TY - JOUR

T1 - Duality of 2D Gravity as a Local Fourier Duality

AU - Luu, Martin T.

N1 - Publisher Copyright:
© 2015, Springer-Verlag Berlin Heidelberg.

PY - 2015/8/1

Y1 - 2015/8/1

N2 - The p–q duality is a relation between the (p, q) model and the (q, p) model of two-dimensional 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 Fukuma-Kawai-Nakayama. 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 D-modules. 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.

AB - The p–q duality is a relation between the (p, q) model and the (q, p) model of two-dimensional 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 Fukuma-Kawai-Nakayama. 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 D-modules. 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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U2 - 10.1007/s00220-015-2380-2

DO - 10.1007/s00220-015-2380-2

M3 - Article

AN - SCOPUS:84929071371

SN - 0010-3616

VL - 338

SP - 251

EP - 265

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

IS - 1

ER -