Chandrasekharan, S, *Anomaly cancellation in 2+1 dimensions in the presence of a domain wall mass.*,
Physical Review D, vol. 49 no. 4
(February, 1994),
pp. 1980-1987 [10017182] .
**Abstract:**

*A fermion in 2+1 dimensions, with a mass function which
depends on one spatial coordinate and passes through a zero
(a domain wall mass), in the background of an Abelian gauge
field is considered. In this model, originally proposed in a
non-Abelian version by Callan and Harvey, the gauge
variation of the effective gauge action mainly consists of
two terms. One comes from the induced Chern-Simons term and
the other from the chiral fermions, bound to the
(1+1)-dimensional wall, and they are expected to cancel each
other. Though there exist arguments in favor of this, based
on the possible forms of the effective action valid far from
the wall and some facts about theories of chiral fermions in
1+1 dimensions, a complete calculation is lacking. In this
paper we present an explicit calculation of this
cancellation at one loop which is valid even close to the
wall. We show that integrating out the ``massive'' modes of
the theory does produce the Chern-Simons term, as
appreciated previously. In addition, we show that it
generates a term that softens the high energy behavior of
the (1+1)-dimensional effective chiral theory thereby
resolving an ambiguity present in a general
(1+1)-dimensional theory.*