The Hausdorff dimension of surfaces in two-dimensional quantum gravity coupled to Ising minimal matter

Mark J. Bowick, Varghese John, Gudmar Thorleifsson

Research output: Contribution to journalArticle

11 Scopus citations

Abstract

Within the framework of string field theory the intrinsic Hausdorff dimension dH of the ensemble of surfaces in two-dimensional quantum gravity has recently been claimed to be 2m for the class of unitary minimal models (p = m+1, q = m). This contradicts recent results from numerical simulations, which consistently find dH ≈ 4 in the cases m = 2, 3, 5 and ∞. The string field calculations rely on identifying the scaling behavior of geodesic distance and area with respect to a common length scale l. This length scale is introduced by formulating the models on a disk with fixed boundary length l. In this paper we study the relationship between the mean area and the boundary length for pure gravity and the Ising model coupled to gravity. We discuss how this relationship is modified by relevant perturbations in the Ising model. We discuss how this leads to a modified value for the Hausdorff dimension.

Original languageEnglish (US)
Pages (from-to)197-202
Number of pages6
JournalPhysics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics
Volume403
Issue number3-4
DOIs
StatePublished - Jun 26 1997

ASJC Scopus subject areas

  • Nuclear and High Energy Physics

Fingerprint Dive into the research topics of 'The Hausdorff dimension of surfaces in two-dimensional quantum gravity coupled to Ising minimal matter'. Together they form a unique fingerprint.

  • Cite this