Abstract
We study the string worldsheet description of the background geometry of the exotic $5^2_2$-brane where two isometries are gauged. This is an extension of the gauged linear sigma model (GLSM) for the exotic $5^2_2$-brane with a single gauged isometry. The new GLSM with two gauged isometries has only ${\mathcal N}=(2,2)$ supersymmetry rather than ${\mathcal N}=(4,4)$ 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 $5^2_2$-brane with ${\mathcal N}=(4,4)$ supersymmetry. We also investigate the worldsheet instanton corrections to the background geometry of the exotic $5^2_2$-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.
Highlights
The spacetime metric is single-valued if the spacetime is probed by a point particle
We study the string worldsheet description of the background geometry of the exotic 522-brane where two isometries are gauged
The string worldsheet instanton corrections can be traced by the soliton configurations of the gauge theory, which can be interpreted as the quantum deformations of the Kahler moduli
Summary
We briefly review a construction of the worldsheet sigma model whose target space is the background geometry of the exotic 522-brane [17]. Performing the duality transformations [19] to the GLSM for the H-monopole, and taking the IR limit, we find that the supersymmetric NLSM whose target space is the geometry of the exotic 522-brane. The low energy effective theory can be interpreted as the string worldsheet sigma model whose target space denotes the background geometry of multi-centered H-. We should notice that (2.6) is not the final description of the IR effective theory as the string worldsheet sigma model for the exotic 522-brane of codimension two. It is noticeable that the coordinate fields y2 and θ is democratically involved in the NLSM (2.9) This denotes that the physical coordinates X8 and X9 in the background geometry of the exotic 522-brane. We will mention this procedure more concretely
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