Superstring Research Articles

Line bundle embeddings for heterotic theories

In heterotic string theories consistency requires the introduction of a non-trivial vector bundle. This bundle breaks the original ten-dimensional gauge groups E8 × E8 or SO(32) for the supersymmetric heterotic string theories and SO(16) × SO(16) for the non-supersymmetric tachyon-free theory to smaller subgroups. A vast number of MSSM-like models have been constructed up to now, most of which describe the vector bundle as a sum of line bundles. However, there are several different ways of describing these line bundles and their embedding in the ten-dimensional gauge group. We recall and extend these different descriptions and explain how they can be translated into each other.

Heat kernels on cone of AdS2 and k-wound circular Wilson loop in AdS5 × S5 superstring

We compute the one-loop world-sheet correction to partition function of superstring that should be representing k-fundamental circular Wilson loop in planar limit. The 2d metric of the minimal surface ending on k-wound circle at the boundary is that of a cone of AdS2 with deficit . We compute the determinants of 2d fluctuation operators by first constructing heat kernels of scalar and spinor Laplacians on the cone using the Sommerfeld formula. The final expression for the k-dependent part of the one-loop correction has simple integral representation but is different from earlier results.

Towards the gravity/CYBE correspondence — the current status —

We give a brief summary of Yang-Baxter deformations of the AdS5 × S5 superstring by focusing upon four examples, 1) gravity duals for noncommutative gauge theories, 2) γ-deformations of S5, 3) Schrödinger spacetimes and 4) abelian twists of the global AdS5.

Universe and Matter Conjectured as a 3-Dimensional Lattice with Topological Singularities

One fundamental problem of modern physics is the search for a theory of everything able to explain the nature of space-time, what matter is and how matter interacts. There are various propositions, as Grand Unified Theory, Quantum Gravity, Supersymmetry, String and Superstring Theories, and M-Theory. However, none of them is able to consistently explain at the present and same time electromagnetism, relativity, gravitation, quantum physics and observed elementary particles. In this paper, one summarizes the content of a new book, published in English [2] and in French [3], in which it is suggested that Universe could be a massive elastic 3D-lattice, and that fundamental building blocks of Ordinary Matter could consist of topological singularities of this lattice, namely diverse dislocation loops and disclination loops. For an isotropic elastic lattice obeying Newton’s law, with specific assumptions on its elastic properties, one obtains the result that the behaviours of this lattice and of its topological defects display “all” known physics, unifying electromagnetism, relativity, gravitation and quantum physics, and resolving some longstanding questions of modern cosmology. Moreover, studying lattices with axial symmetries, represented by “colored” cubic 3D-lattices, one has identified a lattice structure whose topological defect loops coincide with the complex zoology of elementary particles, which could open a very promising field of research. Here, only main steps and principal results of the new theory are presented and discussed, without showing the mathematical concepts and developments contained in the book.

Scale invariance of the η-deformed AdS5 × S5 superstring, T-duality and modified type II equations

We consider the ABF background underlying the η-deformed AdS5×S5 sigma model. This background fails to satisfy the standard IIB supergravity equations which indicates that the corresponding sigma model is not Weyl invariant, i.e. does not define a critical string theory in the usual sense. We argue that the ABF background should still define a UV finite theory on a flat 2d world-sheet implying that the η-deformed model is scale invariant. This property follows from the formal relation via T-duality between the η-deformed model and the one defined by an exact type IIB supergravity solution that has 6 isometries albeit broken by a linear dilaton. We find that the ABF background satisfies candidate type IIB scale invariance conditions which for the R–R field strengths are of the second order in derivatives. Surprisingly, we also find that the ABF background obeys an interesting modification of the standard IIB supergravity equations that are first order in derivatives of R–R fields. These modified equations explicitly depend on Killing vectors of the ABF background and, although not universal, they imply the universal scale invariance conditions. Moreover, we show that it is precisely the non-isometric dilaton of the T-dual solution that leads, after T-duality, to modification of type II equations from their standard form. We conjecture that the modified equations should follow from κ-symmetry of the η-deformed model. All our observations apply also to η-deformations of AdS3×S3×T4and AdS2×S2×T6models.

Removing the big rip singularity from anisotropic universe in super string theory

Recently, various observational data predict the possibility that dark energy could be in the form of phantom field. The positive phantom-energy density grows without limit with the expansion of the Universe and leads to a big-rip singularity at a finite future time. The main question arises: what is the origin of the big rip singularity in a four-dimensional Universe? To answer this question, in this paper, we propose a new model in super string theory that allows taking into account the Dirac and vector string tachyon in addition to the scalar one, which stretches between branes and antibranes. In this model, scalar and Dirac string tachyons cancel each other’s effects and the only effect induced by the vector tachyon can be observed in density and pressures of the universe. We observe that different scale factors, pressures, and dark energy equation of state parameters are produced in different directions because of inhomogeneous tachyon dynamics and consequently one anisotropic universe is formed. Also, these observations are given in terms of effective tachyon potential and the separation between branes and antibranes. Thus, we have shown that the expansion of the anisotropic Universe is controlled by the vector string tachyon and evolves from the non-phantom phase to the phantom one and consequently, the phantom-dominated era of the universe accelerates and ends up in a big-rip singularity.

On classical Yang-Baxter based deformations of the AdS5 × S5 superstring

Interesting deformations of AdS5 × S5 such as the gravity dual of noncommutative SYM and Schödinger spacetimes have recently been shown to be integrable. We clarify questions regarding the reality and integrability properties of the associated construction based on R matrices that solve the classical Yang-Baxter equation, and present an overview of manifestly real R matrices associated to the various deformations. We also discuss when these R matrices should correspond to TsT transformations, which not all do, and briefly analyze the symmetries preserved by these deformations, for example finding Schrödinger superalgebras that were previously obtained as subalgebras of $$ \mathfrak{p}\mathfrak{s}\mathfrak{u} $$ (2, 2|4). Our results contain a (singular) generalization of an apparently non-TsT deformation of AdS5 × S5, whose status as a string background is an interesting open question.

Foundations of analysis on superspace — 1: Differential calculus

The recent experimental confirmation of the existence of Higgs boson stimulates theoretical research on supersymmetric models; in particular, mathematics of such modeling. Therefore we plan to present essentials of one special approach to “super-mathematics”, so called functional superanalysis (in the spirit of De Witt, Rogers, Vladimirov and Volovich, and the author of this review) in compact and clear form in series of review-type papers. This first paper is a review on super-differential calculus for the concrete model of the superspace (invented by Vladimirov and Volovich). In the next review we plan to present the integral supercalculus. The main distinguishing feature of functional superanalysis is that this is a real super-extension of analysis of Newton and Leibniz, opposite to algebraic models of Martin and Berezin. Here functions of commuting and anticommuting variables are no simply algebraic elements belonging to Grassmann algebras, but point-wise maps, from superspace into superspace. Finally, we remark that the first non-Archimedean physical model was based on invention by Vladimirov and Volovich of superspaces based on supercommutative Banach superalgebras over non-Archimedean (in particular, p-adic) fields. This model plays the basic role in theory of p-adic superstrings.

On the asymptotic states and the quantum S matrix of the η-deformed AdS5 × S5 superstring

We investigate the worldsheet S matrix of string theory in η-deformed AdS5×S5. By computing the six-point tree-level S matrix we explicitly show that there is no particle production at this level, ...

Classifying bions in Grassmann sigma models and non-Abelian gauge theories by D-branes

We classify bions in the Grassmann |$Gr_{N_{\rm F},N_{\rm C}}$| sigma model (including the |${\mathbb C}P^{N_{\rm F}-1}$| model) on |${\mathbb R}^{1}\times S^{1}$| with twisted boundary conditions. We formulate these models as |$U(N_{\rm C})$| gauge theories with |$N_{\rm F}$| flavors in the fundamental representations. These theories can be promoted to supersymmetric gauge theories and, further, can be embedded into D-brane configurations in type-II superstring theories. We focus on specific configurations composed of multiple fractional instantons, termed neutral bions and charged bions, which are identified as perturbative infrared renormalons by Ünsal and his collaborators [G. V. Dunne and M. Ünsal, J. High Energy Phys. 1211, 170 (2012); G. V. Dunne and M. Ünsal, Phys. Rev. D 87, 025015 (2013)]. We show that D-brane configurations, as well as the moduli matrix, offer a very useful tool to classify all possible bion configurations in these models. In contrast to the |${\mathbb C}P^{N_{\rm F}-1}$| model, there exist Bogomol’nyi–Prasad–Sommerfield (BPS) fractional instantons with topological charges greater than unity (of order |$N_{\rm C}$|⁠) that cannot be reduced to a composite of an instanton and fractional instantons. As a consequence, we find that the Grassmann sigma model admits neutral bions made of BPS and anti-BPS fractional instantons, each of which has a topological charge greater (less) than one (minus one), that are not decomposable into an instanton–anti-instanton pair and the rest. The |${\mathbb C}P^{N_{\rm F}-1}$| model is found to have no charged bions. In contrast, we find that the Grassmann sigma model admits charged bions, for which we construct exact non-BPS solutions of the field equations.

A Research of New Zero-Voltage Switching Equalization for Super-Capacitor Energy Storage System

An expatiation to analyze and verification for zero-voltage-switching (ZVS) is proposed for cell voltage equalization control in a series connected super capacitors string. Resonant circuit was designed to achieve the ZVS to reduce the switching loss in equalization circuit. Analyze result indicates that the switching loss and equalization efficiency can be improved with the ZVS technology. The simulation and experimental results shows the ZVS equalization technology can achieve voltage equalization performance and reduce MOSFET switches power loss and increase the efficiency by 20% compared with the traditional equalizer.

Quantum effects in topological and Schwarzschild de Sitter brane: Aspects of torsion on $(D\!{\bar D})_4$-brane

We investigate an effective torsion curvature in a second-order formalism underlying a two-form world-volume dynamics in a D5-brane. In particular, we consider the two form in presence of a background (open string) metric in a U(1) gauge theory. Interestingly the formalism may be viewed via a noncoincident pair of [Formula: see text]-brane with a global Nereu–Schwarz (NS) two form on an anti-brane and a local two form on a brane. The energy–momentum tensor is computed in the six-dimensional (6D) conformal field theory (CFT). It is shown to source a metric fluctuation on a vacuum created pair of [Formula: see text]-brane at a cosmological horizon by the two-form quanta in the gauge theory. The emergent gravity scenario is shown to describe a low-energy (perturbative) string vacuum in 6D with a nonperturbative (NP) quantum correction by a lower (p < 5) dimensional Dp-brane or an anti-brane in the formalism. A closed string exchange between a pair of [Formula: see text]-brane, underlying a closed/open string duality, is argued to describe the Einstein vacuum in a low-energy limit. We obtain topological de Sitter (TdS) and Schwarzschild brane universe in six dimensions. The brane/anti-brane geometries are analyzed to explore some of their characteristic and thermal behaviors in presence of the quantum effects. They reveal an underlying nine-dimensional type IIA and IIB superstring theories on S1.

Kerr Black Hole Geometry Leading to Dark Matter and Dark Energy via E-Infinity Theory and the Possibility of a Nano Spacetime Singularities Reactor

The present paper is basically a synthesis resulting from incorporating Kerr spinning black hole geometry into E-infinity topology, then letting the result bares on the vacuum zero point Casimir effect as well as the cosmic dark energy and dark matter density. In E-infinity theory a quantum particle is represented by a Hausdorff dimension Φ where Φ =2/(√5+1) . The quantum wave on the other hand is represented by Φ2 . To be wave and a particle simultaneously intersection theory leads us to (Φ) (Φ)2= Φ3 which will be shown here to be twice the value of the famous Casimir force of the vacuum for a massless scalar field. Thus in the present work a basically topological interpretation of the Casimir effect is given as a natural intrinsic property of the geometrical topological structure of the quantum-Cantorian micro spacetime. This new interpretation compliments the earlier conventional interpretation as vacuum fluctuation or as a Schwinger source and links the Casimir energy to the so called missing dark energy density of the cosmos. From the view point of the present work Casimir pressure is a local effect acting on the Casimir plates constituting the local boundary condition while dark energy is nothing but the global combined effect of infinitely many quantum waves acting on the M&#246bius-like boundary of the holographic boundary of the entire universe. Since this higher dimensional M&#246bius-like boundary is one sided, there is no outside to balance the internal collective Casimir pressure which then manifests itself as the force behind cosmic expansion, that is to say, dark energy. Thus analogous to the exact irrational value of ordinary energy density of spacetime E(O)=(Φ5/2) mc2 we now have P (Casimir) = (Φ3/2)(ch/d2) where c is the speed of light, m is the mass, h is the Planck constant and d is the plate separation. In addition the new emerging geometry combined with the topology of E-infinity theory leads directly to identifying dark matter with the quasi matter of the ergosphere. As a direct consequence of this new insight E=mc2 which can be written as E = E (O) + E (D) where the exact rational approximation is E (O)=mc2/22 is the ordinary energy density of the cosmos and the exact rational approximation E (D)=mc2/(21/22) is the corresponding dark energy which could be subdivided once more albeit truly approximately into E(D)=mc2/(5/22) +mc2/(16/22) where 5 is the Kaluza Klein spacetime dimension, 16 are the bosonic extra dimensions of Heterotic superstrings and 5/22 □ 22% is approximately the density of the dark matter-like energy of the ergosphere of the Kerr geometry. As for the actual design of our nano reactor, this is closely related to branching clusters of polymer, frequently called lattice animals. In other words we will have Casimir spheres instead of Casimir plates and these spheres will be basically nano particles modelling lattice animals. Here D= 4 will be regarded as spacetime dimensionality while D=6 of percolations are the compactified super string dimensions and D=8 is the dimension of a corresponding super space.

Integrable deformations of the AdS5×S5 superstring and the classical Yang-Baxter equation - Towards the gravity/CYBE correspondence -

Based on the formulation of Yang-Baxter sigma models developed by Klimcik and Delduc-Magro-Vicedo, we explain that various deformations of type IIB superstring on AdS5 × S5 can be charactered by classical r-matrices satisfying the classical Yang-Baxter equation (CYBE). The relation may be referred to as the gravity/CYBE correspondence. We present non-trivial examples of the correspondence including Lunin-Maldacena backgrounds for β-deformations of the N = 4 super Yang-Mills theory and the gravity duals for non-commutative gauge theories. We also discuss non-integrable backgrounds such as AdS5 × T1,1 as a generalization.

Bianchi Type I Cosmology with Scalar and Spinor Tachyon

Recently, some authors propose a scenario where inflation is driven by scalar and spinor fields. In this scenario, the universe undergoes anisotropic inflationary expansion due to a preferred direction dominated by spinor. The main question arises that what is the origin of spinor inflation in 4D Universe? To answer to this question , we propose a new model in super string theory that allows to take into account the spinor string tachyon in additional to scalar one which stretch between branes and antibranes. In this model, the inflation of 4D Universe is controlled by the spinor type of tachyon and evolves from non-phantom phase to phantom one and consequently, phantom-dominated era of the universe accelerates and ends up in big-rip singularity. We test our model against WMAP and Planck data and obtain the ripping time. We find that the finite time that Big Rip singularity occurs is t = 65(Gyr). According to our calculations, N ≃ 60 case leads to ns ≃ 0.96, where N and ns are the number e-folds and the spectral index respectively. Thus our results are consistent with experimental data and thus the spinor inflationary model works.

BPS state counting in N=8 supersymmetric string theory for pure D-brane configurations

Exact results for the BPS index are known for a class of BPS dyons in type II string theory compactified on a six dimensional torus. In this paper we set up the problem of counting the same BPS states in a duality frame in which the states carry only Ramond-Ramond charges. We explicitly count the number of states carrying the lowest possible charges and find agreement with the result obtained in other duality frames. Furthermore, we find that after factoring out the supermultiplet structure, each of these states carry zero angular momentum. This is in agreement with the prediction obtained from a representation of these states as supersymmetric black holes.

Stringlike structures in the real and complex Kerr-Schild geometry

Four-dimensional Kerr-Schild (KS) geometry displays remarkable relationships with quantum world and theory of superstrings. In particular, the Kerr-Newman (KN) solution has gyromagnetic ratio g = 2, as that of the Dirac electron and represents a consistent background for gravitational and electromagnetic field of the electron. As a consequence of very big spin/mass ratio, black hole horizons disappear, exposing the naked Kerr singular ring. We consider four-decade history of development of this structure which took finally the form of a point-string-membrane-bubble complex which is reminiscent of the enhancon model of string/M-theory. A complex string obtained in the complex structure of the Kerr geometry gives an extra dimension to the world-sheet of the real Kerr string, forming a membrane by analogue with the string/M-theory unification. By analysis of the orientifold parity of the complex Kerr string, we obtain that the determined by the Kerr theorem principal null congruence of the Kerr geometry is described by a quartic equation in projective twistor space CP3, and therefore, it creates the known Calabi- Yau twofold (K3 surface) in twistor space of the 4d KS geometry. We connect it with N=2 superstring which has (complex) critical dimension two and may be embedded into complex KS geometry.

Universal property of quantum gravity implied by uniqueness theorem of Bekenstein-Hawking entropy

We have searched for a universal property of quantum gravity, where "universal" means to be independent of any existing model of quantum gravity (such as the super string theory, loop quantum gravity, causal dynamical triangulation, and so on). To do so, we have investigated carefully the basis of black hole thermodynamics. The uniqueness of Bekenstein-Hawking entropy lets us extract a reasonable universal property of quantum gravity from the conditions justifying Boltzmann formula. The universal property indicates a repulsive gravity at Planck length scale, otherwise stationary black holes can not be regarded as thermal equilibrium states of gravity.

Small representations, string instantons, and Fourier modes of Eisenstein series

TextThis paper concerns some novel features of maximal parabolic Eisenstein series at certain special values of their analytic parameter, s. These series arise as coefficients in the R4 and ∂4R4 interactions in the low energy expansion of the scattering amplitudes in maximally supersymmetric string theory reduced to D=10−d dimensions on a torus, Td (0⩽d⩽7). For each d these amplitudes are automorphic functions on the rank d+1 symmetry group Ed+1. Of particular significance is the orbit content of the Fourier modes of these series when expanded in three different parabolic subgroups, corresponding to certain limits of string theory. This is of interest in the classification of a variety of instantons that correspond to minimal or “next-to-minimal” BPS orbits. In the limit of decompactification from D to D+1 dimensions many such instantons are related to charged 12-BPS or 14-BPS black holes with euclidean world-lines wrapped around the large dimension. In a different limit the instantons give non-perturbative corrections to string perturbation theory, while in a third limit they describe non-perturbative contributions in eleven-dimensional supergravity. A proof is given that these three distinct Fourier expansions have certain vanishing coefficients that are expected from string theory. In particular, the Eisenstein series for these special values of s have markedly fewer Fourier coefficients than typical maximal parabolic Eisenstein series. The corresponding mathematics involves showing that the wavefront sets of the Eisenstein series in question are supported on only a limited number of coadjoint nilpotent orbits – just the minimal and trivial orbits in the 12-BPS case, and just the next-to-minimal, minimal and trivial orbits in the 14-BPS case. Thus as a byproduct we demonstrate that the next-to-minimal representations occur automorphically for E6, E7, and E8, and hence the first two nontrivial low energy coefficients in scattering amplitudes can be thought of as exotic θ-functions for these groups. The proof includes an appendix by Dan Ciubotaru and Peter E. Trapa which calculates wavefront sets for these and other special unipotent representations. VideoFor a video summary of this paper, please click here or visit http://youtu.be/QHhgpfOy_ww.

Synchrotron radiation of superconducting cosmic strings

AbstractCosmic strings are topological defects which can be formed during the symmetry breaking phase transitions in the early Universe. Their existence finds support in modern superstring theories, both in compactification models and in theories with extended additional dimensions. Strings predicted in most grand unified models respond to external electromagnetic fields as thin superconducting wires. As they move through the cosmic magnetic fields, strings develop tremendous electric currents. Superconducting cosmic strings can serve as powerful sources of nonthermal radiation in a wide energy range, viz. as synchrotron radiation of electrons accelerated by bow shock waves which are created by the magnetosphere of strings moving relativistically through the intergalactic medium (IGM). Calculations of the expected radiation fluxes show that for typical parameters of the strings and the IGM the existing detectors can see loops at average string distances. According to our calculations they can also be observed if they are located in clusters of galaxies. (© 2013 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)