394 research outputs found
On globally nilpotent differential equations
In a previous work of the authors, a middle convolution operation on the
category of Fuchsian differential systems was introduced. In this note we show
that the middle convolution of Fuchsian systems preserves the property of
global nilpotence. This leads to a globally nilpotent Fuchsian system of rank
two which does not belong to the known classes of globally nilpotent rank two
systems. Moreover, we give a globally nilpotent Fuchsian system of rank seven
whose differential Galois group is isomorphic to the exceptional simple
algebraic group of type $G_2.
Duality Between String Junctions and D-Branes on Del Pezzo Surfaces
We revisit local mirror symmetry associated with del Pezzo surfaces in
Calabi-Yau threefolds in view of five-dimensional N=1 E_N theories compactified
on a circle. The mirror partner of singular Calabi-Yau with a shrinking del
Pezzo four-cycle is described as the affine 7-brane backgrounds probed by a
D3-brane. Evaluating the mirror map and the BPS central charge we relate
junction charges to RR charges of D-branes wrapped on del Pezzo surfaces. This
enables us to determine how the string junctions are mapped to D-branes on del
Pezzo surfaces.Comment: 35 pages, Latex, 1 figure; typos corrected, references update
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