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In this paper we prove that Broue's abelian defect group conjecture holds for the Tits group $^2F_4(2)'$. Also we prove that under certain conditions we are able to lift derived equivalences and use this to prove Broue's conjecture for the group $^2F_4(2)$., Comment: 23 pages

In a model-independent formalism of gauge mediation, Meade, Seiberg, and Shih have shown that hidden sector effects are captured by two-point correlation functions of the gauge current superfields and that, generically, many of the characteristic features of gauge mediated SUSY breaking do not survive. We review the general story, particularly the way that the correlators enter the low-energy effective action and give rise to soft-breaking terms. We then specialize to the case where there is a small parameter, F/m^2, where m is the mass scale characterizing the hidden sector, and F is the strength of the SUSY breaking. To leading nontrivial order in this small parameter, we show that many of the classic predictions of gauge mediated SUSY breaking are recovered., Comment: 18 pages, LaTeX, using utarticle class, v2: Section on D-term breaking added. Miscellaneous improvements in the prose

We consider compactifications of type II string theory in which a d-dimensional torus is fibered over a base X. In string theory, the transition functions of this fibration need not be simply diffeomorphisms of T^d but can involve elements of the T-duality group Spin(d,d,Z). We precisely define the notion of a T-fold with NSNS flux. Given such a T-fold, we define the Z_2-graded cohomology theory describing the unquantized RR field strengths and discuss how the data of a T-fold can be interpreted in terms of generalized NSNS fluxes and the twisted differential of Shelton-Taylor-Wecht., Comment: 35 pages, uses utarticle.cls, v2: minor changes and references added

Orientifolds of type II string theory admit a certain set of generalized NS-NS fluxes, including not only the three-form field strength H, but also metric and non-geometric fluxes, which are related to H by T-duality. We describe in general how these fluxes appear as parameters of an effective N=1 supergravity theory in four dimensions, and in particular how certain generalized NS-NS fluxes can act as charges for R-R axions, leading to D-term contributions to the effective scalar potential. We illustrate these phenomena in type IIB with the example of a certain orientifold of T^6/Z_4., Comment: 31+1 pages, uses utarticle.cls; v2: references added

Type IIA toroidal orientifolds offer a promising toolkit for model builders, especially when one includes not only the usual fluxes from NS-NS and R-R field strengths, but also fluxes that are T-dual to the NS-NS three-form flux. These new ingredients are known as metric fluxes and non-geometric fluxes, and can help stabilize moduli or can lead to other new features. In this paper we study two approaches to these constructions, by effective field theory or by toroidal fibers twisted over a toroidal base. Each approach leads us to important observations, in particular the presence of D-terms in the four-dimensional effective potential in some cases, and a more subtle treatment of the quantization of the general NS-NS fluxes. Though our methods are general, we illustrate each approach on the example of an orientifold of T^6/Z_4., Comment: 59 pages, references added

The null-brane space-time provides a simple model of a big crunch/big bang singularity. A non-perturbative definition of M-theory on this space-time was recently provided using matrix theory. We derive the fermion couplings for this matrix model and study the leading quantum effects. These effects include particle production and a time-dependent potential. Our results suggest that as the null-brane develops a big crunch singularity, the usual notion of space-time is replaced by an interacting gluon phase. This gluon phase appears to constitute the end of our conventional picture of space and time., Comment: 31 pages, reference added

The null-brane background is a simple smooth 1/2 BPS solution of string theory. By tuning a parameter, this background develops a big crunch/big bang type singularity. We construct the DLCQ description of this space-time in terms of a Yang-Mills theory on a time-dependent space-time. Our dual Matrix description provides a non-perturbative framework in which the fate of both (null) time, and the string S-matrix can be studied., Comment: 26 pages, LaTeX; references added

We consider the generation of a non-perturbative superpotential in F-theory compactifications with flux. We derive a necessary condition for the generation of such a superpotential in F-theory. For models with a single volume modulus, we show that the volume modulus is never stabilized by either abelian instantons or gaugino condensation. We then comment on how our analysis extends to a larger class of compactifications. From our results, it appears that among large volume string compactifications, metastable de Sitter vacua (should any exist) are non-generic., Comment: 14 pages, comments added

We consider scalar field theory with space and space-time-dependent non-commutativity. In perturbation theory, we find that the structure of the UV/IR mixing is quite different from cases with constant non-commutativity. In particular, UV/IR mixing becomes intertwined in an interesting way with violations of momentum conservation., Comment: 15 pages, LaTeX, References added

We describe the supergravity solutions dual to D6-branes with both time-dependent and time-independent B-fields. These backgrounds generalize the Taub-NUT metric in two key ways: they have asymmetric warp factors and background fluxes. In the time-dependent case, the warping takes a novel form. Kaluza-Klein reduction in these backgrounds is unusual, and we explore some of the new features. In particular, we describe how a localized gauge-field emerges with an analogue of the open string metric and coupling. We also describe a gravitational analogue of the Seiberg-Witten map. This provides a framework in supergravity both for studying non-commutative gauge theories, and for constructing novel warped backgrounds., Comment: 32 pages, LaTeX, references added