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

Date of publication: 2. 11. 2022
Mathematical physics seminar
Thursday, 3.11.2022, at 14:15 in Kuščer seminar. More information on the seminar webpage https://chaos.fmf.uni-lj.si

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.

  • Timotej Lemut, Faculty for Mathematics and Physics, University of Ljubljana