  We measure the evolution of the X-ray luminosity-temperature (L_X-T) relation
since z~1.5 using a sample of 211 serendipitously detected galaxy clusters with
spectroscopic redshifts drawn from the XMM Cluster Survey first data release
(XCS-DR1). This is the first study spanning this redshift range using a single,
large, homogeneous cluster sample. Using an orthogonal regression technique, we
find no evidence for evolution in the slope or intrinsic scatter of the
relation since z~1.5, finding both to be consistent with previous measurements
at z~0.1. However, the normalisation is seen to evolve negatively with respect
to the self-similar expectation: we find E(z)^{-1} L_X = 10^{44.67 +/- 0.09}
(T/5)^{3.04 +/- 0.16} (1+z)^{-1.5 +/- 0.5}, which is within 2 sigma of the zero
evolution case. We see milder, but still negative, evolution with respect to
self-similar when using a bisector regression technique. We compare our results
to numerical simulations, where we fit simulated cluster samples using the same
methods used on the XCS data. Our data favour models in which the majority of
the excess entropy required to explain the slope of the L_X-T relation is
injected at high redshift. Simulations in which AGN feedback is implemented
using prescriptions from current semi-analytic galaxy formation models predict
positive evolution of the normalisation, and differ from our data at more than
5 sigma. This suggests that more efficient feedback at high redshift may be
needed in these models.
