The quantum integrability of continuous models and the computation of scattering amplitudes

• Grant number: 11/20242-3
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Effective date (Start): February 01, 2012
• Effective date (End): January 31, 2014
• Field of knowledge: Physical Sciences and Mathematics - Physics - Elementary Particle Physics and Fields
• Principal Investigator: Diego Trancanelli
• Grantee: Gabrielle Weber Martins
• Host Institution: Instituto de Física (IF). Universidade de São Paulo (USP). São Paulo , SP, Brazil

Abstract

We plan to study the quantum integrability of continuous models, which involves the analysis of the regularization process required for dealing with the severe singularities in the operator algebras, as well as the subsequent construction of the physical Hilbert spaces. We will consider these problems in the case of the su(2) Landau-Lifshitz model and the Alday-Arutyunov-Frolov model, which arise as subsectors of string theory on AdS5 × S5 and provide representative examples of the difficulties associated with the quantization of string theory. Quantizing the superstring theory on AdS5 × S5 is a key step in the context of the AdS/CFT correspondence, not only helping us to further understand it, but also to prove it.We would also like to consider the new and efficient methods to compute scattering amplitudes in gauge theories that have been recently developed. Besides the purely theoretical interest, the computation of scattering amplitudes in gauge theories is of crucial phenomenological importance. The relation between these new methods and string theory, integrable models and algebraic geometry is intriguing and should be properly investigated. (AU)

Scientific publications

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

MELIKYAN, A.; WEBER, G.. The r-matrix of the Alday-Arutyunov-Frolov model. Journal of High Energy Physics, n. 11, NOV 2012. (11/20242-3)

MELIKYAN, A.; WEBER, G.. The r-matrix of the Alday-Arutyunov-Frolov model. Journal of High Energy Physics, v. N/A, n. 11, p. 42-pg., 2012-11-01. (11/20242-3)

MELIKYAN, A.; WEBER, G.. Integrable theories and generalized graded Maillet algebras. Journal of Physics A-Mathematical and Theoretical, v. 47, n. 6, FEB 14 2014. (11/20242-3)