  We explore entanglement negativity, a measure of the distillable entanglement
contained in a quantum state, in relativistic field theories in various
dimensions. We first give a general overview of negativity and its properties
and then explain a well known result relating (logarithmic) negativity of pure
quantum states to the Renyi entropy (at index $1/2$), by exploiting the simple
features of entanglement in thermal states. In particular, we show that the
negativity of the thermofield double state is given by the free energy
difference of the system at temperature $T$ and $2\,T$ respectively. We then
use this result to compute the negativity in the vacuum state of conformal
field theories in various dimensions, utilizing results that have been derived
for free and holographic CFTs in the literature. We also comment upon general
lessons to be learnt about negativity in holographic field theories.
