Giandomenico Palumbo, Roberto Catenacci, Annalisa Marzuoli
Dirac fermions have a central role in high energy physics but it is well known that they emerge also as quasiparticles in several condensed matter systems supporting topological order. We present a general method for deriving the topological effective actions of (3+1) massless Dirac fermions living on general backgrounds and coupled with vector and axial-vector gauge fields. Our strategy consists in connecting the determinants of Dirac operators with the corresponding analytical indices through the zeta-function regularization and then in applying the Atiyah-Singer index theorem which computes the analytical index in topological terms. A well-defined extension of this method to the non Hermitian cases is proposed. Quantum systems supporting relativistic fermions can thus be topologically classified on the basis of their response to the presence of (external or emergent) gauge fields through the corresponding topological effective field theories.
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http://arxiv.org/abs/1303.6468
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