On decoupled theories in (5+1) dimensions from (F,D1,NS5,D5) supergravity configuration

TL;DR

This paper explores the duality properties of decoupled theories derived from (F,D1,NS5,D5) supergravity configurations in (5+1) dimensions, focusing on how SL(2,Z) transformations relate different noncommutative and string theories.

Contribution

It analyzes the SL(2,Z) duality transformations of various decoupled theories from supergravity, revealing conditions under which theories are self-dual or map to different theories.

Findings

NCOS is related to OD1 by S-duality when axion is rational.

SL(2,Z) maps OD5 to Little String Theory for rational axion.

Irrational axion leads to different NCOS theories under SL(2,Z).

Abstract

It is well-known that ($N$, $M$) 5-branes of type IIB supergravity form a non-threshold bound state with ($N'$, $M'$) strings called the (F, D1, NS5, D5) bound state where the strings lie along one of the spatial directions of the 5-branes (hep-th/9905056). By taking low energy limits in appropriate ways on this supergravity configuration, we obtain the supergravity duals of various decoupled theories in (5+1) dimensions corresponding to noncommutative open string (NCOS) theory, open D-string (OD1) theory and open D5-brane (OD5) theory. We then study the $SL(2, Z)$ transformation properties of these theories. We show that when the asymptotic value of the axion ($\chi_0$) is rational (for which $\chi_0$ can be put to zero), NCOS theory is always related to OD1 theory by strong-weak or S-duality symmetry. We also discuss the self-duality conjecture (hep-th/0006062) of both NCOS and OD1 theories. On the other hand, when $\chi_0$ is irrational, we find that $SL(2, Z)$ duality on NCOS theory gives another NCOS theory with different values of the parameters, but for OD1 theory $SL(2,Z)$ duality always gives an NCOS theory. $SL(2, Z)$ transformation on OD5 theory reveals that it gives rise to Little String Theory (LST) when $\chi_0$ = rational, but it gives another OD5 theory with different values of the parameters when $\chi_0$ is irrational.