title of Journal: Commun Math Phys

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Abbravation: Communications in Mathematical Physics

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Springer Berlin Heidelberg

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DOI

10.1016/0378-4320(89)90133-4

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1432-0916

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Duality of 2D Gravity as a Local Fourier Duality

Authors: Martin T Luu
Publish Date: 2015/05/03
Volume: 338, Issue: 1, Pages: 251-265
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Abstract

The p–q duality is a relation between the p q model and the q p model of twodimensional quantum gravity Geometrically this duality corresponds to a relation between the two relevant points of the Sato Grassmannian Kharchev and Marshakov have expressed such a relation in terms of matrix integrals Some explicit formulas for small p and q have been given in the work of FukumaKawaiNakayama Already in the duality between the 2 3 model and the 3 2 model the formulas are long In this work a new approach to p–q duality is given It can be realized in a precise sense as a local Fourier duality of Dmodules This result is obtained as a special case of a local Fourier duality between irregular connections associated to Kac–Schwarz operators Therefore since these operators correspond to Virasoro constraints this allows us to view the p–q duality as a consequence of the duality of the relevant Virasoro constraints

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