Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Non-Fermi liquid Superconductivity: Eliashberg versus the
  Renormalization Group   We address the problem of superconductivity for non-Fermi liquids using two
commonly adopted, yet apparently distinct methods: 1) the renormalization group
(RG) and 2) Eliashberg theory. The extent to which both methods yield
consistent solutions for the low energy behavior of quantum metals has remained
unclear. We show that the perturbative RG beta function for the 4-Fermi
coupling can be explicitly derived from the linearized Eliashberg equations,
under the assumption that quantum corrections are approximately local across
energy scales. We apply our analysis to the test case of phonon mediated
superconductivity and show the consistency of both the Eliashberg and RG
treatments. We next study superconductivity near a class of quantum critical
points and find a transition between superconductivity and a "naked" metallic
quantum critical point with finite, critical BCS couplings. We speculate on the
applications of our theory to the phenomenology of unconventional metals.

11
The categories of this paper are: hep-lat
32
The categories of this paper are: atom-ph
36
The categories of this paper are: cmp-lg
9
The categories of this paper are: nlin
13
The categories of this paper are: quant-ph
21
The categories of this paper are: adap-org
30
The categories of this paper are: q-alg
8
The categories of this paper are: hep-ex
34
The categories of this paper are: chem-ph
10
The categories of this paper are: q-bio
28
The categories of this paper are: alg-geom
17
The categories of this paper are: q-fin
2
The categories of this paper are: math
5
The categories of this paper are: gr-qc
24
The categories of this paper are: dg-ga
29
The categories of this paper are: funct-an