Non-critical strings at high energy

Abstract

We consider scattering amplitudes in non-critical string theory of $N$ external states in the limit where the energy of all external states is large compared to the string tension. We argue that the amplitudes are naturally complex analytic in the matter central charge $c$ and we propose to define the amplitudes for arbitrary value of $c$ by analytic continuation. We show that the high energy limit is dominated by a saddle point that can be mapped onto an equilibrium electro-static energy configuration of an assembly of $N$ pointlike (Minkowskian) charges, together with a density of charges arising from the Liouville field. We argue that the Liouville charges accumulate on segments of curves, and produce quadratic branch cuts on the worldsheet. The electro-statics problem is solved for string tree level in terms of hyper-elliptic integrals and is given explicitly for 3- and 4-point functions. We show that the high energy limit should behave in a string-like fashion with exponential dependence on the energy scale for generic values of $c$.

34pp, 8 figures, harvmac, epsf (TeXing problems fixed)

References in corpus (6)

• On the Liouville three-point function
• Anomalies, Dualities, and Topology of D=6 N=1 Superstring Vacua
• Infrared Regularization of Superstring Theory and the One-Loop Calculation of Coupling Constants
• The Box Graph In Superstring Theory
• Self Avoiding Surfaces in the 3D Ising Model
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Cited by in corpus (6)

• Scattering Equations: Real Solutions and Particles on a Line
• Seiberg-Witten Theory of Rank Two Gauge Groups and Hypergeometric Series
• Scattering and Strebel graphs
• Evaluation of Periods via Fibrations in Seiberg-Witten Theories and in Type-II String
• D-Instantons in Non-Critical Open String Theory
• High energy scattering of non-critical strings