  Active matter consumes energy from the environment and transforms it into
mechanical work. Notable examples from biology include cell division, bacterial
swarms, and muscle contraction. In this work, we investigate the nature of
active matter systems using the powerful effective field theory toolbox. This
allows us to construct the most general theory without ambiguity up to a given
order in the derivative expansion. Our primary focus is active nematics --
liquid crystal systems that spontaneously break rotational but not
translational symmetry -- in two spatial dimensions. (Such spontaneous symmetry
breaking is allowed if the nematic is embedded in a higher dimensional space.)
While we focus on this one particular class of physical system, the tools
developed here can in principle be applied to any active matter system. Our
theories give unambiguous predictions for the relationship between fluctuations
and equations of motion in the presence of activity, generalizing the standard
fluctuation-dissipation relations characteristic of passive systems.
