### 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 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.

Original language | English |
---|---|

Pages (from-to) | 40-74 |

Number of pages | 35 |

Journal | Nuclear Physics B |

Volume | 490 |

Issue number | 1-2 |

Publication status | Published - 1997 Apr 14 |

### Fingerprint

### Keywords

- High-energy scattering
- Non-critical strings

### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

*Nuclear Physics B*,

*490*(1-2), 40-74.

**Non-critical strings at high energy.** / Aoki, Kenichiro; D'Hoker, Eric.

Research output: Contribution to journal › Article

*Nuclear Physics B*, vol. 490, no. 1-2, pp. 40-74.

}

TY - JOUR

T1 - Non-critical strings at high energy

AU - Aoki, Kenichiro

AU - D'Hoker, Eric

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

UR - http://www.scopus.com/inward/record.url?scp=0031567245&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0031567245&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0031567245

VL - 490

SP - 40

EP - 74

JO - Nuclear Physics B

JF - Nuclear Physics B

SN - 0550-3213

IS - 1-2

ER -