A scenario for the c > 1 barrier in non-critical bosonic strings
Abstract
The c ⩽ 1 and c > 1 matrix models are analyzed within the large- N renormalization group taking into account touching (or branching) interactions. The c < 1 modified matrix model with string exponent overlineγ > 0 is naturally associated with an unstable fixed point, separating the Liouville phase ( γ < 0) from the branched polymer phase ( γ = {1}/{2}). It is argued that at c = 1 this multicritical fixed point and the Liouville fixed point coalesce, and that both fixed points disappear for c > 1. In this picture, the critical behavior of c > 1 matrix models is generically that of branched polymers, but only within a scaling region which is exponentially small when c → 1. Large crossover effects occur for c - 1 small enough, with a c ∼ 1 pseudo-scaling which explains the numerical results.
- Publication:
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Nuclear Physics B
- Pub Date:
- February 1997
- DOI:
- 10.1016/S0550-3213(96)00716-X
- arXiv:
- arXiv:hep-th/9610037
- Bibcode:
- 1997NuPhB.487..633D
- Keywords:
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- High Energy Physics - Theory
- E-Print:
- 20 pages, REVTeX3.0 + epsf, 10 figures. 1 reference added. To appear in Nucl. Phys. B