Abstract:
We compute superpotentials for quiver gauge theories arising from marginal D-Brane decay on collapsed del Pezzo cycles S in a Calabi-Yau X. This is done using the machinery of A∞ products in the derived category of coherent sheaves of X, which in turn is related to the derived category of S and quiver path algebras. We confirm that the superpotential is what one might have guessed from analyzing the moduli space, i.e., it is linear in the fields corresponding to the Ext2s of the quiver and that each such Ext 2 multiplies a polynomial in Ext1s equal to precisely the relation represented by the Ext2. © SISSA 2006.
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