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Abstract

Solitons provide a window into regimes of integrable quantum field theories not directly accessible by the perturbative degrees of freedom. In this thesis we develop techniques for the semiclassical analysis of string solitons on two of the AdS3 backgrounds with maximal amount of supersymmetry, AdS3×S3×T4 and AdS3×S3×S3×S1. As the main application of these techniques, we explicitly construct the four and two fermion zero modes for the mixed-flux AdS3 generalization of the Hofman-Maldacena giant magnon, and show how to match the semiclassically quantized zero modes to the odd generators of the centrally extended psu(1|1)4 and su(1|1)2 off shell residual symmetry algebras. We further obtain explicit formulas for the eight bosonic and eight fermionic fluctuations around the mixed-flux magnon, confirming that the semiclassical quantization of these fluctuations leads to a vanishing one-loop correction to the magnon energy, as expected from symmetry based arguments. Lastly, we consider the fermion zero modes for an AdS3 × R string soliton and a simple scattering state of two magnons, confirming the relation between fermion zero modes and representations of the residual algebras.

Publication Type:	Thesis (Doctoral)
Subjects:	Q Science > QA Mathematics
Departments:	Doctoral Theses School of Science & Technology > School of Science & Technology Doctoral Theses School of Science & Technology > Mathematics

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