Chern-Simons action for zero-mode supporting gauge fields in three   dimensions
  Recent results on zero modes of the Abelian Dirac operator in three dimensions support to some degree the conjecture that the Chern-Simons action admits only certain quantized values for gauge fields that lead to zero modes of the corresponding Dirac operator. Here we show that this conjecture is wrong by constructing an explicit counter-example. 
C. Adam, B. Muratori, C. Nash