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In the first part of the talk, I will discuss the effects of short-range interactions in generalized Weyl semimetals with a monopole charge (n) greater than one. I will show that a strong enough short range interaction may lead to the onset of a translational symmetry breaking axion insulator or a gapless nematic state . To address this problem, I will use a new renormalization group scheme in which the monopole charge is an expansion parameter. Computed critical exponents indicate non-Gaussian nature of the quantum phase transition for any n>1.
The second part of the talk is devoted to the role of the long-range Coulomb interaction in a simple (n=1) Weyl semimetal. In particular, I will show that this interaction leads to a universal enhancement of the zero-temperature optical conductivity that depends solely on the number of Weyl points at the Fermi level . This scaling is a remarkable consequence of an interplay between the quantum-critical nature of an interacting Weyl liquid, marginal irrelevance of the long-range Coulomb interaction and the violation of hyperscaling in three dimensions, and can directly be measured in recently discovered Weyl and Dirac materials.
 B. Roy, P. Goswami, and V. Juricic, Phys. Rev. B 95, 201102 (R) (2017).
 B. Roy and V. Juricic, arXiv; 1707.08564 (to appear in Phys. Rev. B)."