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

Sašo Grozdanov*, Timotej Lemut

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract / Description of output

Assuming only a known dispersion relation of a single mode in the spectrum of a meromorphic two-point function (in the complex frequency plane at fixed wavevector) 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.
Original languageEnglish
Article number131
Pages (from-to)1-44
Number of pages44
JournalJournal of High Energy Physics
Volume2023
Issue number2
DOIs
Publication statusPublished - 13 Feb 2023

Keywords / Materials (for Non-textual outputs)

  • Effective Field Theories
  • Gauge-Gravity Correspondence
  • Holography and Hydrodynamics

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