Effect of non-conformal deformation on the gapped quasinormal modes and its holographic implications

The spectral curve of quasinormal modes for a massive real scalar field in the background of a non-conformal black brane geometry has been obtained by utilizing a Frobenius type near-horizon expansion. The gauge/gravity duality maps this to the computation of spectral curve of a scalar operator $\mathcal{O}_{\phi}$ with conformal dimension $\Delta_{\phi}$ for a large-$N$ conformal field theory with irrelevant type non-conformal deformation. In this context, non-conformality has been holographically introduced by using the Einstein-dilaton theory with Liouville type dilaton potential as the bulk theory. It has been observed that the obtained quasinormal modes are characterized by specific gapped dispersion relations. The pole-skipping points have also been computed and classified based upon different dispersion relations satisfied by them. The effect of non-conformality is evident from these results. Analytic form of the mentioned gapped dispersion relation have been obtained in the long wavelength limit by setting the mass of the scalar field to zero. The coefficients appearing in the momenta of the dispersion relation also captures the signature of non-conformal deformation. The radius of convergence of the derivative expansion in the momentum space is then computed from the critical points of the spectral curve. It has been observed that presence of non-conformality increases the domain of applicability for the derivative expansion in momentum space, as it increases the radius of convergence for a given conformal dimension. The comparison between the convergence radii and the absolute momenta corresponding to lowest order pole-skipping points also leads to some interesting findings.