1994/09/12 by Igor R. Klebanov, Akikazu Hashimoto · 2 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Quantum many-body systems #Theoretical and Computational Physics #hep-th
paper · pdf · doi:10.1016/0550-3213(94)00518-j
published as Nucl.Phys. B434 (1995) 264-282 · 26 pages, PUPT-1498
arxiv created 1994/09/12 · openalex publication_date 1995/01/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present a non-perturbative solution of large N matrix models modified by terms of the form g(\TrΦ4)2, which add microscopic wormholes to the random surface geometry. For g<gt the sum over surfaces is in the same universality class as the g=0 theory, and the string susceptibility exponent is reproduced by the conventional Liouville interaction ∼ eα+ ϕ. For g=gt we find a different universality class, and the string susceptibility exponent agrees for any genus with Liouville theory where the interaction term is dressed by the other branch, eα- ϕ. This allows us to define a double-scaling limit of the g=gt theory. We also consider matrix models modified by terms of the form g O2, where O is a scaling operator. A fine-tuning of g produces a change in this operator's gravitational dimension which is, again, in accord with the change in the branch of the Liouville dressing.