Exact critical exponents for the antiferromagnetic quantum critical metal near three dimensions

We study the low energy field theory that describes the antiferromagnetic quantum critical metal. Earlier works have approached this problem by extending the spatial dimension from $d = 2$ to $d = 3 - \epsilon$ to gain perturbative control. We extend this work and find that the low energy theory can be studied in a controlled way even when $\epsilon$ is not small due to an emergent control parameter. This allows us to find exact values for the critical exponents of the theory. We describe the limitation of the $\epsilon$ expansion and the strategy of the non-perturbative framework that eventually lead to the solution in $d=2$. \newline S. Sur, S.-S. Lee, \textit{Phys. Rev. B} \textbf{91}, 125136 (2015). \newline P. Lunts, A. Schlief, and S.-S. Lee, arXiv:1701.08218 \newline A. Schlief, P. Lunts, and S.-S. Lee, arXiv:1608.06927 \newline A. Schlief, P. Lunts, and S.-S. Lee, \textit{in preparation}