Duality Twists, Orbifolds, and Fluxes

We investigate compactifications with duality twists and their relation to orbifolds and compactifications with fluxes. Inequivalent compactifications are classified by conjugacy classes of the U-duality group and result in gauged supergravities in lower dimensions with nontrivial Scherk-Schwarz potentials on the moduli space. For certain twists, this mechanism is equivalent to introducing internal fluxes but is more general and can be used to stabilize some of the moduli. We show that the potential has stable minima with zero energy precisely at the fixed points of the twist group. In string theory, when the twist belongs to the T-duality group, the theory at the minimum has an exact CFT description as an orbifold. We also discuss more general twists by nonperturbative U-duality transformations.Comment: 30 pages, harvmac, references and brief comments on gauged supergravity adde

(Twisted) Toroidal Compactification of pp-Waves

The maximally supersymmetric type IIB pp-wave is compactified on spatial circles, with and without an auxiliary rotational twist. All spatial circles of constant radius are identified. Without the twist, an S$^1$ compactification can preserve 24, 20 or 16 supercharges. $T^2$ compactifications can preserve 20, 18 or 16 supercharges; $T^3$ compactifications can preserve 18 or 16 supercharges and higher compactifications preserve 16 supercharges. The worldsheet theory of this background is discussed. The T-dual and decompactified type IIA and M-theoretic solutions which preserve 24 supercharges are given. Some comments are made regarding the AdS parent and the CFT description.Comment: 22 pages REVTeX 4 and AMSLaTeX. v3: References and a paragraph on nine dimensional Killing spinors were added. v4: A few typos corrected and a footnote was modifie

Waves, boosted branes and BPS states in M-theory

Certain type II string non-threshold BPS bound states are shown to be related to non-static backgrounds in 11-dimensional theory. The 11-d counterpart of the bound state of NS-NS and R-R type IIB strings wound around a circle is a pure gravitational wave propagating along a generic cycle of 2-torus. The extremal (q_1,q_2) string with non-vanishing momentum along the circle (or infinitely boosted black string) corresponds in D=11 to a 2-brane wrapped around 2-torus with momentum flow along the (q_1,q_2) cycle. Applying duality transformations to the string-string solution we find type IIA background representing a bound state of 2-brane and 0-brane. Its lift to 11 dimensions is simply a 2-brane finitely boosted in transverse direction. This 11-d solution interpolates between a static 2-brane (zero boost) and a gravitational wave in 11-th dimension (infinite boost). Similar interpretations are given for various bound states involving 5-branes. Relations between transversely boosted M-branes and 1/2 supersymmetric non-threshold bound states 2+0 and 5+0 complement relations between M-branes with momentum in longitudinal direction and 1/4 supersymmetric threshold bound states 1+0 and 4+0. In the second part of the paper we establish the correspondence between the BPS states of type IIB strings on a circle and oscillating states of a fundamental supermembrane wrapped around a 2-torus. We show that the (q_1,q_2) string spectrum is reproduced by the membrane BPS spectrum, determined using a certain limit. This supports the picture suggested by Schwarz.Comment: 26 pages, harvmac (minor corrections; T-duality relation between IIB string-string solution and boosted 0-brane made explicit

pp-waves in 11-dimensions with extra supersymmetry

The Killing spinor equations for pp-wave solutions of eleven dimensional supergravity are analysed and it is shown that there are solutions that preserve 18,20,22 and 24 supersymmetries, in addition to the generic solution preserving 16 supersymmetries and the Kowalski-Glikman solution preserving 32 supersymmetries.Comment: 13 pages. Reference added, typos corrected, new examples of 7-parameter case presente

Magnetic flux tube models in superstring theory

Superstring models describing curved 4-dimensional magnetic flux tube backgrounds are exactly solvable in terms of free fields. We first consider the simplest model of this type (corresponding to `Kaluza-Klein' Melvin background). Its 2d action has a flat but topologically non-trivial 10-dimensional target space (there is a mixing of angular coordinate of the 2-plane with an internal compact coordinate). We demonstrate that this theory has broken supersymmetry but is perturbatively stable if the radius R of the internal coordinate is larger than R_0=\sqrt{2\a'}. In the Green-Schwarz formulation the supersymmetry breaking is a consequence of the presence of a flat but non-trivial connection in the fermionic terms in the action. For R < R_0 and the magnetic field strength parameter q > R/2\a' there appear instabilities corresponding to tachyonic winding states. The torus partition function Z(q,R) is finite for R > R_0 (and vanishes for qR=2n, n=integer). At the special points qR=2n (2n+1) the model is equivalent to the free superstring theory compactified on a circle with periodic (antiperiodic) boundary condition for space-time fermions. Analogous results are obtained for a more general class of static magnetic flux tube geometries including the a=1 Melvin model.Comment: 28 pages, harvmac. Minor changes, final version to appear in NP

Constant magnetic field in closed string theory: an exactly solvable model

We consider a simple model describing a closed bosonic string in a constant magnetic field. Exact conformal invariance demands also the presence of a non-trivial metric and antisymmetric tensor (induced by the magnetic field). The model is invariant under target space duality in a compact Kaluza-Klein direction introduced to couple the magnetic field. Like open string theory in a constant gauge field, or closed string theory on a torus, this model can be straightforwardly quantized and solved with its spectrum of states and partition function explicitly computed. Above some critical value of the magnetic field an infinite number of states become tachyonic, suggesting a presence of phase transition. We also construct heterotic string generalisations of this bosonic model in which the constant magnetic field is embedded either in the Kaluza-Klein or internal gauge group sector.Comment: 39 pages, harvmac (some corrections and addenda; version to appear in Nuclear Physics

Localized Intersections of Non-Extremal p-branes and S-branes

A class of solutions to Supergravity in 10 or 11 dimensions is presented which extends the non-standard or semi-local intersections of Dp-branes to the case of non-extremal p-branes. The type of non-extremal solutions involved in the intersection is free and we provide two examples involving black-branes and/or D-\bar{D} systems. After a rotation among the time coordinate and a relatively transverse radial direction the solutions admit the interpretation of an intersection among D-branes and S-branes. We speculate on the relevance of these configurations both to study time dependent phenomena in the AdS/CFT correspondence as well as to construct cosmological brane-world scenarios within String Theory admitting accelerating expansion of the Universe.Comment: 31 pages, latex file; v2: typos corrected and references adde

T-Duality and Penrose limits of spatially homogeneous and inhomogeneous cosmologies

Penrose limits of inhomogeneous cosmologies admitting two abelian Killing vectors and their abelian T-duals are found in general. The wave profiles of the resulting plane waves are given for particular solutions. Abelian and non-abelian T-duality are used as solution generating techniques. Furthermore, it is found that unlike in the case of abelian T-duality, non-abelian T-duality and taking the Penrose limit are not commutative procedures.Comment: 16 pages, 4 figures. Discussion on non-abelian T-duality expande

Impact of CP phases on the search for sleptons tau and nu_tau

We study the decays of the tau-sleptons (stau_{1,2}) and tau-sneutrino (snu_tau) in the Minimal Supersymmetric Standard Model (MSSM) with complex parameters A_tau, mu and M_1 (U(1) gaugino mass). We show that the effect of the CP phases of these parameters on the branching ratios of stau_{1,2} and snu_tau decays can be quite strong in a large region of the MSSM parameter space. This could have an important impact on the search for stau_{1,2} and snu_tau and the determination of the MSSM parameters at future colliders.Comment: 15 pages, 5 figures, LaTeX2

The necessity of historical inquiry in educational research: the case of Religious Education

publication-status: PublishedThis is an Author's Original Manuscript of an article whose final and definitive form, the Version of Record, has been published in the British Journal of Religious Education, July 2010. Available online at: http://www.tandfonline.com/ or DOI: 10.1080/01416200.2010.498612This article explores the mixed fortunes of historical inquiry as a method in educational studies and exposes evidence for the neglect of this method in religious education research in particular. It argues that historical inquiry, as a counterpart to other research methods, can add depth and range to our understanding of education, including religious education, and can illuminate important longer‐term, broader and philosophical issues. The article also argues that many historical voices have remained silent in the existing historiography of religious education because such historiography is too generalised and too biased towards the development of national policy and curriculum and pedagogical theory. To address this limitation in educational research, this article promotes rigorous historical studies that are more substantially grounded in the appropriate historiographical literature and utilise a wide range of original primary sources. Finally, the article explores a specific example of the way in which a historical approach may be fruitfully applied to a particular contemporary debate concerning the nature and purpose of religious education