Modern Methods for Scattering Amplitudes in Field (Gauge Theories and Gravity) and String Theory

• Grant number: 19/07286-3
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date until: October 01, 2019
• End date until: December 31, 2021
• Field of knowledge: Physical Sciences and Mathematics - Physics - Elementary Particle Physics and Fields
• Principal Investigator: Nathan Jacob Berkovits
• Grantee: Diego Medrano Jiménez
• Host Institution: Instituto de Física Teórica (IFT). Universidade Estadual Paulista (UNESP). Campus de São Paulo. São Paulo , SP, Brazil
• Associated research grant: 16/01343-7 - ICTP South American Institute for Fundamental Research: a regional center for theoretical physics, AP.ESP

Abstract

My research is taking place in general terms inside the field of 'Scattering Amplitudes'. In particular, I have been focusing lately on the study of gauge theories and gravity in the context of the Cachazo-He-Yuan (CHY) formalism. In this set-up, the Scattering Equations (SE) turn out to be a crucial object independently of the theory of interest, although a complete analytic description for their solutions is still missing. Therefore, it would be really useful to dig into the structure of those solutions, unveiling a possible hierarchy and correspondence to the different helicity sectors. Sudakov variables seem to be a useful parametrization for that, besides providing the formalism with a novel geometrical interpretation of the corresponding punctures. Moreover, these variables allow for a natural way to study the factorizability properties of both gauge and gravity amplitudes in Multi-Regge-Kinematics (MRK).Apart from that, I have been studying the connection between the soft behavior and asymptotic symmetries of a theory. Much progress has been made for QED and perturbative gravity in order to construct a well-defined IR-finite S-matrix, whereas non-abelian gauge theories lack a systematic way to procced for the moment. Finding the appropiate dressing states and definition of the asymptotic charges would allow to solve the problem 'a la Faddeev & Kulish'. This is something I am working on in collaboration with some colleagues at Trinity College of Dublin.As a possible continuation of my thesis, 'planar radiation zeros' are a feature of scattering amplitudes that may allow to extract information about the asymptotic behavior of a particular theory when characterized inside some projective space of the kinematic variables. Already studied in scalar-Yang-Mills and Einstein-Hilbert gravity for MHV tree-level amplitudes, it would be interesting to generalize the obtained results at loop-level and for the remaining N^(k)MHV helicity sectors.Finally, I will start working on the field of 'Scattering Amplitudes' from the point of view of 'integrability', where the S-matrix turns out to be one of the most fundamental objects in quantum integrable theories.