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Register a new userString Theory on Parallelizable PP-Waves
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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.
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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.
Recently, Berenstein et al. have proposed a duality between a sector of N=4 super-Yang-Mills theory with large R-charge J, and string theory in a pp-wave background. In the limit considered, the effective t Hooft coupling has been argued to be lambda=g_{YM}^2 N/J^2=1/(mu p^+ alpha)^2. We study Yang-Mills theory at small lambda (large mu) with a view to reproducing string interactions. We demonstrate that the effective genus counting parameter of the Yang-Mills theory is g_2^2=J^4/N^2=(4 pi g_s)^2 (mu p^+ alpha)^4, the effective two-dimensional Newton constant for strings propagating on the pp-wave background. We identify g_2 sqrt{lambda} as the effective coupling between a wide class of excited string states on the pp-wave background. We compute the anomalous dimensions of BMN operators at first order in g_2^2 and lambda and interpret our result as the genus one mass renormalization of the corresponding string state. We postulate a relation between the three-string vertex function and the gauge theory three-point function and compare our proposal to string field theory. We utilize this proposal, together with quantum mechanical perturbation theory, to recompute the genus one energy shift of string states, and find precise agreement with our earlier computation.
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.
In string models with brane supersymmetry breaking exponential potentials emerge at (closed-string) tree level but are not accompanied by tachyons. Potentials of this type have long been a source of embarrassment in flat space, but can have interesting implications for Cosmology. For instance, in ten dimensions the logarithmic slope |V/V| lies precisely at a critical value where the Lucchin--Matarrese attractor disappears while the scalar field is emph{forced} to climb up the potential when it emerges from the Big Bang. This type of behavior is in principle perturbative in the string coupling, persists after compactification, could have trapped scalar fields inside potential wells as a result of the cosmological evolution and could have also injected the inflationary phase of our Universe.
We discuss a universality property of any covariant field theory in space-time expanded around pp-wave backgrounds. According to this property the space-time lagrangian density evaluated on a restricted set of field configurations, called universal s
ector, turns out to be same around all the pp-waves, even off-shell, with same transverse space and same profiles for the background scalars. In this paper we restrict our discussion to tensorial fields only. In the context of bosonic string theory we consider on-shell pp-waves and argue that universality requires the existence of a universal sector of world-sheet operators whose correlation functions are insensitive to the pp-wave nature of the metric and the background gauge flux. Such results can also be reproduced using the world-sheet conformal field theory. We also study such pp-waves in non-polynomial closed string field theory (CSFT). In particular, we argue that for an off-shell pp-wave ansatz with flat transverse space and dilaton independent of transverse coordinates the field redefinition relating the low energy effective field theory and CSFT with all the massive modes integrated out is at most quadratic in fields. Because of this simplification it is expected that the off-shell pp-waves can be identified on the two sides. Furthermore, given the massless pp-wave field configurations, an iterative method for computing the higher massive modes using the CSFT equations of motion has been discussed. All our bosonic string theory analyses can be generalised to the common Neveu-Schwarz sector of superstrings.
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