Dual Frobenius manifolds of minimal gravity on disk
Liouville field theory approach to 2-dimensional gravity possesses the duality (b ↔ b−1). The matrix counterpart of minimal gravity ℳ(q, p) (q < p co-prime) is effectively described on Aq−1 Frobenius manifold, which may exhibit a similar duality p ↔ q, and allow a description on Ap−1 Frobenius manifold. We have positive results from the bulk one-point and the bulk-boundary two-point correlations on disk that the dual description of the Frobenius manifold works for the unitary series ℳ(q, q + 1). However, for the Lee-Yang series ℳ(2, 2q + 1) on disk the duality is checked only partially. The main difficulty lies in the absence of a canonical description of trace in the continuum limit.
Keywords2D Gravity Conformal Field Theory Matrix Models
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
- P.H. Ginsparg, M. Goulian, M.R. Plesser and J. Zinn-Justin, (p, q) string actions, Nucl. Phys. B 342 (1990) 539 [INSPIRE].
- M.R. Douglas, Strings in Less Than One-dimension and the Generalized K − D − V Hierarchies, Phys. Lett. B 238 (1990) 176 [INSPIRE].
- V.G. Knizhnik, A.M. Polyakov and A.B. Zamolodchikov, Fractal Structure of 2D Quantum Gravity, Mod. Phys. Lett. A 3 (1988) 819 [INSPIRE].