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Register a new userRelation between non trivial M2-branes and D2-branes with fluxes
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We show the relation between three non trivial sectors of M2-brane theory formulated in the LCG connected among them by canonical transformations. These sectors correspond to the supermembrane theory formulated on a $M_9times T^2$ on three different constant three-form backgrounds: M2-brane with constant $C_{-}$, M2-brane with constant $C_{pm}$ and M2-brane with a generic constant $C_3$ denoted as CM2-brane. The first two exhibit a purely discrete supersymmetric spectrum once the central charge condition, or equivalently, the corresponding flux condition has been turned on. The CM2-brane is conjectured to share this spectral property once that fluxes $C_{pm}$ are turned on. As shown in [1] they are duals to three inequivalent sectors of the D2-branes with specific worldvolume and background RR and NSNS quantization conditions on each case.
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We propose a natural generalisation of the BLG multiple M2-brane action to membranes in curved plane wave backgrounds, and verify in two different ways that the action correctly captures the non-trivial space-time geometry. We show that the M2 to D2 reduction of the theory along a non-trivial direction in field space is equivalent to the D2-brane world-volume Yang-Mills theory with a non-trivial (null-time dependent) dilaton in the corresponding IIA background geometry. As another consistency check of this proposal we show that the properties of metric 3-algebras ensure the equivalence of the Rosen coordinate version of this action (time-dependent metric on the space of 3-algebra valued scalar fields, no mass terms) and its Brinkmann counterpart (constant couplings but time-dependent mass terms). We also establish an analogous result for deformed Yang-Mills theories in any dimension which, in particular, demonstrates the equivalence of the Rosen and Brinkmann forms of the plane wave matrix string action.
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