String Theory in Interacting String Picture
Abstract
String theory, due to its geometric nature, has a large symmetry group and many constraints associated with it. As a consequence we can not maintain both manifest Lorentz invariance and manifest unitarity in quantum string theory. We follow Mandelstam's manifestly unitary approach choosing light cone gauge. Here Lorentz invariance is a nontrivial problem, since the interaction vertex is given in terms of transverse variables only. We will prove the Lorentz invariance at the off-shell level by constructing the nonlinear generators of the Lorentz algebra for the closed bosonic string and by showing that the algebra closes if the space-time dimension is 26. The corresponding result for the super string is established subsequently using the super lightcone diagram (SLD) formalism. A Lorentz transformation induces a coordinate transformation in the (super)moduli space, hence the integrand of the S-matrix changes by a total derivative in the (super) moduli space under Lorentz transformations. One of the major analytic tools in the unitary approach is the lightcone diagram. It has been established that any punctured Riemann surface can be represented as a lightcone diagram. We consider bosonization on the light cone diagram and show that the global issues, which are the main difficulty in the general fermionic b - c system, can be avoided on the light cone diagram. The coupling to the background curvature is implemented by certain vertex operators sitting at the metric singularities. As an application we derive the relation between the functional determinants of various conformal weights. This result is important to prove the unitarity of the Polyakov string. Conformal field theories (CFTs) play a major role in string theory. Any string vacuum will be a CFT. We apply the above techniques to get the correlation functions of the conformal field theories. For minimal models, due to the degeneracy of the theory, there arises the serious issue of dividing out the null state contribution. We solve this problem by generalizing Felder's result on the torus to higher genus Riemann surfaces using the sewing technique.
- Publication:
-
Ph.D. Thesis
- Pub Date:
- 1989
- Bibcode:
- 1989PhDT.......259S
- Keywords:
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- CONFORMAL FIELD THEORY;
- Physics: Electricity and Magnetism