Universal fermionic spectral functions from string theory

TL;DR

This work provides the first top-down holographic calculation of a fermionic response for a strongly coupled $d=3$ theory with an explicit string/M-theory dual, focusing on the universal spin-$\tfrac{3}{2}$ supercurrent sector in $d=3$, $N=2$ SCFTs. By solving the linearised gravitino equations in the $AdS_4$-RN background and using a KK truncation to minimal $N=2$ gauged supergravity in $D=4$, the authors compute the retarded supercurrent correlator, reducing it to a single function $t_{11}(\omega,k)$ and its spectral function $A(\omega,k)=\mathrm{Im}\,t_{11}(\omega,k)$. The key findings are the absence of a Fermi surface at finite density, the presence of a phonino pole at $(\tilde{\omega},k)=(0,0)$, and a low-frequency depletion with a power-law scaling controlled by an IR $AdS_2$ region, $A(\omega,k)\propto \omega^{2\nu_k}$ with $\nu_k=\sqrt{\frac{7}{12}+\frac{k^2}{2\mu^2}}$, indicating a locally quantum critical phase rather than a Mott-like gap. These results highlight the robustness of universal holographic features in top-down constructions and their link to IR criticality in strongly coupled systems.

Abstract

We carry out the first holographic calculation of a fermionic response function for a strongly coupled $d=3$ system with an explicit D=10 or D=11 supergravity dual. By considering the supersymmetry current, we obtain a universal result applicable to all d=3 N=2 SCFTs with such duals. Surprisingly, the spectral function does not exhibit a Fermi surface, despite the fact that the system is at finite charge density. We show that it has a phonino pole and at low frequencies there is a depletion of spectral weight with a power-law scaling which is governed by a locally quantum critical point.

Figures (1)

• Figure 1: The spectral function $A(\omega,k)$ The top panel is for $T/\mu=0.44$ and momenta $k\ell\in (0.1,1.1)$, with larger values of $k$ in darker shades of grey. The bottom panel is for $T=0$ and $k\ell\in (1.2,2.1)$.