Class Problem!: Why the Inconsistent Application of Rule 23\u27s Class Certification Requirements During Overbreadth Analysis is a Threat to Litigant Certainty

Rule 23 of the Federal Rules of Civil Procedure is home to the class action device. It is well-documented that this rule significantly impacts our legal system. As a result, the need for its effective utilization has been apparent since its introduction. Despite this, federal courts have inconsistently applied the rule during their analyses of overbroad class definitions at the class certification stage. Consequently, parties involved in such litigation have been exposed to unnecessary costs and the potential for forum shopping. Nonetheless, this judicial inconsistency has gone largely unrecognized because it does not implicate the results of class certification. Hence, courts here must first recognize the general need for uniformity before a precise standard for overbreadth analysis may be chosen. Only then, this Note argues, may the aforementioned detrimental consequences be avoided

Supersymmetry for Gauged Double Field Theory and Generalised Scherk-Schwarz Reductions

Previous constructions of supersymmetry for double field theory have relied on the so called strong constraint. In this paper, the strong constraint is relaxed and the theory is shown to possess supersymmetry once the generalised Scherk-Schwarz reduction is imposed. The equivalence between the generalised Scherk-Schwarz reduced theory and the gauged double field theory is then examined in detail for the supersymmetric theory. As a byproduct we write the generalised Killing spinor equations for the supersymmetric double field theory.Comment: 29 pages, LateX, v2 typos fixed and some improved discussion, version as in Journa

The string partition function in Hull's doubled formalism

T-duality is one of the essential elements of string theory. Recently, Hull has developed a formalism where the dimension of the target space is doubled so as to make T-duality manifest. This is then supplemented with a constraint equation that allows the connection to the usual string sigma model. This paper analyses the partition function of the doubled formalism by interpreting the constraint equation as that of a chiral scalar and then using holomorphic factorisation techniques to determine the partition function. We find there is quantum equivalence to the ordinary string once the topological interaction term is included.Comment: 16 pages, latex, v2 typos corrected, v3 some comments adde

Branes are Waves and Monopoles

In a recent paper it was shown that fundamental strings are null waves in Double Field Theory. Similarly, membranes are waves in exceptional extended geometry. Here the story is continued by showing how various branes are Kaluza-Klein monopoles of these higher dimensional theories. Examining the specific case of the E7 exceptional extended geometry, we see that all branes are both waves and monopoles. Along the way we discuss the O(d; d) transformation of localized brane solutions not associated to an isometry and how true T-duality emerges in Double Field Theory when the background possesses isometries.Comment: 32 pages, Latex, v2, typos correcte

Duality Symmetric String and M-Theory

We review recent developments in duality symmetric string theory. We begin with the world sheet doubled formalism which describes strings in an extended space time with extra coordinates conjugate to winding modes. This formalism is T-duality symmetric and can accommodate non-geometric T-fold backgrounds which are beyond the scope of Riemannian geometry. Vanishing of the conformal anomaly of this theory can be interpreted as a set of spacetime equations for the background fields. These equations follow from an action principle that has been dubbed Double Field Theory (DFT). We review the aspects of generalised geometry relevant for DFT. We outline recent extensions of DFT and explain how, by relaxing the so-called strong constraint with a Scherk Schwarz ansatz, one can obtain backgrounds that simultaneously depend on both the regular and T-dual coordinates. This provides a purely geometric higher dimensional origin to gauged supergravities that arise from non-geometric compactification. We then turn to M-theory and describe recent progress in formulating an E_{n(n)} U-duality covariant description of the dynamics. We describe how spacetime may be extended to accommodate coordinates conjugate to brane wrapping modes and the construction of generalised metrics in this extend space that unite the bosonic fields of supergravity into a single object. We review the action principles for these theories and their novel gauge symmetries. We also describe how a Scherk Schwarz reduction can be applied in the M-theory context and the resulting relationship to the embedding tensor formulation of maximal gauged supergravities.Comment: Review article. 122 pages. V2 Published Version in Physics Report

In Cold Blood: The Vietnam War in Textbooks

An analysis of textbook coverage of the Vietnam War