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We report on the first simultaneous high-time resolution X-ray and infrared(IR) observations of a neutron star low mass X-ray binary in its hard state. Weperformed $\approx 2\,$h of simultaneous observations of 4U 1728-34 usingHAWK-I@VLT, XMM-Newton and NuSTAR. The source displayed significant X-ray andIR variability down to sub-second timescales. By measuring thecross-correlation function between the infrared and X-ray lightcurves, wediscovered a significant correlation with an infrared lead of $\approx30-40\,$ms with respect to the X-rays. We analysed the X-ray energy dependenceof the lag, finding a marginal increase towards higher energies. Given the signof the lag, we interpret this as possible evidence of Comptonization fromexternal seed photons. We discuss the origin of the IR seed photons in terms ofcyclo-synchrotron radiation from an extended hot flow. Finally, we alsoobserved the IR counterpart of a type-I X-ray burst, with a delay of$\approx7.2\,$s. Although some additional effects may be at play, by assumingthat this lag is due to light travel time between the central object and thecompanion star, we find that 4U 1728-34 must have an orbital period longer than$3\,$h and an inclination higher than 8$^\circ$.

Sub-second infrared variability from the archetypal accreting neutron star 4U~1728-34