Massless fermions in uniform flux background on T2 x R : Vacuum quantum numbers from single-particle filled modes using lattice regulator

The quantum numbers of monopoles in R 3 in the presence of massless fermions have been analyzed using a uniform flux background in S 2 x R coupled to fermions. An analogous study in T 2 x R is performed by studying the discrete symmetries of the Dirac Hamiltonian in the presence of a static uniform field on T 2 with a total flux of Q in the continuum. The degenerate ground states are classified based on their transformation properties under 2 pi rotations of T 2 that leave the background field invariant. We find that the lattice analysis with overlap fermions exactly reproduces the transformation properties of the single- particle zero modes in the continuum. Whereas the transformation properties of the single-particle negative energy states can be studied in the continuum and the lattice, we are also able to study the transformation properties and the particle number (charge) of the many-body ground state on a finite lattice, and we show that the contributions from the fully filled single-particle states cannot be ignored.