(NS5,D5,D3) bound state, OD3, OD5 limits and SL(2,Z) duality

TL;DR

This paper explores the properties of (NS5,D5,D3) bound states in type IIB supergravity, analyzing their decoupling limits, the effects of SL(2,Z) duality, and the relationships between OD3, OD5, NCYM, and little string theories.

Contribution

It generalizes (NS5,D5,D3) bound states to include a non-zero axion and studies their duality properties and decoupling limits, revealing self-duality and connections to NCYM and little string theories.

Findings

OD3-theory is self-dual under SL(2,Z)

Special SL(2,Z) transformations relate OD3 to NCYM

OD5-theory is S-dual to little string theory when axion is rational

Abstract

We generalize the non-threshold bound state in type IIB supergravity of the form (NS5, D5, D3) constructed by the present authors (in hep-th/0011236) to non-zero asymptotic value of the axion $(\chi_0$). We identify the decoupling limits corresponding to both the open D3-brane theory and open D5-brane theory for this supergravity solution as expected. However, we do not find any non-commutative Yang-Mills theory (NCYM) limit for this solution in the presence of NS5 branes. We then study the $SL(2, Z)$ duality symmetry of type IIB theory for both OD3-limit and OD5-limit. We find that for OD3 theory, a generic $SL(2, Z)$ duality always gives another OD3-theory irrespective of the value of $\chi_0$ being rational or not. This indicates that OD3-theory is self-dual. But, under a special set of $SL(2, Z)$ transformations for which $\chi_0$ is rational OD3-theory goes over to a 5+1 dimensional NCYM theory and these two theories in this case are related to each other by strong-weak duality symmetry. On the other hand, for OD5-theory, a generic $SL(2, Z)$ duality gives another OD5-theory if $\chi_0$ is irrational, but when $\chi_0$ is rational it gives the little string theory limit indicating that OD5-theory is S-dual to the type IIB little string theory.