D-Brane Amplitudes in Topological String on Conifold

TL;DR

This paper explores the relationship between two types of topological amplitudes of non-compact D-branes on the conifold, revealing a transformation linking A-model and B-model descriptions and its implications for string background deformation.

Contribution

It establishes a precise integral transformation connecting fermion operator amplitudes in the A-model with determinant operator amplitudes in the B-model for D-branes on the conifold.

Findings

The A-model amplitudes are expressed by the quantum dilogarithm.

The B-model amplitudes are given by the Stieltjes-Wigert polynomial.

The integral transformation encodes the deformation of the closed string background.

Abstract

We study the relation between two kinds of topological amplitudes of non-compact D-branes on conifold. In the A-model, D-branes are represented by fermion operators in the melting crystal picture and the amplitudes are given by the quantum dilogarithm. In the mirror B-model, D-branes correspond to the determinant operator det(x-M) in the Chern-Simons matrix model and the amplitudes are given by the Stieltjes-Wigert polynomial. We show that these two amplitudes are related by a certain integral transformation. We argue that this transformation represents the deformation of closed string background due to the presence of D-branes.