A transformation of variables which relates soliton theory to string theory is discussed. Scattering amplitudes of bosonic strings with arbitrary momenta off fermionic (compactified bosonic) loops are shown to satisfy Hirota's bilinear difference equation, which is equivalent to infinite family of Kadomtsev-Petviashvili type of soliton equations.
The String AmplitudesThe string theory is a theory of elementary particles in which the fundamental object is not a point particle but a string. The supersymmetric version of this theory[1] is a unique candidate of consIstent field theory which unifies all fundamental forces in nature including gravity. In this talk we are going to show how this theory is connected with the soliton theory. Particularly we will show that integrands of string amplitudes are characterized by a soliton equation. [2] Let us begin with a brief introduction of the string theory. First we consider a point particle of momentum ki which propagates and emitts same kind of particles of momenta k~, k~, ... , kj. at time T = T2, T3, ... , TN, successively. The scattering amplitude of this process is given bywhere H = tp2 and Ikl > is the momentum eigenstateIf the interaction is point like V( k) is of the form g constant.In the first quantized level only zl' and pi' are quantized quantities satisfying [zl',pV] = igl'v.Using (4), we can rewrite (1) as where
Theory of l-reduction of KP hierarchy is investigated from a view point of conformal field theory. Twisted conformal field theory emerges naturally in the discussion. Possible application of this kind of connection between hierarchy and CFT is suggested.
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