Reconstruction of spectra and an algorithm based on the theorems of Darboux and Puiseux

Septiembre 19, 2022
De 11:30am hasta 12:30pm

Aula Gris 3

Specialist level
Sašo Grozdanov
University of Edinburgh / University of Ljubljana

Aula Gris 3


Assuming only a known dispersion relation of a single mode in the spectrum of a two-point function in some quantum field theory, we investigate when and how the reconstruction of the complete spectrum of physical excitations is possible. In particular, we develop a constructive algorithm based on the theorems of Darboux and Puiseux that allows for such a reconstruction of all modes connected by level-crossings. For concreteness, we focus on theories in which the known mode is a gapless excitation described by the hydrodynamic gradient expansion, known at least to some (preferably high) order. We first apply the algorithm to a simple algebraic example and then to the transverse momentum excitations in the holographic theory that describes a stack of M2 branes and includes momentum diffusion as its gapless excitation.