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We calculate the topological string partition function to all genus on theconifold, in the presence of branes. We demonstrate that the partitionfunctions for different brane backgrounds (smoothly connected along a quantumcorrected moduli space) can be interpreted as the same wave function indifferent polarizations. This behavior has a natural interpretation in theChern-Simons target space description of the topological theory. Our detailedanalysis however indicates that non-perturbatively, a modification of realChern-Simons theory is required to capture the correct target space theory ofthe topological string.  We perform our calculations in the framework of a free fermion representationof the open topological string, demonstrating that this framework extendsbeyond the simple C^3 geometry. The notion of a fermionic brane creationoperator arises in this setting, and we study to what extent the wave functionproperties of the partition function can be extended to this operator.Comment: 43 pages; v2: small clarification, typos corrected, reference added;  v3: exposition improved, typos corrected; v4: discussion of phase space  improved, subsection on non-perturbative terms added, version published in  JHE

The wave function behavior of the open topological string partition function on the conifold