Superstring Research Articles

A FIELD THEORETICAL MODEL IN NONCOMMUTATIVE MINKOWSKI SUPERSPACE

In this talk we present a field theoretical model constructed in Minkowski [Formula: see text] superspace with a deformed supercoordinate algebra. Our study is motivated in part by recent results from super-string theory, which show that in a particular scenario in Euclidean superspace the spinor coordinates θ do not anticommute. Field theoretical consequences of this deformation were studied in a number of articles. We present a way to extend the discussion to Minkowski space, by assuming non-vanishing anticommutators for both θ, and [Formula: see text]. We give a consistent supercoordinate algebra, and a star product that is real and preserves the (anti)chirality of a product of (anti)chiral superfields. We also give the Wess-Zumino Lagrangian [Formula: see text] that gains only Lorentz-invariant corrections due to non(anti)commutativity within our model. The Lagrangian in Minkowski superspace is also always manifestly Hermitian.

The Rise and Fall of the Cosmic String Theory for Cosmological Perturbations

The cosmic string theory for cosmological fluctuations is a good example of healthy scientific progress in cosmology. It is a well defined physically motivated model that has been tested by cosmological observations and has been ruled out as a primary source of primordial fluctuations. Until about fifteen years ago, the cosmic string theory of cosmological perturbations provided one of the two physically motivated candidate theories for the generation of primordial perturbations. The cosmological data that appeared during the last decade have been compared with the well defined predictions of the theory and have ruled out cosmic strings as a primary source of primordial cosmological perturbations. Since cosmic strings are predicted to form after inflation in a wide range of microphysical theories (including supersymmetric and fundamental string theories) their observational bounds may serve a source of serious constraints for these theories. This is a pedagogical review of the historical development, the main predictions of the cosmic string theory and the constraints that have been imposed on it by cosmological observations. Recent lensing events that could be attributed to lighter cosmic strings are also discussed.

The Existence of Supersymmetric String Theory with Torsion

We derived an existence criterion to the Supersymmetric String Theory with Torsion proposed by Strominger and proved the existence of such theory for a class of Calabi-Yau threefolds.

A VISUALIZABLE REPRESENTATION OF THE ELEMENTARY PARTICLES

Rudimentary knots are invoked to generate a representation of the elementary particles, a model that endows the particles with visualizable structure. The model correlates with the basic tenets, taxonomy, and interactions of the Standard Model, but goes beyond it in a number of important ways, the most significant being that all particles (hadrons and leptons, fermions and bosons) and interactions share a common topology. Among other consequences of the modeling are the topological basis for isospin invariance and its connection to electric charge, the necessary identity of electron and proton charge magnitudes, and the existence of precisely three generations on the particle family tree. The salient feature of the model is that the elementary particles are viewed not as discrete, point-like objects in a vacuum but rather as sustainable, membrane-like distortions embodying curvature and torsion in and of an otherwise featureless continuum and that their manifest physical attributes correlate with the distortion. There are additional connections to the theories of fiber bundles, superstrings and instantons and, historically, to the work of Kelvin in the mid-nineteenth century and Cartan in the 1920s among others.

Ramifications of non commutative space time

Abstract We review Cantorian and non commutative space time, work which has occupied El Naschie in the past several years. These concepts are now the subject of intense research, thanks to quantum gravity, quantum super string theory and a few other approaches. It now appears that we are on the verge of a breakthrough in finding solutions to longstanding problems, like the unification of gravitation with other fundamental interactions and the question of the mass spectrum, another recent area of El Naschie’s work.

Determining the number of Higgs particles starting from general relativity and various other field theories

The Riemann–Einstein tensor of general relativity as well as chiral and super-symmetry are utilized to develop various extended versions of the standard model of high energy physics. Based on these models, it is possible to predict that few new elementary particles conjectured to be the Higgs are likely to be found experimentally at an energy scale which is just above that of the electroweak. Connections to the massless states of different super-string theories as well as super-gravity are also discussed.

ACCELERATING COSMOLOGIES AND INFLATION FROM M/SUPERSTRING THEORIES

We review the recent developments in obtaining accelerating cosmologies and/or inflation from higher-dimensional gravitational theories, in particular superstring theories in ten dimensions and M-theory in 11 dimensions. We first discuss why it is difficult to obtain inflationary behavior in the effective low-energy theories of superstring/M-theory, i.e. supergravity theories. We then summarize interesting solutions including S-branes that give rise to accelerating cosmologies and inflationary solutions in M-theory with higher order corrections. Other approaches to inflation in the string context are also briefly discussed.

Black holes and the spectrum of half-BPS states in $N=4$ supersymmetric string theory

The entropy of a half-BPS black hole in N=4 supersymmetric heterotic string compactification is independent of the details of the charge vector and is a function only of the norm of the charge vector calculated using the appropriate Lorenzian metric. Thus in order for this to agree with the degeneracy of the elementary string states, the latter must also be a function of the same invariant norm. We show that this is true for generic CHL compactifications to all orders in a power series expansion in the inverse charges, but there are exponentially suppressed corrections which do depend on the details of the charge vector. This is consistent with the hypothesis that the black hole entropy reproduces the degeneracy of elementary string states to all orders in a power series expansion in the inverse charges, and helps us extend the earlier conjectured relation between black hole entropy and degeneracy of elementary string states to generic half-BPS electrically charged states in generic N=4 supersymmetric heterotic string compactification. Using this result we can also relate the black hole entropy to the statistical entropy calculated using an ensemble of elementary string states that contains all BPS states along a fixed null line in the lattice of electric charges.

Light cone quantization, Heterotic strings and E–infinity derivation of the number of Higgs bosons

Abstract Using light cone quantization as well as a variety of super and Heterotic string theories in conjunction with E –infinity theory we show that while a minimum of one Higgs particle is absolutely necessary for a consistent standard model of elementary particles, the number could be as large as 12 particles and include one or more graviton.

Determining the number of Higgs particles starting from general relativity and various other field theories

The Riemann–Einstein tensor of general relativity as well as chiral and super-symmetry are utilized to develop various extended versions of the standard model of high energy physics. Based on these models, it is possible to predict that few new elementary particles conjectured to be the Higgs are likely to be found experimentally at an energy scale which is just above that of the electroweak. Connections to the massless states of different super-string theories as well as super-gravity are also discussed.

Brane-World Gravity

The observable universe could be a 1 + 3-surface (the “brane”) embedded in a 1 + 3 + d-dimensional spacetime (the “bulk”), with Standard Model particles and fields trapped on the brane while gravity is free to access the bulk. At least one of the d extra spatial dimensions could be very large relative to the Planck scale, which lowers the fundamental gravity scale, possibly even down to the electroweak (∼ TeV) level. This revolutionary picture arises in the framework of recent developments in M theory. The 1 + 10-dimensional M theory encompasses the known 1 + 9-dimensional superstring theories, and is widely considered to be a promising potential route to quantum gravity. General relativity cannot describe gravity at high enough energies and must be replaced by a quantum gravity theory, picking up significant corrections as the fundamental energy scale is approached. At low energies, gravity is localized at the brane and general relativity is recovered, but at high energies gravity “leaks” into the bulk, behaving in a truly higher-dimensional way. This introduces significant changes to gravitational dynamics and perturbations, with interesting and potentially testable implications for high-energy astrophysics, black holes, and cosmology. Brane-world models offer a phenomenological way to test some of the novel predictions and corrections to general relativity that are implied by M theory. This review discusses the geometry, dynamics and perturbations of simple brane-world models for cosmology and astrophysics, mainly focusing on warped 5-dimensional brane-worlds based on the Randall-Sundrum models.

The Higgs––physical and number theoretical arguments for the necessity of a triple elementary particle in super symmetric spacetime

Abstract Die Elementarteilchen k o nnen mit den regul a ren K o rpern in Platos “Timaios” verglichen werden. Sie sind die Urbilder, die Ideen der Materie . (Werner Heisenberg) A careful counting routine of all experimentally confirmed elementary particles plus the theoretically conjectured ones needed for a sound formulation of a mathematically consistent field theory is undertaken within a minimal N =1 super symmetric extension of the standard model of high energy physics. The number arrived at is subsequently linked to certain massless on shell representations connected to the quantized gravity interaction. Finally with the help of number theoretical arguments arising from a rigorous application of the formalism of transfinite Heterotic super string and E-infinity theory, we show that the proposed scheme would lack mathematical consistency and elegant simplicity unless we retain a postulated triplet which is logically identified as the H + , H − and H 0 Higgs particles. Connections to the 11 dimensional M theory and Harari's extended “sub-quarks” theory is also discussed.

Topology and H-flux of T-dual manifolds.

We present a general formula for the topology and H-flux of the T-dual of a type II compactification. Our results apply to T-dualities with respect to any free circle action. In particular, we find that the manifolds on each side of the duality are circle bundles whose curvatures are given by the integral of the dual H-flux over the dual circle. As a corollary we conjecture an obstruction to multiple T-dualities, generalizing the obstruction known to exist on the twisted torus. Examples include SU(2) Wess-Zumino-Witten models, lens spaces, and the supersymmetric string theory on the nonspin AdS5 x CP2 x S1 compactification.

Gauss–Bonnet black holes at the LHC: beyond the dimensionality of space

The Gauss–Bonnet invariant is one of the most promising candidates for a quadratic curvature correction to the Einstein action in expansions of supersymmetric string theory. We study the evaporation of such Schwarzschild–Gauss–Bonnet black holes which could be formed at future colliders if the Planck scale is of order of TeV, as predicted by some modern brane world models. We show that, beyond the dimensionality of space, the corresponding coupling constant could be measured by the LHC. This opens new windows for physics investigation in spite of the possible screening of microphysics due to the event horizon.

The open superstring and the non-abelian born-infeld theory

Abstract In the recent years new interest has arised in determining the Superstring Theory corrections to the Yang-Mills lagrangian. For a long time only the O (α′ 2 ) terms were known, together with some partial knowledge of the O (α′ 3 ) ones. On this contribution we report in the recent progress on this subject, carried over in the last two years, emphasizing the scattering amplitude approach and the recent calculation of the five-point amplitude.

On the possibility of two new “elementary” particles with mass equal to m( k)=1.80339 MeV and [formula omitted] MeV

To sustain the global symplictic structure of the VAK of vacuum fluctuation, transfinite quantities of energy of the order of k= φ 3(1− φ 3)=0.18033989 MeV and k 0= φ 5(1− φ 5)=0.08203939 MeV must be added to it. In the ten dimensional core of the super string space this leads to the formation of particle masses of the order of m( k)=(10)( k)=1.8033989 MeV. Using ε (∞) theory and the M-dualities between high and low energy domains, one could make a second prediction regarding a unification-related particle m( α ̄ gs )=10/2(m(k))(φ+1) 7=26.18033989 MeV. The possible experimental ramifications of the theory are also discussed.

Penrose limit and enhançon geometry

We study superstring theories on the Penrose limit of the enhancon geometry realized by the D(p+4)-branes wrapped on a K3 surface. We first examine the null geodesics with fixed radius in general brane backgrounds, which give solvable superstring theories with constant masses. In most cases, the superstring theories contain negative mass-squared. We clarify a condition that the world-sheet free fields have positive mass-squared. We then apply this condition to the enhancon geometry and find that the null geodesics with fixed radius exist only for p=0 case. They define the superstring theories with positive mass-squared. For p>0 case, we show that there is no null geodesic with fixed radius. We also discuss the decoupling limit which gives the dual geometry of super Yang-Mills theory with 8 supercharges. We discuss the K3-volume dependence of the superstring spectrum.

Open and Closed Superstring Five-Point Amplitudes at Tree-Level

In this contribution the tree-level effective actions for gluons and gravitons, as derived from Open and Closed Superstring theories, are reviewed respectively. As known for a long time, at zero order in α′ (the string fundamental constant) the first action is pure Yang-Mills while the second one is pure Einstein-Hilbert. The first Superstring Theory corrections turn up to appear at [Formula: see text] order in the first case while they appear at [Formula: see text] in the second one, as known from the three and four-point scattering amplitudes for gluons and gravitons, respectively. Recent work involving the [Formula: see text] order contributions to the Yang-Mills action is reviewed with some detail, including the authors' present line of research. Also, the uncharted territory of five graviton scattering is commented, looking forward to derive the [Formula: see text] Superstring Theory corrections to the Einstein-Hilbert action.

Off-shell extension of S-matrix elements and tachyonic effective actions

We show that the on-shell S-matrix elements of four open string massless scalars, two scalars and two tachyons, and four open string tachyons in the super string theory can be written in a unique form. We then propose an off-shell extension for the S-matrix element of four scalars which is consistent, in the low energy limit, with the Dirac-Born-Infeld effective action. Using a similar off-shell extension for the S-matrix element of two scalars and two tachyons and for the S-matrix element of four tachyons, we show that they are fully consistent with the tachyonic DBI action.

On the absence of large‐order divergences in superstring theory

Fortschritte der PhysikVolume 51, Issue 2-3 p. 267-267 Erratum On the absence of large-order divergences in superstring theory S. Davis, S. Davis davis@math.uni-potsdam.de Institut für Mathematik, Universität Potsdam, 14415 Potsdam, GermanySearch for more papers by this author S. Davis, S. Davis davis@math.uni-potsdam.de Institut für Mathematik, Universität Potsdam, 14415 Potsdam, GermanySearch for more papers by this author First published: 26 February 2003 https://doi.org/10.1002/prop.200310038AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat No abstract is available for this article. Volume51, Issue2-3March 2003Pages 267-267 RelatedInformation