  The Sagnac interference mode arises when two interfering counterpropogating
beams traverse a loop, but with their velocities detuned by a small amount
$2u$, with $v_{R/L}=v_F\pm u$. In this paper we perform a perturbative
non-equilibrium calculation of Sagnac interference in single channel wires as
well as armchair nanotube loops. We study the dependence of the Sagnac
conductance oscillations on temperature and interactions. We find that the
Sagnac interference is not destroyed by strong interactions, but becomes weakly
dependent on the velocity detuning $u$. In armchairs nanotubes with typical
interaction strength, $0.25 \leq g \leq 0.5$, we find that the necessary
temperature for observing the interference effect, $T_{SAG}$ is also only
weakly dependent on the interaction, and is enhanced by a factor of 8 relative
to the temperature necessary for observing Fabry-Perot interference in the same
system, $T_{FP}$.
