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Register a new userM-theory on pp-waves with a holomorphic superpotential and its membrane and matrix descriptions
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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.
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The most general parallelizable pp-wave backgrounds which are non-dilatonic solutions in the NS-NS sector of type IIA and IIB string theories are considered. We demonstrate that parallelizable pp-wave backgrounds are necessarily homogeneous plane-waves, and that a large class of homogeneous plane-waves are parallelizable, stating the necessary conditions. Such plane-waves can be classified according to the number of preserved supersymmetries. In type IIA, these include backgrounds preserving 16, 18, 20, 22 and 24 supercharges, while in the IIB case they preserve 16, 20, 24 or 28 supercharges. An intriguing property of parallelizable pp-wave backgrounds is that the bosonic part of these solutions are invariant under T-duality, while the number of supercharges might change under T-duality. Due to their alpha exactness, they provide interesting backgrounds for studying string theory. Quantization of string modes, their compactification and behaviour under T-duality are studied. In addition, we consider BPS $Dp$-branes, and show that these $Dp$-branes can be classified in terms of the locations of their world volumes with respect to the background $H$-field.
Supersymmetrizable theories, such as M(em)branes and associated matrix-models related to Yang-Mills theory, possess r-matrices
We present four infinite series of new quantum theories with super-Poincare symmetry in six dimensions, which are not local quantum field theories. They have string like excitations but the string coupling is of order one. Compactifying these theories on $T^5$ we find a Matrix theory description of M theory on $T^5$ and on $T^5/IZ_2$, which is well defined and is manifestly U-duality invariant.
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.
The behaviour of matrix string theory in the background of a type IIA pp wave at small string coupling, g_s << 1, is determined by the combination M g_s where M is a dimensionless parameter proportional to the strength of the Ramond-Ramond background. For M g_s << 1, the matrix string theory is conventional; only the degrees of freedom in the Cartan subalgebra contribute, and the theory reduces to copies of the perturbative string. For M g_s >> 1, the theory admits degenerate vacua representing fundamental strings blown up into fuzzy spheres with nonzero lightcone momenta. We determine the spectrum of small fluctuations around these vacua. Around such a vacuum all N-squared degrees of freedom are excited with comparable energies. The spectrum of masses has a spacing which is independent of the radius of the fuzzy sphere, in agreement with expected behaviour of continuum giant gravitons. Furthermore, for fuzzy spheres characterized by reducible representations of SU(2) and vanishing Wilson lines, the boundary conditions on the field are characterized by a set of continuous angles which shows that generically the blown up strings do not ``close.
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