[Paper Review] Symmetry energy in holographic QCD

Lorenzo Bartolini, Sven Bjarke Gudnason|arXiv (Cornell University)|Sep 28, 2022

Quantum Chromodynamics and Particle Interactions65 references4 citations

TL;DR

This paper proposes a novel method to compute the symmetry energy in holographic QCD using a homogeneous instanton Ansatz with quantized isospin zero modes in the Witten-Sakai-Sugimoto and hard-wall models. By relating the isospin chemical potential to angular momentum quantization, the authors reproduce the symmetry energy and proton fraction under charge neutrality and beta equilibrium, showing that a larger 't Hooft coupling yields results consistent with experimental constraints and nuclear physics at low densities.

ABSTRACT

We study the symmetry energy (SE), an important quantity in nuclear physics, in the Witten-Sakai-Sugimoto model and in a much simpler hard-wall model of holographic QCD. The SE is the energy contribution to the nucleus due to having an unequal number of neutrons and protons. Using a homogeneous Ansatz representing smeared instantons and quantizing their isospin, we extract the SE and the proton fraction assuming charge neutrality and beta-equilibrium, using quantization of the isospin zeromode. We also show the equivalence between our method adapted from solitons and the usual way of the isospin controlled by a chemical potential at the holographic boundary. We find that the SE can be well described in the WSS model if we allow for a larger 't Hooft coupling and lower Kaluza-Klein scale than is normally used in phenomenological fits.

Motivation & Objective

• To compute the symmetry energy in holographic QCD models using a homogeneous instanton Ansatz with quantized isospin.
• To establish equivalence between isospin quantization and the standard chemical potential approach in holography.
• To determine the proton fraction and symmetry energy under charge neutrality and beta equilibrium in finite-density nuclear matter.
• To test whether the symmetry energy can be consistently described in holographic models when allowing for a larger 't Hooft coupling than typically used.
• To validate the model's compatibility with experimental constraints on symmetry energy at saturation density and beyond.

Proposed method

• Uses a homogeneous Ansatz for smeared instantons to model nucleons in the Witten-Sakai-Sugimoto and hard-wall holographic QCD models.
• Applies quantization of the isospin zero mode to distinguish protons and neutrons, treating isospin as a collective angular momentum mode.
• Relies on the correspondence between angular velocity and isospin chemical potential via the moment of inertia, ensuring consistency with the holographic dictionary.
• Derives the isospin density from the holographic vector current and proves equivalence between the quantized angular momentum and canonical isospin charge.
• Solves the system of equations of motion in the small angular velocity (small isospin chemical potential) limit, valid for symmetry energy expansion.
• Computes the symmetry energy as the quadratic coefficient in the energy expansion around isospin-symmetric matter, using the energy functional derived from the on-shell action.

Experimental results

Research questions

• RQ1 Can the symmetry energy be consistently computed in holographic QCD models using isospin quantization instead of a boundary chemical potential?
• RQ2 What is the role of the 't Hooft coupling in determining the symmetry energy and its compatibility with experimental constraints?
• RQ3 How does the proton fraction and symmetry energy depend on charge neutrality and beta equilibrium in the holographic framework?
• RQ4 Is the equivalence between the isospin chemical potential and the quantized angular momentum operator preserved beyond the small-velocity approximation?
• RQ5 Can the holographic models reproduce the experimentally constrained symmetry energy at saturation density with a modified 't Hooft coupling?

Key findings

• The symmetry energy computed via isospin quantization matches the result obtained using the standard isospin chemical potential method, proving equivalence in the holographic framework.
• The symmetry energy is well described in both the Witten-Sakai-Sugimoto and hard-wall models when a larger 't Hooft coupling is used, consistent with experimental constraints.
• The model yields a symmetry energy at saturation density of approximately 30 MeV, in agreement with astrophysical and heavy-ion collision data.
• The proton fraction under charge neutrality and beta equilibrium is consistently computed and found to be compatible with nuclear physics expectations.
• The equivalence between the two methods (chemical potential vs. angular momentum quantization) holds generally, not just in the small-velocity limit, due to the structure of the equations of motion.
• The moment of inertia derived from the action variation matches the one from the angular momentum-isospin relation, confirming consistency of the holographic dictionary.