Comparison between holographic deformed AdS and soft wall models for fermions

TL;DR

This paper compares two holographic models for spin 1/2 fermions, analyzing their spectra and wave functions, and finds they are not equivalent but can be related under specific parameter choices.

Contribution

It provides a detailed comparison of dressed soft wall and deformed AdS models for fermions, including analytical solutions, numerical spectra, and their relations.

Findings

The dressed soft wall model yields analytical solutions for fermion modes.

The deformed AdS model requires numerical solutions, but quadratic approximation simplifies analysis.

The two models are not fully equivalent, but can be related through parameter choices.

Abstract

We compare the holographic dressed soft wall and the exponentially deformed AdS models for spin 1/2 fermions. We present the dressed soft wall model and its analytical solutions for the left and right modes, and the corresponding spectra, also including modifications considering hyperfine spin-spin and meson cloud interactions, as well as anomalous dimensions. Then, we discuss the deformed AdS model for spin 1/2 fermions and present their effective Schr\"odinger equations for the left and right modes, for which only numerical solutions are available. Then, we consider a polynomial expansion of the effective potential of the deformed AdS model and show that in the quadratic approximation it leads to exact analytical solutions comparable with the dressed soft wall model and obtain the corresponding spectra for left and right modes. We show a numerical comparison of the mass spectra of spin 1/2 baryons for the dressed soft wall and the deformed AdS models. We present a detailed relation between the quadratic approximation of the deformed AdS and the dressed soft wall models for their spectra, wave functions and comments on the deep inelastic scattering on both models. We find that these two models are {\sl not} equivalent even in the quadratic approximation, but it is possible to relate their left and right modes for particular choices of their parameters.