  We establish a double dualization in two-dimensional supersymmetric gauge
theory. We construct a gauged linear sigma model (GLSM) which contains a
complex twisted linear superfield coupled to two sets of Abelian vector
superfields. In the IR regime, the GLSM provides a string sigma model whose
target spaces are a defect NS5-brane, a Kaluza-Klein vortex and an exotic
$5^2_2$-brane. All of them are five-branes of codimension two and are related
by T-duality. This model is a natural extension of the GLSM proposed by Tong
which gives a sigma model for an H-monopole, i.e., a smeared NS5-brane of
codimension three. This is also regarded as an alternative system of the GLSM
for exotic five-branes proposed by the present authors. In this analysis, we
confirm that the T-duality transformation procedure in terms of the complex
twisted linear superfield is applicable to dualize both the real and imaginary
parts of the twisted chiral superfield even at the UV level, beyond the IR
limit. This indicates that the T-duality transformations at finite gauge
couplings can be performed in terms of reducible superfields in the same way as
irreducible (twisted) chiral superfields. Furthermore, we study quantum vortex
corrections to the GLSM at the UV level. In the IR limit, these corrections are
mapped to string worldsheet instanton corrections to the five-branes of
codimension two. The result completely agrees with those in double field theory
analysis.
