Gauss-Bonnet correction to the $R$-current correlator in $\mathcal{N}=4$ theory at strong coupling

We consider higher-curvature corrections to the $R$-current correlator by studying the propagation of a $U(1)$ field in Einstein–Gauss–Bonnet gravity with a negative cosmological constant. We numerically solve the Maxwell equations and plot an $R$-current spectral function with lightlike momenta, which contains pivotal information of thermal photon emission. We also analytically compute the $R$-current correlator in the long-distance limit by using the holographic membrane paradigm. In the high-energy regime, the inelastic scattering between $R$-current and gauge theory plasma is expected to happen, which will reveal the structure of the plasma at strong coupling. It turns out that the Gauss–Bonnet correction effectively rescales all physical quantities considered here by some functions of the Gauss–Bonnet coefficient. In particular, the Gauss–Bonnet terms will enhance or weaken signatures calculated here in accordance with the sign of the Gauss–Bonnet coefficient.

Figure 1

Trace of the spectral function divided by frequency for lightlike momenta, ${\eta }^{\mu \nu }{\chi }_{\mu \nu }(q=\omega )/\omega$, in units of ${\mathcal{N}}^{\prime }=N_c^2{T}^2/2$. The different curves correspond to different strengths of Gauss–Bonnet corrections: $\alpha =0.1$, 0.05, 0, $-0.05$, $-0.1$ (from top to bottom).

Figure 2

Differential photoemission rate $d{\mathrm{\Gamma }}_{\gamma }^T/d\omega$, measured with a weight function ${\mathcal{N}}^{\prime }\frac{e^2}{4\pi }$. As in Fig. 1, different curves indicate different choices of the Gauss–Bonnet coefficient $\alpha$.

Figure 3

Real part of the ac conductivity $\sigma (\omega )$, in units of ${\mathcal{N}}^{\prime }$. Here, different curves are in accordance with the choices of Gauss–Bonnet coefficients $\alpha =0.1$ (blue, dotted), 0 (red, solid), and $-0.1$ (black, dashed), respectively.