Superstring Research Articles

Derivation of Exact Results of Gauge Theories through Superstring Theories

Derivation of Exact Results of Gauge Theories through Superstring Theories

A note on the modified uncertainity principle

We briefly examine the modification to Heisenberg’s uncertainity principle that is required in quantum super string theory, quantum gravity, and more generally, where there is a minimum spacetime extension.

ASTROD–AN OVERVIEW

The objectives of the Astrodynamical Space Test of Relativity using Optical Devices (ASTROD) Mission concept are threefold. The first objective is to discover and explore fundamental physical laws governing matter, space and time via testing relativistic gravity with 3-6 orders of magnitude improvement. Relativistic gravity is an important cornerstone of physics, astronomy and cosmology. Its improved test is crucial to cosmology and modern theories of gravitation including superstring theories. Included in this objective is the precise determination of the relativistic parameters β and γ, the improved measurement of Ġ and a precise determination of an anomalous, constant acceleration directed towards the Sun. The second objective of the ASTROD mission is the high-precision measurement of the solar-system parameter. This includes: (i) a measurements of solar angular momentum via Lense-Thirring effect and the detection of solar g-mode oscillations via their changing gravity field, thus, providing a new eye to see inside the Sun; (ii) precise determination of the planetary orbit elements and masses; (iii) better determination of the orbits and masses of major asteroids. These measurements give better solar dynamics and probe the origin of our solar system. The third objective is to detect and observe gravitational waves from massive black holes and galactic binary stars in the frequency range 50 μHz to 5 mHz. Background gravitational -waves will also be explored. A desirable implementation is to have two spacecraft in separate solar orbit carrying a payload of a proof mass, two telescopes, two 1-2 W lasers, a clock and a drag-free system, together with an Earth reference system. the two spacecraft range coherently with the Earth reference system using lasers. When they are near, they range coherently to each other. The Earth reference system could be ground stations, Earth satellites and/or spacecraft near Earth-Sun Lagrange points. In this overview, we discuss the payload concept, the technological requirements, technological developments, orbit design, orbit simulation, the measurement of solar angular momentum, the gravitational-wave detection sensitivity, and the solar g-mode detection possibility for this mission concept. A simplified mission, Mini-ASTROD with one spacecraft ranging optically with ground stations, together with Super-ASTROD with four spacecraft of 5 AU (Jupiter-like) orbits, will be mentioned in the end. Super-ASTROD is a dedicated low-frequency gravitational-wave detection concept. For Mini-ASTROD, the first objective of ASTROD will be largely achieved; the second objective will be partially achieved; for gravitational wave detection, the sensitivity will be better than the present-day sensitivity using Doppler tracking by radio waves.

The open superstring 5-point amplitude revisited

We derive the complete five-gluon scattering amplitude at tree level, within the context of Open Superstring theory. We find the general expression in terms of kinematic factors, and also find its complete expansion up to ${\cal O}({\alpha'}^3)$ terms. We use our scattering amplitude to test three non-equivalent ${\cal O}({\alpha'}^3)$ effective lagrangians that have recently been matter of some controversy.

Superstrings on PP-Wave Backgrounds and Symmetric Orbifolds

We study the superstring theory on pp-wave background with NSNS-flux that is realized as the Penrose limit of AdS_3 x S^3 x M^4, where M^4 is T^4 or T^4/Z_2(~ K3). Quantizing this system in the covariant gauge, we explicitly construct the space-time supersymmetry algebra and the complete set of DDF operators. We analyse the spectrum of physical states by using the spectrally flowed representations of current algebra. This spectrum is classified by the ``short string sectors'' and the ``long string sectors'' as in AdS_3 string theory. The states of the latter propagate freely along the transverse plane of pp-wave background, but the states of the former do not. We compare the short string spectrum with the BPS and almost BPS states which have large R-charges in the symmetric orbifold conformal theory, which is known as the candidate of dual theory of superstrings on AdS_3 x S^3 x M^4. We show that every short string states can be embedded successfully in the single particle Hilbert space of symmetric orbifold conformal theory.

Integrable models of black holes and their generalizations in the theories of supergravity and superstrings

A new class of integrable models of (0+1)-and (1+1)-dimensional dilaton gravity coupled to any number of scalar fields is introduced and briefly discussed. These models can be reduced to a system of Liouville equations that are coupled through energy and momentum constraints. The constraints can be explicitly solved, thus giving an explicit analytic solution of the theory. In particular, these integrable models describe spherically symmetric black holes and branes of supergravity theories in higher dimensions.

On heterotic orbifolds,M-theory and type I' brane engineering

Horava-Witten M theory↔ heterotic string duality poses special problems for the twisted sectors of heterotic orbifolds. In our previous paper [1] we explained how in M theory the twisted states couple to gauge fields apparently living on M9 branes at both ends of the eleventh dimension at the same time. The resolution involves 7D gauge fields which live on fixed planes of the (T4/N) × (1/2) × 5,1 orbifold and lock onto the 10D gauge fields along the intersection planes. The physics of such intersection planes does not follow directly from the M theory but there are stringent kinematic constraints due to duality and local consistency, which allowed us to deduce the local fields and the boundary conditions at each intersection. In this paper we explain various phenomena at the intersection planes in terms of duality between Horava-Witten and type I' superstring theories. The orbifold fixed planes are dual to stacks of D6 branes, the M9 planes are dual to O8 orientifold planes accompanied by D8 branes, and the intersections are dual to brane junctions. We engineer several junction types which lead to distinct patterns of 7D/10D gauge field locking, 7D symmetry breaking and/or local 6D fields. Another aspect of brane engineering is putting the junctions together; sometimes, the combined effect is rather spectacular from the HW point of view and the quantum numbers of some twisted states have to `bounce' off both ends of the eleventh dimension before their heterotic identity becomes clear. Some models involve D6/O8 junctions where the string coupling diverges towards the orientifold plane. We use the heterotic ↔ HW ↔ I' duality to predict what should happen at such junctions. For example, pinning down an NS5 half-brane to a definite location on a λ = ∞ O8 plane requires precisely four D6 branes.

Superstrings in curved Ramond-Ramond backgrounds

We discuss the main issues related to understanding closed string spectrum in Ramond-Ramond backgrounds on the example of AdS5 × S5 and and its special limit – the maximally supersymmetric plane-wave background with constant null 5-form field strength. As we describe, in the latter case the spectrum can be found explicitly. We compare the plane-wave string spectrum with the expected form of the light-cone gauge spectrum of the AdS5 × S5 superstring and comment on the tensionless string limit.

Introduction to Branes and M-Theory for Relativists and Cosmologists

We review the recent developments in superstrings. We start with a brief summary of various consistent superstring theories and discuss T-duality which necessarily leads to the presence of D-branes. The properties of D-branes are summarized and we discuss how these suggest the existence of 11-dimensional quantum theory, M-theory, which is believed to give rise to various superstrings as perturbative expansions around particular backgrounds in the theory. We also discuss the interpretation of brane solutions as black holes in string theories and statistical explanation of Bekenstein-Hawking entropy. The idea behind this interpretation is that there is a fundamental duality between closed (gravity) and open (gauge theory) string degrees of freedom, one of whose manifestation is what is kown as AdS/CFT correspondence. The idea is used to discuss the greybody factors for BTZ black holes. Finally the entropy of various balck holes are discussed in connection with Cardy-Verlinde formula.

Non-BPS D-branes and M-theory

A dual pair of supersymmetric string theories that involves an asymmetric orbifold and an orientifold of Type II is considered. The D-branes of the orbifold theory (that were recently determined by Gutperle) are all non-BPS and do not carry any conserved gauge charges. It is shown that they carry non-trivial K-theory charges, and that they can be understood in terms of branes wrapping certain homology classes of the M-theory compactification. Using the adiabatic argument, dual partners of some of these non-BPS D-branes are proposed. The relations between these dual states are found to be in agreement with the M-theory description of the D-branes.

Supersymmetry and the systematics of T-duality rotations in type-II superstring theories

We describe a systematic method of studying the action of the T-duality group O( d, d) on space-time fermions and R-R field strengths and potentials in type-II string theories, based on space-time supersymmetry. The formalism is then used to show that the couplings of non-Abelian D-brane charges to R-R potentials can be described by an appropriate Clifford multiplication.

Quantum superstrings and quantized fractal space-time

Though quantum superstring (QSS) theory has shown promise, there are some puzzling features like the extra dimensions, which are curled up in the Kaluza–Klein sense. On the other hand a recent formulation of what may be called quantized fractal space-time (QFST) leads to a surprising interface with QSS – we deal with the Planck length, the same number of extra dimensions and an identical non-commutative geometry. It is shown that this is not accidental. On the contrary it gives us insight into the otherwise inexplicable features of QSS.

COFRAME TELEPARALLEL MODELS OF GRAVITY: EXACT SOLUTIONS

The superstring and superbrane theories include gravity as a necessary and fundamental part of a (future) unified field theory. Thus it is important to consider the alternative representations of general relativity as well as the alternative models of gravity.We study the coframe teleparallel theory of gravity with a most general quadratic Lagrangian. The coframe field on a differentiable manifold is a basic dynamical variable. A metric tensor as well as a metric compatible connection is generated by a coframe in a unique manner.The Lagrangian is a general linear combination of Weitzenböck's quadratic invariants with free dimensionless parameters ρ1, ρ2, ρ3. Every independent term of the Lagrangian is a global SO(1,3)-invariant 4-form. For a special choice of parameters which confirms with the local SO(1,3) invariance this theory gives an alternative description of Einsteinian gravity — teleparallel equivalent of GR.The field equations of the theory is studied by a "diagonal" coframe ansatz which is a subclass of a most general spherical-nsymmetric Einstein–Mayer ansatz. The restricted Lagrangian depends only on two free parameters ρ1, ρ3.We obtain a formula for scalar curvature of a pseudo-Riemannian manifold with a metric constructed from the static "diagonal" solution of the field equation. It is proved that the sign of the scalar curvature depends only on a relation between the parameters ρ1and ρ3. Thus by a specific choice of free parameters a manifold of positive or negative curvature can be obtained. The scalar curvature vanishes only for a subclass of models with ρ1=0. This subclass includes the teleparallel equivalent of GR.We obtain the explicit form of all spherically symmetric static solutions of the "diagonal" type to the field equations for an arbitrary choice of free parameters. We prove that the unique asymptotic-flat solution with Newtonian limit is the Schwarzschild solution that holds for a subclass of teleparallel models with ρ1=0. Thus the Yang–Mills-type term of the general quadratic coframe Lagrangian should be rejected.

Nonrelativistic closed string theory

We construct a Galilean invariant nongravitational closed string theory whose excitations satisfy a nonrelativistic dispersion relation. This theory can be obtained by taking a consistent low energy limit of any of the conventional string theories, including the heterotic string. We give a finite first order worldsheet Hamiltonian for this theory and show that this string theory has a sensible perturbative expansion, interesting high energy behavior of scattering amplitudes and a Hagedorn transition of the thermal ensemble. The strong coupling duals of the Galilean superstring theories are considered and are shown to be described by an eleven-dimensional Galilean invariant theory of light membrane fluctuations. A new class of Galilean invariant nongravitational theories of light-brane excitations are obtained. We exhibit dual formulations of the strong coupling limits of these Galilean invariant theories and show that they exhibit many of the conventional dualities of M theory in a nonrelativistic setting.

Gravitational instantons, extra dimensions and form fields.

A broad class of higher dimensional instanton solutions are found for a theory which contains gravity, a scalar field and antisymmetric tensor fields of arbitrary rank. The metric used, a warp product of an arbitrary number of any compact Einstein manifolds, includes many of great interest in particle physics and cosmology. For example 4D FRW universes with additional dimensions compactified on a Calabi-Yau three fold, a torus, a compact hyperbolic manifold or a sphere are all included. It is shown that the solution of this form which dominates the Hartle Hawking path integral is always a higher dimensional generalisation of a Hawking Turok instanton when the potential of the scalar field is such that these instantons can exist. On continuation to Lorentzian signature such instantons give rise to a spacetime in which all of the spatial dimensions are of equal size and where the spatial topology is that of a sphere. The extra dimensions are thus not hidden. In the case where the potential for the scalar field is generated solely by a dilatonic coupling to the form fields we find no integrable instantons at all. In particular we find no integrable solutions of the type under consideration for the supergravity theories which are the low energy effective field theories of superstrings.

Two-dimensional conformal field theory and beyond. Lessons from a continuing fashion

Two-dimensional conformal field theory (CFT) has several sources: the search for simple examples of quantum field theory, the description of surface critical phenomena, and the study of (super)string vacua.

BOOK REVIEW: String Theory. Volume I: An Introduction to the Bosonic String. by Joseph Polchinski. String Theory. Volume II: Superstring Theory And Beyond. by Joseph Polchinski

BOOK REVIEW: String Theory. Volume I: An Introduction to the Bosonic String. by Joseph Polchinski. String Theory. Volume II: Superstring Theory And Beyond. by Joseph Polchinski

Hagedorn behaviour of little string theory from string corrections to NS5-branes

Following the conjectured duality between near-horizon NS5-branes and little string theory, the string-corrected thermodynamics of near-horizon NS5-branes is studied and found to agree with the statistical thermodynamics of a 5+1 dimensional supersymmetric string theory near the Hagedorn temperature. Specifically, tree-level corrections to the temperature are argued to vanish, in accordance with the duality, while the one-loop string correction to the NS5-brane thermodynamics is shown to generate the correct temperature dependence of the entropy.

On the existence and stability of maximally symmetric cosmological solutions in superstring theories

We study the existence and stability of maximally symmetric cosmological solutions in bosonic, heterotic and supersymmetric string theories in the effective Lagrangian approach. We find that, at tree level, de Sitter and anti-de Sitter solutions are excluded for all theories and only Minkowsky spacetime remains a (stable) solution. For type IIB superstrings, however, such solutions exist if the exact higher-curvature corrections to the lowest order effective action, which contain loop as well as non-perturbative D-instanton corrections, are included on the basis of SL(2,Z) invariance.

Evidence for nonvanishing cosmological constant in nonSUSY superstring models

We reanalyse the computation of the cosmological constant $\Lambda$ at two loops in recently proposed Superstring models without massless gravitini, both in the theta-function based formalism and by a detailed computation in the more explicit hyperelliptic description of the underlying genus two Riemann surface. $\Lambda$ is expressed as the integral over the surface moduli of an amplitude which is zero if susy is not completely broken, but we find it to be nonvanishing in the susy breaking models which can be given an explicitly workable fermionic formulation. Thus unfortunately the issue of getting realistic and perturbatively viable models from Superstring Theory remains open.