Superstring theoryをめぐって(放談室)

Beyond the cosmological standard model

心臓病診療プラクティス 16. 心不全を癒す

After a decade and a half of research motivated by the accelerating universe, theory and experiment have a reached a certain level of maturity. The development of theoretical models beyond \Lambda, or smooth dark energy, often called modified gravity, has led to broader insights into a path forward, and a host of observational and experimental tests have been developed. In this review we present the current state of the field and describe a framework for anticipating developments in the next decade. We identify the guiding principles for rigorous and consistent modifications of the standard model, and discuss the prospects for empirical tests. We begin by reviewing attempts to consistently modify Einstein gravity in the infrared, focusing on the notion that additional degrees of freedom introduced by the modification must screen themselves from local tests of gravity. We categorize screening mechanisms into three broad classes: mechanisms which become active in regions of high Newtonian potential, those in which first derivatives become important, and those for which second derivatives are important. Examples of the first class, such as f(R) gravity, employ the familiar chameleon or symmetron mechanisms, whereas examples of the last class are galileon and massive gravity theories, employing the Vainshtein mechanism. In each case, we describe the theories as effective theories. We describe experimental tests, summarizing laboratory and solar system tests and describing in some detail astrophysical and cosmological tests. We discuss future tests which will be sensitive to different signatures of new physics in the gravitational sector. Parts that are more relevant to theorists vs. observers/experimentalists are clearly indicated, in the hope that this will serve as a useful reference for both audiences, as well as helping those interested in bridging the gap between them.

Beyond the Cosmological Standard Model

We review the recent advances towards finding the spectrum of the AdS5 ? S5 superstring. We thoroughly explain the theoretical techniques which should be useful for the ultimate solution of the spectral problem. In certain cases our exposition is original and cannot be found in the existing literature. The present part I deals with foundations of classical string theory in AdS5 ? S5, light-cone perturbative quantization and the derivation of the exact light-cone world-sheet scattering matrix.

Foundations of the AdS5 × S5 superstring: I

Preface 1. Lie groups, fibre bundles and Cartan calculus 2. Connections and characteristic classes 3. A first look at cohomology of groups and related topics 4. An introduction to abstract group extension theory 5. Cohomology groups of a group G and extensions by an abelian kernel 6. Cohomology of Lie algebras 7. Group extensions by non-abelian kernels 8. Cohomology and Wess-Zumino terms: an introduction 9. Infinite-dimensional Lie groups and algebras 10. Gauge anomalies List of symbols References Index.

/pdf/lie-groups-lie-algebras-cohomology-and-some-applications-in-4ikwl6f3cx.pdf

Lie Groups, Lie Algebras, Cohomology and some Applications in Physics

We study how to generate new Lie algebras $\mathcal{G}(N_0,..., N_p,...,N_n)$ from a given one $\mathcal{G}$. The (order by order) method consists in expanding its Maurer-Cartan one-forms in powers of a real parameter $\lambda$ which rescales the coordinates of the Lie (super)group $G$, $g^{i_p} \to \lambda^p g^{i_p}$, in a way subordinated to the splitting of $\mathcal{G}$ as a sum $V_0 \oplus ... \oplus V_p \oplus ... \oplus V_n$ of vector subspaces. We also show that, under certain conditions, one of the obtained algebras may correspond to a generalized \.In\"on\"u-Wigner contraction in the sense of Weimar-Woods, but not in general. The method is used to derive the M-theory superalgebra, including its Lorentz part, from $osp(1|32)$. It is also extended to include gauge free differential (super)algebras and Chern-Simons theories, and then applied to D=3 CS supergravity.

Generating Lie and gauge free differential (super)algebras by expanding Maurer-Cartan forms and Chern-Simons supergravity

Supersymmetric particles with internal symmetries and central charges

This paper reviews the properties and applications of certain n-ary generalizations of Lie algebras in a self-contained and unified way. These generalizations are algebraic structures in which the two entries Lie bracket has been replaced by a bracket with n entries. Each type of n-ary bracket satisfies a specific characteristic identity which plays the role of the Jacobi identity for Lie algebras. Particular attention will be paid to generalized Lie algebras, which are defined by even multibrackets obtained by antisymmetrizing the associative products of its n components and that satisfy the generalized Jacobi identity (GJI), and to Filippov (or n-Lie) algebras, which are defined by fully antisymmetric n-brackets that satisfy the Filippov identity (FI). Three-Lie algebras have surfaced recently in multi-brane theory in the context of the Bagger-Lambert-Gustavsson model. Because of this, Filippov algebras will be discussed at length, including the cohomology complexes that govern their central extensions and their deformations (Whitehead's lemma extends to all semisimple n-Lie algebras). When the skewsymmetry of the n-Lie algebra is relaxed, one is led the n-Leibniz algebras. These will be discussed as well, since they underlie the cohomological properties of n-Lie algebras. 
The standard Poisson structure may also be extended to the n-ary case. We shall review here the even generalized Poisson structures, whose GJI reproduces the pattern of the generalized Lie algebras, and the Nambu-Poisson structures, which satisfy the FI and determine Filippov algebras. Finally, the recent work of Bagger-Lambert and Gustavsson on superconformal Chern-Simons theory will be briefly discussed. Emphasis will be made on the appearance of the 3-Lie algebra structure and on why the A_4 model may be formulated in terms of an ordinary Lie algebra, and on its Nambu bracket generalization.

n-ary algebras: a review with applications

We provide a complete algebraic description of Bogomol'nyi-Prasad-Sommerfield (BPS) states in $M$ theory in terms of primary constituents that we call BPS preons. We argue that any BPS state preserving $k$ of the 32 supersymmetries is a composite of $(32\ensuremath{-}k)$ BPS preons. In particular, the BPS states corresponding to the basic $M2$ and $M5$ branes are composed of 16 BPS preons. By extending the $M$ algebra to a generalized $D\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}11$ conformal superalgebra $\mathrm{osp}(1\ensuremath{\mid}64)$ we relate the BPS preons with its fundamental representation, the $D\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}11$ supertwistors.

http://cds.cern.ch/record/483892/files/0101113.pdf

José A. de Azcárraga

Papers

Lie Groups, Lie Algebras, Cohomology and some Applications in Physics

Generating Lie and gauge free differential (super)algebras by expanding Maurer-Cartan forms and Chern-Simons supergravity

Supersymmetric particles with internal symmetries and central charges

n-ary algebras: a review with applications

BPS States in M Theory and Twistorial Constituents