Eur. Phys. J. A (2013) 49: 88
https://doi.org/10.1140/epja/i2013-13088-5

Regular Article - Theoretical Physics

Banks-Casher-type relation for the BCS gap at high density

¹⁹⁹¹¹ Department of Physics, The University of Tokyo, 113-0033, Tokyo, Japan
²⁹⁹¹¹ Department of Physics, University of Regensburg, 93040, Regensburg, Germany
³⁹⁹¹¹ Yukawa Institute for Theoretical Physics, Kyoto University, 606-8502, Kyoto, Japan
⁴⁹⁹¹¹ Maryland Center for Fundamental Physics, Department of Physics, University of Maryland, 20742-4111, College Park, MD, USA

^* e-mail: tilo.wettig@ur.de

Received: 24 December 2012
Revised: 13 April 2013
Accepted: 19 April 2013
Published online: 17 July 2013

Abstract

We derive a new Banks-Casher-type relation which relates the density of complex Dirac eigenvalues at the origin to the BCS gap of quarks at high density and zero temperature. Our relation is applicable to QCD and QCD-like theories without a sign problem, such as two-color QCD and adjoint QCD with baryon chemical potential, and QCD with isospin chemical potential. It provides us with a method to measure the BCS gap through the Dirac spectrum on the lattice.