  We show that the $\gamma$-ray pulsar observables, i.e., their total
$\gamma$-ray luminosity, $L_{\gamma}$, spectral cut-off energy, $\epsilon_{\rm
cut}$, stellar surface magnetic field, $B_{\star}$, and spin-down power
$\dot{\mathcal{E}}$, obey a relation of the form $L_{\gamma}=f(\epsilon_{\rm
cut},B_{\star},\dot{\mathcal{E}})$, which represents a 3D plane in their 4D
log-space. Fitting the data of 88 pulsars of the second Fermi pulsar catalog,
we show this relation to be $L_{\gamma}\propto \epsilon_{\rm cut}^{1.18\pm
0.24}B_{\star}^{0.17\pm 0.05}\dot{\mathcal{E}}^{0.41\pm 0.08}$, a pulsar
fundamental plane (FP). We show that the observed FP is remarkably close to the
theoretical relation $L_{\gamma}\propto \epsilon_{\rm
cut}^{4/3}B_{\star}^{1/6}\dot{\mathcal{E}}^{5/12}$ obtained assuming that the
pulsar $\gamma$-ray emission is due to curvature radiation by particles
accelerated at the pulsar equatorial current sheet just outside the light
cylinder. Interestingly, the FP seems incompatible with emission by synchrotron
radiation. The corresponding scatter about the FP is $\sim 0.35$dex and can
only partly be explained by the observational errors while the rest is probably
due to the variation of the inclination and observer angles. We predict also
that $\epsilon_{\rm cut}\propto \dot{\mathcal{E}}^{7/16}$ toward low
$\dot{\mathcal{E}}$ for both young and millisecond pulsars implying that the
observed death-line of $\gamma$-ray pulsars is due to $\epsilon_{\rm cut}$
dropping below the Fermi-band. Our results provide a comprehensive
interpretation of the observations of $\gamma$-ray pulsars, setting requirement
for successful theoretical modeling.
