TY - JOUR

T1 - Non-critical strings at high energy

AU - Aoki, Kenichiro

AU - D'Hoker, Eric

N1 - Funding Information:
We are happy to thank Yoshihisa Kitazawa and Norisuke Sakai for collaboration in the early stages of this research, and we are grateful to Jean-Loup Gervais for discussions of his work on Liouville theory. We have benefited from conversations with S. Higuchi, S. Nussinov, D.H. Phong and H. Sonoda. We thank the Aspen Center for Physics, and the CERN theory division, for their hospitality while part of this work was being carried out. We acknowledge support from a US/Japan exchange grant INT-9315099 from the National Science Foundation and the Japan Society for the Promotion of Science. E.D. was supported in part by the National Science Foundation, under grants PHY-92-18990 and PHY-95-31023, while K.A. was supported in part by the Grant-in-Aid from the Ministry of Education, Science, Sports and Culture and Keio University.

PY - 1997/4/14

Y1 - 1997/4/14

N2 - 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 electrostatic 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 world-sheet. The electrostatics problem is solved for string tree level in terms of hyper-elliptic integrals and is given explicitly for three-and four-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.

AB - 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 electrostatic 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 world-sheet. The electrostatics problem is solved for string tree level in terms of hyper-elliptic integrals and is given explicitly for three-and four-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.

KW - High-energy scattering

KW - Non-critical strings

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U2 - 10.1016/s0550-3213(97)00034-5

DO - 10.1016/s0550-3213(97)00034-5

M3 - Article

AN - SCOPUS:0031567245

SN - 0550-3213

VL - 490

SP - 40

EP - 74

JO - Nuclear Physics B

JF - Nuclear Physics B

IS - 1-2

ER -