D1-strings in large RR 3-form flux, quantum Nambu geometry and M5-branes in theC-field

Abstract

We consider D1-branes in a RR flux background and show that there is a low energy -large flux double scaling limit where the D1-branes action is dominated by a Chern-Simons-Myers coupling term. As a classical solution to the matrix model, we find a novel quantized geometry characterized by a quantum Nambu 3-bracket. Infinite dimensional representations of the quantum Nambu geometry are constructed which demonstrate that the quantum Nambu geometry is intrinsically different from the ordinary Lie algebra type noncommutative geometry. Matrix models for the IIB string, IIA string and M-theory in the corresponding backgrounds are constructed. A classical solution of a quantum Nambu geometry in the IIA Matrix string theory gives rise to an expansion of the fundamental strings into a system of multiple D4-branes and the fluctuation is found to describe an action for a non-abelian 3-form field strength which is a natural non-abelian generalization of the PST action for a single D4-brane. In view of the recent proposals [1, 2] of the M5-branes theory in terms of the D4-branes, we suggest a natural way to include all the KK modes and propose an action for the the multiple M5-branes in a constant C-field. The worldvolume of the M5-branes in a C-field is found to be described by a quantum Nambu geometry with self-dual parameters. It is intriguing that our action is naturally formulated in terms of a 1-form gauge field living on a six dimensional quantum Nambu geometry.

(2, 0) supersymmetry and the light-cone description of M5-branes

“…More recently it has been suggested that maximally supersymmetric five-dimensional Yang-Mills theory can be used to define the (2, 0) theory in the case of a space-like compactification, including all the Kaluza-Klein modes [11,12]. Other, even more recent, discussions on formulating the dynamics of the (2, 0) theory are [13][14][15][16][17][18][19][20].…”

Non-abelian self-dual strings in six dimensions from four dimensional 1/2-BPS monopoles

“…On the other hand, the inclusion of a constant NSNS B-field in the BPS monopole simple amounts to a constant shift in the Nahm equation. The availability of the generalized Nahm construction may allow one to include a constant C-field in a simple manner and check against the quantum geometry [39,40] obtained from other pictures of the system. We leave this interesting issue for future discussions.…”

Instanton wave and M-wave in multiple M5-branes system

“…In [26], the logic was reversely applied and it was shown how one can deduce the known form of worldvolume noncommutative geometry of D-branes [27][28][29] from a knowledge of how the B-field modifies the Nahm equation; as well as the noncommutative geometry of M5-brane in a large C-field from a knowledge of how the C-field modifies the Basu-Harvey equation [30]. The found noncommutative geometry takes the form of a quantum Nambu geometry [31]. However there has not been success in reformulating this operatorial geometry in terms of more familiar language of a deformed starproduct.…”