Abstract
The adjoint 2-dimensional QCD
with the gauge group SU(N)/Z_NSU(N)/ZN
admits topologically nontrivial gauge field configurations associated
with nontrivial \pi_1[SU(N)/Z_N] = Z_Nπ1[SU(N)/ZN]=ZN.
The topological sectors are labelled by an integer
k=0,\ldots, N-1k=0,…,N−1.
However, in contrast to QED_2QED2
and QCD_4QCD4,
this topology is not associated with an integral invariant like the
magnetic flux or Pontryagin index. These instantons may admit fermion
zero modes, but there is always an equal number of left-handed and
right-handed modes, so that the Atiyah-Singer theorem, which determines
in other cases the number of the modes, does not apply. The mod. 2 argument [1]
suggests that, for a generic gauge field configuration, there is either
a single doublet of such zero modes or no modes whatsoever. However, the
known solution of the Dirac problem for a wide class of gauge field
configurations indicates the presence of k(N-k)
zero mode doublets in the topological sector
k. In this note, we demonstrate in an explicit way that these modes are not
robust under a generic enough deformation of the gauge background and
confirm thereby the conjecture of Ref. [1]. The implications for the
physics of this theory (screening vs. confinement issue) are briefly
discussed.
Subject
General Physics and Astronomy
Cited by
6 articles.
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