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Register a new userD2-brane with RR and NSNS fluxes and its dual M-theory origin
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In this paper we obtain the Light Cone Gauge (LCG) Hamiltonian of the D2-brane in the presence of certain Ramond-Ramond and Neveau Schwarz-Neveau Schwarz fields. We analyze two different cases. We impose quantization conditions on the background fields for the cases considered in order to induce background and worldvolume fluxes. We obtain their associated LCG D2-brane actions and Hamiltonians. These Hamiltonians are duals to the ones associated to sector of the M2-brane with fluxes that possess good quantum properties, i.e. discreteness of the supersymmetric spectrum. The M2-branes considered are embedded on a flat target space toroidally compactified $M_9times T^2$ with a constant three form. Imposing a quantization condition it leads to a nonvanishing target-space 2-form flux. Once the dualization process is realized, it implies the existence of a D2-brane in the presence of RR and NSNS field background. The M2-brane theory flux quantization condition implies quantization conditions over the RR and NSNS background fields that act on the target as well as on the worldvolume by means of its pullback. This fact may be considered an indication that it could exists a top-down requeriment introduction of fluxes in String phenomenological constructions. The new D2-branes contains a new worldvolume symplectic gauge field with a symplectic curvature.
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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.
The dissertation consists of two parts. The first presents an account of the effective worldvolume description of $N$ coincident M2-branes ending on an M5-brane in M-theory. It reviews Basu and Harveys recent description of the worldvolume theory of the M2-branes in terms of a Bogomolnyi equation, and its solution via a fuzzy (three-) funnel. Tests of the consistency of this picture are then performed and many of the issues with it are addressed. This is followed by a discussion of how a refinement of the fuzzy three-sphere algebra used can lead to the correct $N^{3/2}$ scaling of degrees of freedom for this system. A reduction of this Basu-Harvey picture to the D1-string picture of the D1-D3 intersection is then performed via constructing a reduction of the fuzzy-three sphere to the fuzzy two-sphere. The second part of the dissertation describes how a holomorphic factorisation argument can be used to demonstrate quantum equivalence of the doubled formalism of string theory with the standard formalism by deriving the partition function, including instanton and oscillator sectors.
A complete analysis of the canonical structure for a gauge fixed PST bosonic five brane action is performed. This canonical formulation is quadratic in the dependence on the antisymmetric field and it has second class constraints. We remove the second class constraints and a master canonical action with only first class constraints is proposed. The nilpotent BRST charge and its BRST invariant effective theory is constructed. The construction does not assume the existence of the inverse of the induced metric. Singular configurations are then physical ones. We obtain the physical Hamiltonian of the theory and analyze its stability properties. Finally, by studying the algebra of diffeomorphisms we find under mild assumptions the general structure for the Hamiltonian constraint for theories invariant under 6 dimensional diffeomorphisms and we give an algebraic characterization of the constraint associated with the bosonic five brane action. We also identify the constraint for the bosonic five brane action upgraded with a cosmological term, it contains a Born-Infeld type term.
We study a new class of inhomogeneous pp-wave solutions with 8 unbroken supersymmetries in D=11 supergravity. The 9 dimensional transverse space is Euclidean and split into 3 and 6 dimensional subspaces. The solutions have non-constant gauge flux, which are described in terms of an arbitrary holomorphic function of the complexified 6 dimensional space. The supermembrane and matrix theory descriptions are also provided and we identify the relevant supersymmetry transformation rules. The action also arises through a dimensional reduction of N=1, D=4 supersymmetric Yang-Mills theory coupled to 3 gauge adjoint and chiral multiplets, whose interactions are determined by the holomorphic function of the supergravity solution now constituting the superpotential.
We study the M-theory five-brane wrapped around the Seiberg-Witten curves for pure classical and exceptional groups given by an integrable system. Generically, the D4-branes arise as cuts that collapse to points after compactifying the eleventh dimension and going to the semiclassical limit, producing brane configurations of NS5- and D4-branes with N=2 gauge theories on the world volume of the four-branes. We study the symmetries of the different curves to see how orientifold planes are related to the involutions needed to obtain the distinguished Prym variety of the curve. This explains the subtleties encountered for the Sp(2n) and SO(2n +1). Using this approach we investigate the curves for exceptional groups, especially G_2 and E_6, and show that unlike for classical groups taking the semiclassical ten dimensional limit does not reduce the cuts to D4-branes. For G_2 we find a genus two quotient curve that contains the Prym and has the right properties to describe the G_2 field theory, but the involutions are far more complicated than the ones for classical groups. To realize them in M-theory instead of an orientifold plane we would need another object, a kind of curved orientifold surface.
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