Bogomol’nyi-Prasad-Sommerfield solitons in M5-brane worldvolume theory with a constant three-form field

Recently, noncommutative theories have received renewed interest, after it was found that noncommutative theories can be naturally realized in M theory compactified in the presence of constant three-form field background @1# and within string theories as the worldvolume theory of a D-brane with a nonzero constant Neveu-Schwarz ~NS! B field @2,3#. In the case of a D-brane with a constant magnetic NS B field, one can take a decoupling limit of the D-brane worldvolume theory to achieve a noncommutative field theory with space-space noncommutativity. However, in the case of an electric NS B-field background, one cannot take a zero slope limit in such a way that the noncommutativity parameter is nonzero in order to obtain a field theory with space-time noncommutativity since the electric NS B field cannot be scaled to infinity due to its critical value, beyond which the open string parameters are not well defined @4#. It is conjectured @4,5# that nearby a critical electric B field with an appropriate scaling limit, a novel noncritical open string theory, called noncommutative open string ~NCOS! theory, which decouples from closed strings ~and therefore, also gravity! in the bulk, emerges. It is conjectured @6,7# that the strong coupling limit of the NCOS theory in 411 dimensions is the so-called open M-brane ~OM! theory, which is the decoupled ~from gravity! theory of light open M2-brane ending on M5-brane in the constant three-form field background. It would, therefore, be interesting to study worldvolume solitons of the M5-brane with constant three-form field. The solitons of the brane worldvolume theories are interpreted as the intersections of the interesting branes @8#, with the intersection being the source for the charge carried by the worldvolume soliton @9–11#. For example, the M5-brane worldvolume soliton counterpart to the open M2-brane ending on M5-brane is the self-dual string @12#, and the three-brane soliton @13# on the M5-brane worldvolume is interpreted as the three-brane intersection of two intersecting M5-branes. The solitons in the D-brane worldvolume theory, i.e., BI solitons, or bions @14,15,12#, with a constant NS B field, were previously studied, for example, in Refs. @16–21#. In the case