D1/D5 System with B-field, Noncommutative Geometry and the CFT of the Higgs Branch

TL;DR

This work analyzes the D1/D5 system in the presence of a NS $B$-field, presenting an explicit ${1\over 4}$-BPS supergravity solution with no D3 sources and a true bound state, while showing a Liouville-type binding potential for a separated D1-brane. It develops a 2D $\mathcal{N}=4$ gauge theory with FI terms identified with the self-dual part of $B$, demonstrating a Higgs-phase bound state with moduli space $M= T^*\mathbb{CP}^{Q_1Q_5-1}$ and connecting the IR SCFT to the resolved symmetric product $\mathrm{Sym}_{Q_1Q_5}(\tilde{T}^4)$. The paper also proposes a link between the D1/D5 system with $B$-field and noncommutative YM on $T^4$, arguing that the moduli space of self-dual NC connections provides a conformal sigma-model target and that the marginal deformations correspond to the NS-NS and RR moduli. Overall, it elucidates how $B$-field induced noncommutativity resolves Higgs-branch singularities and enables bound-state formation, with implications for holography and the structure of Higgs-branch SCFTs in D1/D5 setups.

Abstract

The D1/D5 system is considered in the presence of the NS B field. An explicit supergravity solution in the asymptotically flat and near horizon limits is presented. Explicit mass formulae are presented in both cases. This solution has no D3 source branes and represents a true bound state of the D1/D5 system. We study the motion of a separated D1-brane in the background geometry described above and reproduce the Liouville potential that binds the D1 brane. A gauge theory analysis is also presented in the presence of Fayet-Iliopoulos (FI) parameters which can be identified with the self-dual part of the NS B field. In the case of a single D5-brane and an arbitrary number of D1 branes we can demonstrate the existence of a bound state in the Higgs branch. We also point out the connection of the SCFT on the resolved Sym$_{Q_1Q_5}(\tilde T^4)$ with recent developments in non-commutative Yang-Mills theory.