Pseudospectra in Holographic QCD Models

Abstract

We investigate the spectral stability of quasinormal modes in nonconformal holographic QCD models using pseudospectral analysis. We first consider the soft-wall model, focusing on scalar and vector fields, and then extend the analysis to the analytic Improved Holographic QCD (IHQCD) model, where we study tensor glueball fluctuations. In both cases, the equations of motion are formulated as linear eigenvalue problems, allowing the instability of the quasinormal spectrum to small perturbations to be quantified through the pseudospectrum. We find that the spectral stability of the quasinormal modes exhibits a nontrivial dependence on temperature, reflecting the presence of intrinsic dimensionful scales in holographic QCD models. As the temperature increases, the magnitude of the imaginary part of the quasinormal frequencies grows, signaling an increasing decay rate and the progressive loss of coherence of the corresponding hadronic excitations. At sufficiently high temperatures, the quasinormal frequencies approach an approximately linear dependence on temperature, although this regime is reached only after the associated hadronic states have melted. We further compare the pseudospectral instability with the behavior of the corresponding spectral functions. Our results indicate that the growth of pseudospectral instability provides a complementary characterization of the loss of spectral stability and can serve as a useful diagnostic of hadronic dissociation and melting in holographic QCD.