Description:
<jats:title>A<jats:sc>bstract</jats:sc>
</jats:title>
<jats:p>It was known that the U(<jats:italic>N</jats:italic> )<jats:sup>4</jats:sup> super Chern-Simons matrix model describing the worldvolume theory of D3-branes with two NS5-branes and two (1<jats:italic>, k</jats:italic>)5-branes in IIB brane configuration (dual to M2-branes after taking the T-duality and the M-theory lift) corresponds to the <jats:italic>D</jats:italic>
<jats:sub>5</jats:sub> quantum curve. For deformations of these two objects, on one hand the super Chern-Simons matrix model has three degrees of freedom (of relative rank defor- mations interpreted as fractional branes in brane configurations), while on the other hand the <jats:italic>D</jats:italic>
<jats:sub>5</jats:sub> curve has five degrees of freedom (characterized by point configurations of asymp- totic values). To identify the three-dimensional parameter space of brane configurations in the five-dimensional space of point configurations, we propose the necessity to cut the compact T-duality circle (or the circular quiver diagram) open, which is similar to the idea of “fixing a reference frame” or “fixing a local chart”. Since the parameter space of curves enjoys the <jats:italic>D</jats:italic>
<jats:sub>5</jats:sub> Weyl group beautifully, we are naturally led to conjecture that M2-branes are not only deformed by fractional branes but more obscure geometrical backgrounds.</jats:p>