Isometry of AdS2 And The c=1 Matrix Model

TL;DR

This paper investigates the SL(2,R) symmetry in the c=1 matrix models and demonstrates how it relates to the geometry of AdS_2, revealing topological properties that influence D0-brane charge quantization in string theory.

Contribution

It establishes the equivalence between the c=1 matrix model in the linear dilaton background and the AdS_2 matrix model, highlighting the role of SL(2,R) symmetry and topological features.

Findings

SL(2,R) symmetry acts as an isometry in the AdS_2 matrix model.

Topological properties of AdS_2 quantize D0-brane charges.

Matrix model captures the relation between Poincare patch and global coordinates of AdS_2.

Abstract

Implications of the SL(2,R) symmetry of the c = 1 matrix models are explored. Based on the work of de Alfaro, Fubini and Furlan, we note that when the Fermi sea is drained, the matrix model for 2 dimensional string theory in the linear dilaton background is equivalent to the matrix model of AdS_2 recently proposed by Strominger, for which SL(2,R) is an isometry. Utilizing its Lie algebra, we find that a topological property of AdS_2 is responsible for quantizing D0-brane charges in type 0A theory. We also show that the matrix model faithfully reflects the relation between the Poincare patch and global coordinates of AdS_2.