N = 1 Supersymmetry , Deconstruction and Bosonic Gauge Theories

We show how the full holomorphic geometry of local Calabi-Yau threefold compacti-fications with N = 1 supersymmetry can be obtained from matrix models. In particular for the conifold geometry we relate F-terms to the general amplitudes of c = 1 non-critical bosonic string theory, and express them in a quiver or, equivalently, super matrix model. Moreover we relate, by deconstruction, the uncompactified c = 1 theory to the six-dimensional conformal (2, 0) theory. Furthermore, we show how we can use the idea of deconstruction to connect 4 + k dimensional supersymmetric gauge theories to a k-dimensional internal bosonic gauge theory, generalizing the relation between 4d theories and matrix models. Examples of such bosonic systems include unitary matrix models and gauged matrix quantum mechanics, which deconstruct 5-dimensional supersymmetric gauge theories, and Chern-Simons gauge theories, which deconstruct gauge theories living on branes wrapped over cycles in Calabi-Yau threefolds.