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

It is well-known that ($N$, $M$) 5-branes of type IIB supergravity form anon-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 the5-branes (hep-th/9905056). By taking low energy limits in appropriate ways onthis supergravity configuration, we obtain the supergravity duals of variousdecoupled theories in (5+1) dimensions corresponding to noncommutative openstring (NCOS) theory, open D-string (OD1) theory and open D5-brane (OD5)theory. We then study the $SL(2, Z)$ transformation properties of thesetheories. We show that when the asymptotic value of the axion ($\chi_0$) isrational (for which $\chi_0$ can be put to zero), NCOS theory is always relatedto OD1 theory by strong-weak or S-duality symmetry. We also discuss theself-duality conjecture (hep-th/0006062) of both NCOS and OD1 theories. On theother hand, when $\chi_0$ is irrational, we find that $SL(2, Z)$ duality onNCOS 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 differentvalues of the parameters when $\chi_0$ is irrational.Comment: 28 pages, LaTeX, no figures, v4: a para in the introduction added to emphasize the motivation and a conclusion added, published versio