Topological B-model and ${\hat c}=1$ String Theory

TL;DR

This paper explores the topological B-model on a deformed orbifolded conifold, deriving exact solutions and matrix models that connect it to ${ m ilde{c}}=1$ string theory at a specific compactification radius.

Contribution

It introduces a free fermion realization and a Kontsevich-like matrix model for the B-model, confirming its connection to ${ m ilde{c}}=1$ type 0A string theory.

Findings

Derived Ward identities solving the perturbed free energy exactly.

Established a Kontsevich-like matrix model for the theory.

Confirmed the conjectured link to ${ m ilde{c}}=1$ string theory at a specific radius.

Abstract

We study the topological B-model on a deformed $\Z_2$ orbifolded conifold by investigating variation of complex structures via quantum Kodaira-Spencer theories. The fermionic/brane formulation together with systematic utilization of symmetries of the geometry gives rise to a free fermion realization of the amplitudes. We derive Ward identities which solve the perturbed free energy exactly. We also obtain the corresponding Kontsevich-like matrix model. All these confirm the recent conjecture on the connection of the theory with ${\hat c}=1$ type 0A string theory compactified at the radius $R=\sqrt{\alpha'/2}$.