Critical fields on the M5-brane and noncommutative open strings

Abstract

The M5-brane is investigated near critical field-strength. We show that this limit on the M5-brane reduces to the noncommutative open string limit on the D4-brane. The reduction on a two-torus leads to both the noncommutative open string limit and the noncommutative Yang-Mills limit on the D3-brane. The decoupled noncommutative five-brane is identified with the strong coupling limit of the noncommutative open string theory on the D4-brane and S-duality on the noncommutative D3-brane is identified with a modular transformation on the five-brane. We argue that the open membrane metric defines a finite length scale on the worldvolume of the M5-brane in the decoupling limit. This length scale can be associated to the effective length scale of an open membrane.

IIA/B, wound and wrapped

“…When bound to the fivebranes, the membranes appear as N units of H 01(10) -flux, where H is the (self-dual) three-form field strength on the fivebrane worldvolume. This field (or equivalently, the bulk A 01(10) gauge field) becomes critical in the Wound/DLCQ limit, yielding a framework known as OM theory [6,31]. Reasoning like before, we see that the possibility of setting K = 0 means that it is possible to define an 'OM' limit of M-theory even if there are no M5-branes present, to obtain a theory which contains M2-branes with strictly positive wrapping number on the x 1 -x 10 torus.…”

“…Through diverse dualities, we are driven to define various Wrapped p-brane theories which are the natural generalizations of the Wound string idea: these theories are obtained as limits of string/M-theory with (at least) p compact directions, and all objects in them must carry strictly positive p-brane wrapping number on this p-torus. Just like the various NCOS theories are different classes of states in a single Wound string theory, the recently discovered OM theory [6,31] (see also [32]) and ODp theories [33,6] are specific classes of states in a broader framework: as it will be shown in Section 5, OM theory is the Wrapped M2-brane theory in the presence of M5-branes which wrap the 'Wrapped' directions, whereas each of the ODp theories is understood to be the Wrapped Dp-brane theory in the presence of NS5-branes. Section 5 includes a discussion of the relation of these theories to the known S-duals for NCOS theories [5,6,34] and the theories encountered in Seiberg's derivation of the Matrix description for DLCQ IIA/M-theory [29,30].…”

Non-relativistic non-BPS Dp-brane

“…In 4 General properties of the tachyon effective actions were also discussed in [24,25,26,27,28]. 5 We work in units (2πα ′ ) = 1. Note also that p is odd in type IIA theory while p is even in type IIB theory.…”

“…Non-relativistic string theory was determined some years ago in the context of the study of the string theories in the background with the electric field [1,2,3,4,5,6]. Then it was soon recognised in [7,8,9] that non-relativistic string theory is consistent sector of the string theory with the manifest world-sheet conformal field theory description that has appropriate Galilean symmetry.…”

BV Quantization of Topological Open Membranes

“…Similarly, we expect that the 3-form has a similar effect in M-theory, or viewing the 3-form as the field strength of the 2-form, deforming noncommutative geometry. This model can therefore shed some light on the role of the mysterious generalized theta parameter that is central in decoupling limits of open membranes [3,12,13,14,15,16].…”