Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2010-07-14
Nucl.Phys.B843:602-637,2011
Physics
High Energy Physics
High Energy Physics - Theory
42 pages, v2: references added, typos corrected
Scientific paper
10.1016/j.nuclphysb.2010.10.014
From the worldsheet perspective, the superpotential on a D-brane wrapping internal cycles of a Calabi-Yau manifold is given as a generating functional for disk correlation functions. On the other hand, from the geometric point of view, D-brane superpotentials are captured by certain chain integrals. In this work, we explicitly show for branes wrapping internal 2-cycles how these two different approaches are related. More specifically, from the worldsheet point of view, D-branes at the Landau-Ginzburg point have a convenient description in terms of matrix factorizations. We use a formula derived by Kapustin and Li to explicitly evaluate disk correlators for families of D2-branes. On the geometry side, we then construct a three-chain whose period gives rise to the effective superpotential and show that the two expressions coincide. Finally, as an explicit example, we choose a particular compact Calabi-Yau hypersurface and compute the effective D2-brane superpotential in different branches of the open moduli space, in both geometric and worldsheet approaches.
Baumgartl Marco
Brunner Ilka
Soroush Masoud
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