Folding in quantum groups, fusing defects and transmission matrices

• Grant number: 13/09969-4
• Support Opportunities: Scholarships abroad - Research Internship - Post-doctor
• Start date: October 01, 2013
• End date: September 30, 2014
• Field of knowledge: Physical Sciences and Mathematics - Physics - Elementary Particle Physics and Fields
• Principal Investigator: Abraham Hirsz Zimerman
• Grantee: Alexis Roa Aguirre
• Supervisor: Francis Edward Corrigan
• Host Institution: Instituto de Física Teórica (IFT). Universidade Estadual Paulista (UNESP). Campus de São Paulo. São Paulo , SP, Brazil
• Institution abroad: University of York, England
• Associated to the scholarship: 12/13866-3 - Integrable Defects in Field Theory: Classical Aspects and Quantum Groups, BP.PD

Abstract

The purpose of this research project concerns the application of an algebraic approach to the study of different quantum aspects of the integrable type-II defects in two-dimensional field theories. In particular, we are interested in extending the folding process of the affine Lie algebras for the quantum groups case, and to construct the transmission matrices associated to the integrable defects in non-simply laced affine Toda field theories, especially for b_n and c_n.The algebraic approach has shown to be a powerful tool for constructing transmission matrices because it simplifies the problem to solve a linear intertwining relation between a finite dimensional representation of the relevant Borel subálgebra of the associated quantum groups U_q(G) and a particular infinite dimensional representation expressed in terms of sets of generalized quantum annihilation and creation operators. One motivation of obtaining the transmission matrices is to describe the scattering of the solitons with the type-II defects, which can be considered as a fusing of two type-I defects as suggested for the sine-Gordon case, within these kind of non-simply laced affine Toda models. (AU)