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