Four-Dimensional Twisted Group Lattices

Four-dimensional twisted group lattices are used as models for space-time structure. Compared to other attempts at space-time deformation, they have two main advantages: They have a physical interpretation and there is no difficulty in putting field theories on these structures. We present and discuss ordinary and gauge theories on twisted group lattices. We solve the free field theory case by finding all the irreducible representations. The non-abelian gauge theory on the two-dimensional twisted group lattice is also solved. On twisted group lattices, continuous space-time translational and rotational symmetries are replaced by discrete counterparts. We discuss these symmetries in detail. Four-dimensional twisted group lattices can also be used as models for non-trivial discrete compactifactions of certain ten-dimensional spaces.Comment: 31 pages (no figures) in Late

Truncations of the D9-brane action and type-I strings

The low-energy effective action of type-I superstring theory in ten dimensions is obtained performing a truncation of type-IIB supergravity in a background where D9-branes are present. The open sector corresponds to the first order in the low-energy expansion of the D9-brane action in a type-I background. In hep-th/9901055 it was shown that there are two ways of performing a type-I truncation of the D9-brane action, and the resulting truncated action was obtained in a flat background. We extend this result to a generic type-I background, and argue that the two different truncations are in correspondence with the open sector of the low-energy effective action of the two different consistent ten-dimensional type-I string theories, namely the SO(32) superstring and the $USp(32)$ non-supersymmetric string.Comment: 15 pages, LaTeX file. Refs. adde

Letter from Samuel F. Green to James B. Finley

Samuel is now in Cincinnati where he is a member of the Methodist Episcopal Church. He would like Finley to correspond with him. Abstract Number - 514https://digitalcommons.owu.edu/finley-letters/1811/thumbnail.jp

The Chilcot Report: some thoughts on international law and legal advice

The Report of the Iraq (Chilcot) Inquiry was finally published, 7 years after the Inquiry’s creation, on 6 July 2016. The scope of the Inquiry’s work was vast, and this was reflected in the enormous size of its final Report. The publication of the Report thus raises a multitude of questions requiring further analysis. In this short article, we aim to contribute some initial thoughts, immediately following the Report’s publication, in just two (interrelated) areas. First, we comment on the role of international law in the Chilcot Inquiry. To what extent was international law considered and how was it presented in the Report? We also ask whether the Report reaches any implicit substantive legal conclusions, despite formally refraining from determinations of law. Secondly, we review the Inquiry’s findings concerning international legal advice and legal advisers. In particular, we contribute some thoughts on the Report’s treatment of questions relating to the appropriate recipients of legal advice and its transparency, the timeliness of advice, the perception and treatment of law and legal advice by the Government, and the independence and quality of that advice

Spacetime-Filling Branes in Ten and Nine Dimensions

Type-IIB supergravity in ten dimensions admits two consistent $Z_2$ truncations. After the insertion of D9-branes, one of them leads to the low-energy action of type-I string theory, and it can be performed in two different ways, in correspondence with the fact that there are two different consistent ten-dimensional type-I string theories, namely the SO(32) superstring and the $USp(32)$ model, in which supersymmetry is broken on the D9-branes. We derive here the same results for Type-IIA theory compactified on a circle in the presence of D8-branes. We also analyze the $\kappa$-symmetric action for a brane charged with respect to the S-dual of the RR 10-form of type-IIB, and we find that the tension of such an object has to scale like $g_S^{-2}$ in the string frame. We give an argument to explain why this result is in disagreement with the one obtained using Weyl rescaling of the brane action, and we argue that this brane can only be consistently introduced if the other $Z_2$ truncation of type-IIB is performed. Moreover, we find that one can include a 10-form in type-IIA supersymmetry algebra, and also in this case the corresponding $\kappa$-symmetric brane has a tension scaling like $g_S^{-2}$ in the string frame.Comment: 29 pages, LaTeX file. Refs. added, typos corrected. A comment in the conclusions added. To appear on NP