The low energy expansion of the one-loop type II superstring amplitude

The one-loop four-graviton amplitude in either of the type II superstring theories is expanded in powers of the external momenta up to and including terms of order s^4 log s R^4, where R^4 denotes a specific contraction of four linearized Weyl tensors and s is a Mandelstam invariant. Terms in this series are obtained by integrating powers of the two-dimensional scalar field theory propagator over the toroidal world-sheet as well as the moduli of the torus. The values of these coefficients match expectations based on duality relations between string theory and eleven-dimensional supergravity.Comment: harvmac (b), 25 pages, 3 eps figures. v2: Factors of 2 corrected. Conclusion unchange

Gauge symmetries decrease the number of Dp-brane dimensions

It is known that the presence of antisymmetric background field $B_{\mu\nu}$ leads to noncommutativity of Dp-brane manifold. Addition of the linear dilaton field in the form $\Phi(x)=\Phi_0+a_\mu x^\mu$, causes the appearance of the commutative Dp-brane coordinate $x=a_\mu x^\mu$. In the present article we show that for some particular choices of the background fields, $a^2\equiv G^{\mu\nu}a_\mu a_\nu=0$ and $\tilde a^2\equiv [ (G-4BG^{-1}B)^{-1}\ ]^{\mu\nu}a_\mu a_\nu=0$, the local gauge symmetries appear in the theory. They turn some Neuman boundary conditions into the Dirichlet ones, and consequently decrease the number of the Dp-brane dimensions.Comment: We improve Sec.4. and Conclusion and we added the Appendix in order to clarify result

From bedside to bench: Comroe and dripps revisited

Twenty-five years ago a paper published in Science by Julius Comroe and Robert Dripps purported to demonstrate that 41 per cent of all articles judged to be essential for later clinical advances were not clinically oriented at the time of the study and 62 per cent of key articles were the result of basic research. Since that analysis, support for basic research has increased in the G7 countries. In the UK, Research Council expenditure on basic research has increased from a low of £444 million (or 42 per cent of total civil R&D) in 1991/92 to £769 million (or 61 per cent of total civil R&D) in 1998/99. Although it would be difficult to argue that Comroe and Dripps were directly responsible for a strategic shift (or drift) in the type of science supported by research funders, their arguments are often cited (albeit at times implicitly) in support of the increased funding for basic biomedical research. In 1987 Richard Smith wrote a critical paper reassessing Comroe and Dripps. His main argument was that the original study was in itself ‘unscientific’ and that it should be “followed by bigger and better studies”. This study is, in part, an answer to that challenge. Given the increased support for basic research, and the apparent importance based on the work of Comroe and Dripps, we felt it was important to investigate Smith’s comments by replicating Comroe and Dripps’s study and at the same time try to improve upon the methodology. The current project had two objectives: 1. To see if the original Comroe and Dripps’s methodology was ‘replicable’. 2. To validate the key findings of Comroe and Dripps. By looking at neonatal intensive care (NIC), we concluded that Comroe and Dripps’ study – as reported – is not repeatable, reliable or valid, and thus is an insufficient evidence base for increased expenditure on basic biomedical research. We did, however, develop an alternative methodology which used bibliographic databases and bibliometric techniques to describe the research underpinning five of the most important clinical advances in NIC, as identified through a Delphi survey. Using the revised bibliometric protocol, we demonstrated that after a time-lag of about 17 years, between 2 and 21 per cent of research underpinning the clinical advances could be described as basic. This observation is at odds with Comroe and Dripps’s finding that 62 per cent of key research articles judged to be essential for latter clinical advance were the result of basic research. In reaching this conclusion we are acutely aware of the significant limitations to the revised methodology and, therefore, we caution against the over-interpretation of our results. However, we would argue that there needs to be a greater understanding of how basic research supports healthcare and hope this report will inform part of this wider debate.R&D Directorate of the NHS Executive London; Wellcome Trus

String Bit Models for Superstring

We extend the model of string as a polymer of string bits to the case of superstring. We mainly concentrate on type II-B superstring, with some discussion of the obstacles presented by not II-B superstring, together with possible strategies for surmounting them. As with previous work on bosonic string we work within the light-cone gauge. The bit model possesses a good deal less symmetry than the continuous string theory. For one thing, the bit model is formulated as a Galilei invariant theory in $(D-2)+1$ dimensional space-time. This means that Poincar\'e invariance is reduced to the Galilei subgroup in $D-2$ space dimensions. Naturally the supersymmetry present in the bit model is likewise dramatically reduced. Continuous string can arise in the bit models with the formation of infinitely long polymers of string bits. Under the right circumstances (at the critical dimension) these polymers can behave as string moving in $D$ dimensional space-time enjoying the full $N=2$ Poincar\'e supersymmetric dynamics of type II-B superstring.Comment: 43 pages, phyzzx require

Supersymmetry Constraints on Type IIB Supergravity

Supersymmetry is used to derive conditions on higher derivative terms in the effective action of type IIB supergravity. Using these conditions, we are able to prove earlier conjectures that certain modular invariant interactions of order alpha' **3 relative to the Einstein-Hilbert term are proportional to eigenfunctions of the Laplace operator on the fundamental domain of SL(2,Z). We also discuss how these arguments generalize to terms of higher order in alpha', as well as to compactifications of supergravity.Comment: 31 pages, harvmac (b); minor correction

Teacher Leader Administrators: Part 3 Of A Symposium On Teachers As Leaders

In this latest continuation of our multipart symposium on teacher leadership, we examine what happens when self-defined teacher leaders become school administrators. Do teacher leaders who become administrators maintain a teacher identity? Can they remain committed to their vision of teacher leadership when they take on the normative requirements and responsibilities of school administration? Through a conversation with three teachers leaders, we explore the rewards and trials of teaching, the choice to become teacher leaders and then administrators, and the unique challenges that face administrators who deeply value the professional, political, and collaborative work of teachers

Remarks on the Classical Size of D-Branes

We discuss different criteria for `classical size' of extremal Dirichlet p-branes in type-II supergravity. Using strong-weak coupling duality, we find that the size of the strong-coupling region at the core of the (p<3)-branes, is always given by the asymptotic string scale, if measured in the weakly coupled dual string metric. We also point out how the eleven-dimensional Planck scale arises in the classical 0-brane solution, as well as the ten-dimensional Planck scale in the D-instanton solution.Comment: 8 pp, harvma

Galois covers of the open p-adic disc

This paper investigates Galois branched covers of the open $p$-adic disc and their reductions to characteristic $p$. Using the field of norms functor of Fontaine and Wintenberger, we show that the special fiber of a Galois cover is determined by arithmetic and geometric properties of the generic fiber and its characteristic zero specializations. As applications, we derive a criterion for good reduction in the abelian case, and give an arithmetic reformulation of the local Oort Conjecture concerning the liftability of cyclic covers of germs of curves.Comment: 19 pages; substantial organizational and expository changes; this is the final version corresponding to the official publication in Manuscripta Mathematica; abstract update

Combinatorics of Boundaries in String Theory

We investigate the possibility that stringy nonperturbative effects appear as holes in the world-sheet. We focus on the case of Dirichlet string theory, which we argue should be formulated differently than in previous work, and we find that the effects of boundaries are naturally weighted by $e^{-O(1/g_{\rm st})}$.Comment: 12 pages, 2 figures, LaTe

Mass corrections in string theory and lattice field theory

Kaluza-Klein compactifications of higher dimensional Yang-Mills theories contain a number of four dimensional scalars corresponding to the internal components of the gauge field. While at tree-level the scalar zero modes are massless, it is well known that quantum corrections make them massive. We compute these radiative corrections at 1-loop in an effective field theory framework, using the background field method and proper Schwinger-time regularization. In order to clarify the proper treatment of the sum over KK--modes in the effective field theory approach, we consider the same problem in two different UV completions of Yang-Mills: string theory and lattice field theory. In both cases, when the compactification radius $R$ is much bigger than the scale of the UV completion ($R \gg \sqrt{\alpha'},a$), we recover a mass renormalization that is independent of the UV scale and agrees with the one derived in the effective field theory approach. These results support the idea that the value of the mass corrections is, in this regime, universal for any UV completion that respects locality and gauge invariance. The string analysis suggests that this property holds also at higher loops. The lattice analysis suggests that the mass of the adjoint scalars appearing in $\mathcal N=2,4$ Super Yang-Mills is highly suppressed due to an interplay between the higher-dimensional gauge invariance and the degeneracy of bosonic and fermionic degrees of freedom.Comment: 27 page