The study of string theory in a curved background plays a fundamental role in high energy physics. However, only in a few cases this study can be performed exactly. The most simple observable, the free string spectrum, requires the quantization of a non linear sigma model. In the same cases it is possible to prove that, at the classical level, the equations of motion of such models are integrable, namely they are exactly solvable by virtue of hidden symmetries. In this case, it is possible to quantize the theory using the Zamolodchikov and Zamolodchikov approach, and so by the factorization of the $S$matrix. In this thesis we will study the non linear sigma models linked to string theories formulated on curved backgrounds and we will compute, perturbatively, the scattering matrix on the worldsheet in lightcone gauge. We will focus on models, which in the literature were proposed to be integrable and we will verify that the $S$matrix satisfies the YangBaxter equation, which is a necessary condition for the integrability.
Scattering matrices on the string worldsheet
Bocconcello, Marco
2020/2021
Abstract
The study of string theory in a curved background plays a fundamental role in high energy physics. However, only in a few cases this study can be performed exactly. The most simple observable, the free string spectrum, requires the quantization of a non linear sigma model. In the same cases it is possible to prove that, at the classical level, the equations of motion of such models are integrable, namely they are exactly solvable by virtue of hidden symmetries. In this case, it is possible to quantize the theory using the Zamolodchikov and Zamolodchikov approach, and so by the factorization of the $S$matrix. In this thesis we will study the non linear sigma models linked to string theories formulated on curved backgrounds and we will compute, perturbatively, the scattering matrix on the worldsheet in lightcone gauge. We will focus on models, which in the literature were proposed to be integrable and we will verify that the $S$matrix satisfies the YangBaxter equation, which is a necessary condition for the integrability.File  Dimensione  Formato  

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https://hdl.handle.net/20.500.12608/22968