Title:
Quantum curves and Brane transitions

Abstract:
The ABJM theory is the worldvolume theory of N multiple M2-branes. In IIB string theory,
the ABJM theory is described by the brane configuration of an NS5-brane, a (1,k)5-brane
and N multiple D3-branes between their 5-branes. By the localization technique, this theory
reduces to the matrix model (called ABJM matrix model) and the grand partition function of
this matrix model is written by the quantum curve associated to the local F_0. There are
generalizations written by the quantum curves associated to the del Pezzo curves whose
parameters are transformed by the exceptional Weyl groups. We discuss the brane
transitions from the viewpoint of the curves. When we identify the Weyl group as the brane
transitions, we not only reproduce the Hanany-Witten transitions under the identification,
but also find new transitions and propose the local rule of brane transition for them.