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Pairing induced superconductivity in holography

We study pairing induced superconductivity in large $N$ strongly coupled systems at finite density using holography. In the weakly coupled dual gravitational theory the mechanism is conventional BCS theory. An IR hard wall cut-off is included to ensure that we can controllably address the dynamics of a single confined Fermi surface. We address in detail the interplay between the scalar order parameter field and fermion pairing. Adding an explicitly dynamical scalar operator with the same quantum numbers as the fermion-pair, the theory experiences a BCS/BEC crossover controlled by the relative scaling dimensions. We find the novel result that this BCS/BEC crossover exposes resonances in the canonical expectation value of the scalar operator. This occurs not only when the scaling dimension is degenerate with the Cooper pair, but also with that of higher derivative paired operators. We speculate that a proper definition of the order parameter which takes mixing with these operators into account stays finite nevertheless.