Massless String Research Articles

Towards massive field-theory amplitudes from the cohomology of pure spinor superspace

By analogy with the formula for the massless string disk amplitudes, we define massive field-theory tree amplitudes and conjecture that the BRST cohomology structure of pure spinor superspace fixes their form. We give evidence by deriving the pure spinor superspace expression of the massive field-theory n-point tree amplitude with one first-level massive and n − 1 massless states in two ways: 1) from BRST cohomology arguments in pure spinor superspace and 2) from the α′2 correction to the massless string amplitudes by inverting the unitarity constraint in superspace.

D-Brane effective Lagrangian in spacetimes with boundaries

AbstractIn this study, we explore the transformation of $$D_p$$ D p -branes to $$D_{p-1}$$ D p - 1 -branes under T-duality when the D-brane is embedded in a spacetime with a boundary. Our goal is to derive the higher-derivative corrections to the Dirac–Born–Infeld (DBI) Lagrangian for both the bulk and boundary terms. For the bulk terms, we calculate the $$\alpha '$$ α ′ corrections for the massless open string fields, up to the 8th order in the dimensionless Maxwell field strength. We demonstrate that the bulk Lagrangian can satisfy the T-duality constraint without residual total derivative terms in the base space. This determines the most general independent couplings of the massless open string fields in the bulk Lagrangian, encompassing 145 coupling constants, up to three parameters. Two of these parameters are physical and are determined by disk-level S-matrix elements, while the third is unphysical and can be eliminated by field redefinitions and integration by parts. The final result for the bulk Lagrangian consists of 49 couplings. For the boundary terms, the application of T-duality symmetry to massless open and closed string fields enables us to extend the DBI Lagrangian to include the boundary unit normal vector field $$n_\mu $$ n μ and its first derivative.

Does a physical pendulum ever act like a simple pendulum?

We show that for a physical pendulum comprising a massive sphere swinging from a massive string, there is, in general, a length of string for which its oscillatory period equals the period calculated by the simple pendulum model with a point-like mass swinging from a massless string whose model length equals the summed length of the real string and the sphere’s radius.

A Bare and Gravitationally Dressed Electron Formed from Kerr–Newman Black Hole

The Kerr–Newman (KN) electron model, based on the classical KN black hole solution, is modified by adding a “mirror” sheet of KN metric corresponding to a positron, that creates a heavy electron-positron vacuum core dressed by gravity, and allows us to consider the bare and dressed electron separately. The bare electron is formed as a massless relativistic ring string and is responsible for the wave properties of the electron, while the heavy supersymmetric vacuum core receives the additional mass-energy from two Wilson loops dragged by the KN gravitational field, thus creating a magnetically coupled monopole-antimonopole pair. As a result, the KN electron becomes consistent with wave nature of quantum electron and its gravitational interaction increases dramatically from Planck to Compton scale.

S-matrix on effective string and compactified membrane

Expanding Nambu–Goto action near infinitely long string vacuum one can compute scattering amplitudes of 2d massless fields representing transverse string coordinates. As was shown in (Dubovsky et al 2012 J. High Energy Phys. JHEP09(2012)044), the resulting S-matrix is integrable (provided appropriate local counterterms are added), in agreement with known free string spectrum and also with an interpretation of the static-gauge NG action as a deformation of a free massless theory. We consider a generalization of this computation to the case of a membrane, expanding its 3d action near an infinite membrane vacuum that has cylindrical shape (we refer to such membrane as ‘compactified’). Representing 3d fields as Fourier series in S 1 coordinate we get an effective 2d model in which the massless string modes are coupled to an infinite KK tower of massive 2d modes. We find that the resulting 2d S-matrix is not integrable already at the tree level. We also compute 1-loop scattering amplitude of massless string modes with all compactified membrane modes propagating in the loop. The result is UV finite and is a non-trivial function of the kinematic variables. In the large momentum limit or when the radius of S 1 is taken to infinity we recover the expression for the 1-loop scattering amplitude of the uncompactified membrane. We also consider a 2d model which is the deformation to the free theory with the same massless plus infinite massive tower of modes. The corresponding 2d S-matrix is found, as expected, to be integrable. Contribution to the special issue of Journal of Physics A: ‘Fields, Gravity, Strings and Beyond: In Memory of Stanley Deser’

T-duality of D-brane versus O-plane actions

It is known that, in the static gauge, the world-volume and the transverse Kaluza-Klein (KK) reductions of the O-plane effective actions on a circle satisfy the T-duality constraint for arbitrary base space background. In this paper we show that due to the presence of the second fundamental form in the D-brane couplings at order α′ and higher, the T-duality is satisfied only for a subclass of the couplings for arbitrary base space background. They are m = 0 couplings where m is the number of overset{sim }{B} -field (without derivative on it). For m > 0 couplings, the base space metric must be block-diagonal and the momentum U(1) vector field in the transverse reduction must be zero. However, the derivatives of the metric and the vector field are arbitrary.Using the assumption that the effective actions at the critical dimension are background independent, we then show that the T-duality constraint for the couplings at order α′ and for m = 0, fixes completely both bulk and boundary actions. These couplings indicate that the propagators of the massless open string fields receive α′-correction. We have also imposed the T-duality constraint on m = 1, 2, 3, 4 couplings. Because of the above restriction on the base space background in these cases, however, the T-duality can only partially fix the couplings for m > 0. This study shows that the Dirac-Born-Infeld (DBI) factor appears in both bulk and boundary actions at order α′.

Scale‐Separated AdS3 Vacua from G2‐Orientifolds Using Bispinors

AbstractIn this paper, minimal supersymmetric AdS3 solutions on G2‐orientifolds of type IIA and IIB supergravity are studied. These are obtained by techniques of the bispinor formalism. A straightforward argument is derived against AdS3 solutions in massless type IIA string theory on such G2‐backgrounds. Furthermore, it is shown that some of the AdS3 solutions in massive type IIA do admit a separation of scales, whereas the same cannot be said for the type IIB vacua. Finally, a formula for the 3d superpotential in the bispinor language is given that is valid for both type IIA and type IIB configurations. It is shown that the supersymmetry conditions of this superpotential lead back to the bispinor equations.

6D anomaly-free matter spectrum in F-theory on singular spaces

In this paper we study the 6d localized charged matter spectrum of F-theory directly on a singular elliptic Calabi-Yau 3-fold, i.e. without smoothing via resolution or deformation of the entire fibration. Given only the base surface, discriminant locus, and the SL(2, ℤ) local system, we propose a general prescription for determining the charged matter spectrum localized at intersections of seven-branes, using the technology of string junctions. More precisely, at each codimension-2 collision of seven-branes, we determine the local seven-brane content and compute the number of massless string junctions modulo the action of the SL(2, ℤ) monodromy. We find agreement with the predicted results from 6d anomaly cancellation in all cases considered. Examples include a generic Weierstrass model with arbitrary Kodaira fiber intersecting an I1, as well as cases with jointly charged matter localized at intersections of non-abelian seven-branes.

Interactions of strings on a T-fold

We consider the interactions of strings on T-folds from the world-sheet point of view which are exact in α′. As a concrete example, we take a model where the internal torus at the SO(8) enhancement point is twisted by T-duality (T-folded), and compute the scattering amplitudes of a class of massless strings. The four-point amplitudes involving both twisted and untwisted strings are obtained in a closed form in terms of the hyper- geometric function. By their factorization, the three-point coupling of the twisted and untwisted strings is found to be suppressed by the chiral momenta along the internal torus, and quantized in integer powers of 1/4. The asymptotic forms of the four-point amplitudes in high-energy limits are also obtained. Our results rely only on general properties of the asymmetric orbifold by the T-duality twist and of the Lie algebra lattice from the symmetry enhancement, and thus may be extended qualitatively to more general T-folds.

Normalization of D-instanton amplitudes

D-instanton amplitudes suffer from various infrared divergences associated with tachyonic or massless open string modes, leading to ambiguous contribution to string amplitudes. It has been shown previously that string field theory can resolve these ambiguities and lead to unambiguous expressions for D-instanton contributions to string amplitudes, except for an overall normalization constant that remains undetermined. In this paper we show that string field theory, together with the world-sheet description of the amplitudes, can also fix this normalization constant. We apply our analysis to the special case of two dimensional string theory, obtaining results in agreement with the matrix model results obtained by Balthazar, Rodriguez and Yin.

Supersymmetry, T-duality and heterotic \u03b1\u2032-corrections

Higher-derivative interactions and transformation rules of the fields in the effective field theories of the massless string states are strongly constrained by space-time symmetries and dualities. Here we use an exact formulation of ten dimensional mathcal{N} = 1 supergravity coupled to Yang-Mills with manifest T-duality symmetry to construct the first order α′-corrections of the heterotic string effective action. The theory contains a supersymmetric and T-duality covariant generalization of the Green-Schwarz mechanism that determines the modifications to the leading order supersymmetry transformation rules of the fields. We compute the resulting field-dependent deformations of the coefficients in the supersymmetry algebra and construct the invariant action, with up to and including four-derivative terms of all the massless bosonic and fermionic fields of the heterotic string spectrum.

Stringy-running-vacuum-model inflation: from primordial gravitational waves and stiff axion matter to dynamical dark energy

In previous works, we have derived a Running Vacuum Model (RVM) for a string Universe, which provides an effective description of the evolution of 4-dimensional string-inspired cosmologies from inflation till the present epoch. In the context of this “stringy RVM” version, it is assumed that the early Universe is characterised by purely gravitational degrees of freedom, from the massless gravitational string multiplet, including the antisymmetric tensor field. The latter plays an important role, since its dual gives rise to a ‘stiff’ gravitational axion “matter”, which in turn couples to the gravitational anomaly terms, assumed to be non-trivial at early epochs. In the presence of primordial gravitational wave (GW) perturbations, such anomalous couplings lead to an RVM-like dynamical inflation, without external inflatons. We review here this framework and discuss potential scenarios for the generation of such primordial GW, among which the formation of unstable domain walls, which eventually collapse in a non-spherical-symmetric manner, giving rise to GW. We also remark that the same type of “stiff” axionic matter could provide, upon the generation of appropriate potentials during the post-inflationary eras, (part of) the Dark Matter (DM) in the Universe, which could well be ultralight, depending on the parameters of the string-inspired model. All in all, the new (stringy) mechanism for RVM inflation preserves the basic structure of the original (and more phenomenological) RVM, as well as its main advantages: namely, a mechanism for graceful exit and for generating a huge amount of entropy capable of explaining the horizon problem. It also predicts axionic DM and the existence of mild dynamical Dark Energy (DE) of quintessence type in the present universe, both being “living fossils” of the inflationary stages of the cosmic evolution. Altogether the modern RVM appears to be a theoretically sound (string-based) approach to cosmology with a variety of phenomenologically testable consequences.

The harder they fall, the bigger they become: tidal trapping of strings by microstate geometries

We consider the fate of a massless (or ultra-relativistic massive) string probe propagating down the BTZ-like throat of a microstate geometry in the D1-D5 system. Far down the throat, the probe encounters large tidal forces that stretch and excite the string. The excitations are limited by the very short transit time through the region of large tidal force, leading to a controlled approximation to tidal stretching. We show that the amount of stretching is proportional to the incident energy, and that it robs the probe of the kinetic energy it would need to travel back up the throat. As a consequence, the probe is effectively trapped far down the throat and, through repeated return passes, scrambles into the ensemble of nearby microstates. We propose that this tidal trapping may lead to weak gravitational echoes.

The Dirac Electron Consistent with Proper Gravitational and Electromagnetic Field of the Kerr–Newman Solution

The Dirac electron is considered as a particle-like solution consistent with its own Kerr–Newman (KN) gravitational field. In our previous works we considered the regularized by López KN solution as a bag-like soliton model formed from the Higgs field in a supersymmetric vacuum state. This bag takes the shape of a thin superconducting disk coupled with circular string placed along its perimeter. Using the unique features of the Kerr–Schild coordinate system, which linearizes Dirac equation in KN space, we obtain the solution of the Dirac equations consistent with the KN gravitational and electromagnetic field, and show that the corresponding solution takes the form of a massless relativistic string. Obvious parallelism with Heisenberg and Schrödinger pictures of quantum theory explains remarkable features of the electron in its interaction with gravity and in the relativistic scattering processes.

Relativistic electrodynamics without Lorentz transformations

The object of this exercise is to show that the force between moving charges can be obtained in a very different way than is usual without recourse to the Lorentz transformations. We suppose the spinning electron creates two massless strings which connect to another electron either stationary or moving. Each string carries a wave, one the de Broglie wave and the other a wave that moves at c that mediates the force between charges in addition to guiding the electron’s motion.

Massless Cosmic Strings in Spacetimes with Global Parabolic Isometries

A class of curved spacetimes with global parabolic isometries (GPI) is introduced. These isometries have fixed point sets on two-dimensional null surfaces which can be interpreted as worldsheets of massless cosmic strings. Back reaction effects of the strings in such spacetimes can be described exactly, in terms of a nontrivial holonomy at the worldsheet. We show that the GPI spacetimes are type $N$ geometries of the Petrov classification. We describe a number of features of these spacetimes, including properties of Killing horizons associated to GPI. As an example, we consider a circular massless cosmic string in the de Sitter universe and present the metric in new coordinates centered at the string worldsheet.

Self-force from a conical singularity, without renormalization

We develop an approach to calculate the self-force on a charged particle held in place in a curved spacetime, in which the particle is attached to a massless string and the force is measured by the string's tension. The calculation is based on the Weyl class of static and axially symmetric spacetimes, and the presence of the string is manifested by a conical singularity; the tension is proportional to the angular deficit. A remarkable and appealing aspect of this approach is that the calculation of the self-force requires no renormalization of the particle's field. This is in contract with traditional methods, which incorporate a careful and elaborate subtraction of the singular part of the field. We implement the approach in a number of different situations. First, we examine the case of an electric charge in Schwarzschild spacetime, and recover the classic Smith-Will force in addition to a purely gravitational contribution to the self-force. Second, we turn to the case of electric and magnetic dipoles in Schwarzschild spacetime, and correct expressions for the self-force previously obtained in the literature. Third, we replace the electric charge by a scalar charge, and recover Wiseman's no-force result, which we generalize to a scalar dipole. And fourth, we calculate the force exerted on extended bodies such as Schwarzschild black holes and Janis-Newman-Winicour objects, which describe scalarized naked singularities.

Quantum anomalies in string-inspired running vacuum universe: Inflation and axion dark matter

In this letter, we elaborate further on a Cosmological “Running-Vacuum” type model for the Universe, suggested previously by the authors [1,2], within the context of a string-inspired effective theory in the presence of a Kalb-Ramond (KR) gravitational axion field which descends from the antisymmetric tensor of the massless gravitational string multiplet. In the presence of this field, which has anomalous CP violating interactions with the gravitons, primordial gravitational waves induce gravitational anomalies, which in turn are responsible for the appearance of H2 and H4 contributions to the vacuum energy density, these terms being characteristic of generic “running-vacuum-model (RVM) type”, where H is the Hubble parameter. In this work we prove in detail the appearance of the H4 terms due to gravitational-anomaly-induced condensates in the energy density of the primordial Universe, which can self-consistently induce inflation, and subsequent exit from it, according to the generic features of RVM. We also argue in favour of the robustness of our results, which were derived within an effective low-energy field theory approach, against Ultra Violet completion of the theory. During the radiation and matter-dominated eras, gravitational anomalies cancel, as required for the consistency of the quantum matter/radiation field theory. However, chiral and QCD-axion-type anomalies survive and have important consequences for both cosmic magnetogenesis and axionic dark matter in the Universe. Finally, the stringy RVM scenario presented here predicts quintessence-like dynamical dark energy for the current Universe, which is compatible with the existing fitting analyses of such model against observations.

String correlators: recursive expansion, integration-by-parts and scattering equations

We further elaborate on the general construction proposed in [1], which connects, via tree-level double copy, massless string amplitudes with color-ordered QFT amplitudes that are given by Cachazo-He-Yuan formulas. The current paper serves as a detailed study of the integration-by-parts procedure for any tree-level massless string correlator outlined in the previous letter. We present two new results in the context of heterotic and (compactified) bosonic string theories. First, we find a new recursive expansion of any multitrace mixed correlator in these theories into a logarithmic part corresponding to the CHY integrand for Yang-Mills-scalar amplitudes, plus correlators with the total number of traces and gluons decreased. By iterating the expansion, we systematically reduce string correlators with any number of subcycles to linear combinations of Parke-Taylor factors and similarly for the case with gluons. Based on this, we then derive a CHY formula for the corresponding (DF)2 + YM + ϕ3 amplitudes. It is the first closed-form result for such multitrace amplitudes and thus greatly extends our result for the single-trace case. As a byproduct, it gives a new CHY formula for all Yang-Mills-scalar amplitudes. We also study consistency checks of the formula such as factorizations on massless poles.

Enhancing Scientific Inquiry by Mathematical Reasoning: Case of Applying Limits to Model Motion of a System of Objects

Mathematics and physics constitute parts of STEM that are widely recognized as a leading platform in contemporary education. While the effects of the methods of mathematics on discoveries in physics are unquestionable, using mathematical reasoning to enhance understanding of physics is still being researched. This study is posited to contribute to that research, and it investigates students’ skills to apply limiting the analysis to determine the acceleration of two objects connected by a massless string. Twenty-five (N=24) first-year students enrolled in the algebra-based college physics course took part in this case study. While the pretest showed that the students did not consider limits to answer questions that required limiting analysis, designed instructional unit whose goal was to bring forth the technique helped apply limits and made the solution process more explicit. Posttests results supported the study thesis that integrating more sophisticated mathematical apparatus into the analysis of physical systems opens a gate not only for advancing students’ scientific inquiry skills, but also their general STEM disposition.