Worldsheet description of exotic five-brane with two gauged isometries

We study the string worldsheet description of the background geometry of the exotic -brane where two isometries are gauged. This is an extension of the gauged linear sigma model (GLSM) for the exotic -brane with a single gauged isometry. The new GLSM with two gauged isometries has only = (2, 2) supersymmetry rather than = (4, 4) supersymmetry of the original GLSM. This is caused by a conflict between two different SU(2)_R associated with the two gauge symmetries. However, if we take a certain limit, we can find the genuine string sigma model of the background geometry of the exotic -brane with = (4, 4) supersymmetry. We also investigate the worldsheet instanton corrections to the background geometry of the exotic -brane. The worldsheet instanton corrections to the string sigma model can be traced in terms of the two gauge fields in the new GLSM. This new GLSM gives rise to a different feature of the quantum corrections from the one in the GLSM with the single gauged isometry.