Musings

AdS/Neutron Stars

Quite some time ago, I wrote about an ‘AdS/CFT-inspired’ model for hadron physics. Despite its crudity, it seems to capture surprisingly well the physics of the low-lying mesons ($\pi$, $\rho$, $a_1$).

It also provides a nice laboratory for studying physics at finite baryon density. The 5D vector field, $$\hat{V}=\frac{1}{\sqrt{2N_f}}\mathrm{Tr}(A_L+A_R)$$ couples to baryon number. Choosing boundary conditions $${\hat{V}}_0(z)=A+\frac{1}{2}B{z}^2+\dots$$ corresponds to working at finite chemical potential $${\mu }_b=A{N}_c$$ and baryon number density $$n_b=\frac{1}{24{\pi }^2}B$$

Domokos and Harvey added the 5D Chern-Simons interaction $$S_{\text{CS}}=\frac{N_c}{24{\pi }^2}\int ({\omega }_5(A_L)-{\omega }_5(A_R))$$ (where $d{\omega }_5=\mathrm{Tr}{F}^3$) to the model and found a remarkable effect. At finite baryon density, the 4D effective action contains a term $$S=\int d^{4}x\dots +\mu {ϵ}^{ijk}({\rho }_i^a{\partial }_j{a}_k^a+a_i^a{\partial }_j{\rho }_j^a)+\dots$$ (where $\mu \propto n_b$). Above some critical value of the baryon density, the addition of this term induces a translational- and rotational-invariance breaking condensate of $\rho$ and $a_1$.

At least in this model of Erlich et al, the critical density is in the same ballpark as that of nuclear matter. So, perhaps, this condensate actually forms in neutron stars.

It would be interesting to repeat the calculation in other models, like the Sakai-Sugimoto model, and see how that affects the prediction for the critical density.