Photon and dilepton production in supersymmetric Yang-Mills plasma

TL;DR

<3-5 sentence high-level summary>The paper computes photon and dilepton emission rates in finite-temperature $SU(N_c)$ $\ N=4$ SYM theory with electromagnetism gauged, at both weak and strong coupling, to draw parallels with QCD-like plasmas. At strong coupling, the current-current spectral function is obtained via AdS/CFT, yielding a finite conductivity $\sigma = e^2 N_c^2 T /(16\pi)$ and a hydrodynamic peak without thermal resonances, while at weak coupling the rates are computed with leading-order and resummed contributions, including $2\leftrightarrow 2$ scatterings and near-collinear bremsstrahlung with LPM effects. Dilepton emission at large invariant mass remains nearly insensitive to coupling, and comparisons with QCD highlight qualitative similarities and notable differences in the photon sector. The results illuminate how electromagnetic observables in a strongly coupled plasma compare to those in QCD, and suggest avenues for applying AdS/CFT insights to heavy-ion phenomenology and to theories with fundamental matter.

Abstract

By weakly gauging one of the U(1) subgroups of the R-symmetry group, N=4 super-Yang-Mills theory can be coupled to electromagnetism, thus allowing a computation of photon production and related phenomena in a QCD-like non-Abelian plasma at both weak and strong coupling. We compute photon and dilepton emission rates from finite temperature N=4 supersymmetric Yang-Mills plasma both perturbatively at weak coupling to leading order, and non-perturbatively at strong coupling using the AdS/CFT duality conjecture. Comparison of the photo-emission spectra for N=4 plasma at weak coupling, N=4 plasma at strong coupling, and QCD at weak coupling reveals several systematic trends which we discuss. We also evaluate the electric conductivity of N=4 plasma in the strong coupling limit, and to leading-log order at weak coupling. Current-current spectral functions in the strongly coupled theory exhibit hydrodynamic peaks at small frequency, but otherwise show no structure which could be interpreted as well-defined thermal resonances in the high-temperature phase.

Figures (15)

• Figure 1: Trace of the spectral function for lightlike momenta divided by frequency, $\eta^{\mu\nu}\chi_{\mu\nu}(w{=}q)/w$, in units of ${{\frac{1}{2}}}N_{\rm c}^2 T^2$, plotted as a function of frequency, with $w\equiv k^0/(2\pi T)$ and $q \equiv |{\bm k}|/(2\pi T)$. At small frequency, $\chi^\mu_{\ \mu}(w{=}q)/w$ approaches a constant limiting value, while at large frequency $\chi^\mu_{\ \mu}(w{=}q)/w$ falls as $w^{-1/3}$. The solid (red) line shows the exact result (\ref{['eq:trace-photons']}) while the dashed lines show the low- and high-frequency asymptotics (\ref{['f_grav']}).
• Figure 2: Transverse and longitudinal spectral functions for time-like momenta, shown in the $(w,q)$ plane. Axes are $q_\pm = w\pm q$; the tip of the light-cone is on the left. The graphs show finite-temperature contributions to $\chi^T\equiv\chi_{xx}+\chi_{yy}$ (left), and $\chi^L\equiv-\chi_{tt}+\chi_{zz}$ (right), plotted in units of $\frac{1}{2}N_{\rm c}^2 T^2$. The subtracted zero-temperature contributions are $\chi^T(w,q)|_{T{=}0} = \pi(w^2{-}q^2)$, and $\chi^L(w,q)|_{T{=}0} = \frac{\pi}{2}(w^2{-}q^2)$. Note that $\chi^L(w,q)$ is zero on the light-cone because $\chi_{tt}(k^0{=}k)=\chi_{zz}(k^0{=}k)$.
• Figure 3: Spectral function trace $\chi^\mu_{\ \mu}(k^0,k)$ (left) and $\chi^\mu_{\ \mu}(k^0,k)/w$ (right), in units of $N_{\rm c}^2 T^2/2$, plotted as a function of $w \equiv k^0/(2\pi T)$. The different curves correspond to differing values of the momentum; from left to right, $q \equiv k/(2\pi T) = 0, 1.0, 1.5$. The dotted black lines show the zero-temperature result.
• Figure 4: Deviation of the spectral function trace $\chi^\mu_{\ \mu}(k^0,k)$ from its zero temperature limit, in units of $N_{\rm c}^2 T^2/2$, as a function of $w \equiv k^0/(2\pi T)$. The different curves correspond to differing values of the momentum; $q \equiv k/(2\pi T) = 0$ (blue), 1.0 (red), 1.5 (green), and 2.0 (brown). The curves at non-zero momentum have cusps on the light cone [at $w=1, 1.5$, and 2, respectively] where the zero-temperature result first turns on in a non-analytic fashion. The dotted line showing the envelope of the cusps is the plot of $\chi^\mu_{\ \mu}$ on the lightcone.
• Figure 5: Transverse (left) and longitudinal (right) spectral functions plotted as a function of $q = k/(2\pi T)$, for several values of the frequency, in units of $N_{\rm c}^2 T^2/2$. The different curves correspond to differing values of the frequency; from left to right, $w \equiv k^0/(2\pi T) = 0.2$ (blue), 0.5 (red), and 1.0 (green). The dashed black lines show the corresponding zero temperature result.