D-string fluid in conifold: I. Topological gauge model

TL;DR

This paper models D-string fluids in a deformed conifold with a strong B-field, deriving a topological gauge theory that connects quantum Hall systems and string theory, revealing new insights into their quantum dynamics.

Contribution

It introduces a holomorphic non-commutative gauge invariant action for D-string fluids in conifold, linking quantum Hall systems with topological string theory in a novel way.

Findings

Derived a gauge theory describing D-string fluid dynamics in conifold.

Connected quantum Hall systems on real manifolds to conifold sub-manifolds.

Discussed quantum behavior of string fluids in the context of topological string theory.

Abstract

Motivated by similarities between quantum Hall systems \`{a} la Susskind and aspects of topological string theory on conifold as well as results obtained in hep-th/0601020, we study the dynamics of D-string fluids running in deformed conifold in presence of a strong and constant RR background B-field. We first introduce the basis of D-string system in fluid approximation and then derive the holomorphic non commutative gauge invariant field action describing its dynamics in conifold. This study may be also viewed as embedding Susskind description for Laughlin liquid in type IIB string theory. FQH systems on real manifolds $R\times S^{2}$ and $S^{3}$ are shown to be recovered by restricting conifold to its Lagrangian sub-manifolds. Aspects of quantum behaviour of the string fluid are discussed.