Four-dimensional String Research Articles

Higher-point gauge-theory couplings of massive spin-2 states in four-dimensional string theories

We explicitly compute the Neveu-Schwarz sector conventional type-I superstring tree-level amplitudes at five points after compactifying to 4D, express the QFT building block in the helicity basis, and give several attempts toward arbitrary n points. More specifically, we consider the interaction of one first excited level and otherwise massless states of conventional type-I superstrings, where the four-dimensional states can, for instance, be realized via D3 branes. We construct the amplitude by using the Berends-Giele currents. From the recursion of Berends-Giele currents, we can generate the higher point amplitude. We also apply the BCFW recursion with massive external legs shifted and get the amplitude for arbitrary n points. Published by the American Physical Society 2024

Theory and Phenomenology of a Four-Dimensional String–Corrected Black Hole

We construct an effective four-dimensional string-corrected black hole (4D SCBH) by rescaling the string coupling parameter in a D-dimensional Callan–Myers–Perry black hole. From the theoretical point of view, the most interesting findings are that the string corrections coincide with the so-called generalized uncertainty principle (GUP) corrections to black hole solutions, Bekenstein–Hawking entropy acquires logarithmic corrections, and that there exists a critical value of the coupling parameter for which the black hole temperature vanishes. We also find that, due to the string corrections, the nature of the central singularity may be altered from space-like to time-like singularity. In addition, we study the possibility of testing such a black hole with astrophysical observations. Since the dilaton field does not decouple from the metric, it is not a priori clear that the resulting 4D SCBH offers only small corrections to the Schwarzschild black hole. We used motion of the S2 star around the black hole at the center of our galaxy to constrain the parameters (the string coupling parameter and ADM mass) of the 4D SCBH. To test the weak gravity regime, we calculate the deflection angle in this geometry and apply it to gravitational lensing. To test the strong field regime, we calculate the black hole shadow radius. While we find that the observables change as we change the string coupling parameter, the magnitude of the change is too small to distinguish it from the Schwarzschild black hole. With the current precision, to the leading order terms, the 4D SCBH cannot be distinguished from the Schwarzschild black hole.

Torsion in String-Inspired Cosmologies and the Universe Dark Sector

Several aspects of torsion in string-inspired cosmologies are reviewed. In particular, its connection with fundamental, string-model independent, axion fields associated with the massless gravitational multiplet of the string are discussed. It is argued in favour of the role of primordial gravitational anomalies coupled to such axions in inducing inflation of a type encountered in the “Running-Vacuum-Model (RVM)” cosmological framework, without fundamental inflaton fields. The gravitational-anomaly terms owe their existence to the Green–Schwarz mechanism for the (extra-dimensional) anomaly cancellation, and may be non-trivial in such theories in the presence of (primordial) gravitational waves at early stages of the four-dimensional string universe (after compactification). The paper also discusses how the torsion-induced stringy axions can acquire a mass in the post inflationary era, due to non-perturbative effects, thus having the potential to play the role of (a component of) dark matter in such models. Finally, the current-era phenomenology of this model is briefly described with emphasis placed on the possibility of alleviating tensions observed in the current-era cosmological data. A brief phenomenological comparison with other cosmological models in contorted geometries is also made.

Quantum fluctuations of the metric, three-geometries and conformal embeddings in four-manifolds

In this paper, connections between the path integrals for four-dimensional quantum gravity and string theory are emphasized. It is shown that there is a natural relation between these two path integrals based on the theorems on embeddings of two-dimensional surfaces in four dimensions and four-dimensional manifolds in ten dimensions. The isometry groups of the three-geometries that are spatial hypersurfaces confomally embedded in the four-manifolds are required to be subgroups of [Formula: see text], which is the invariance group of the Pfaffian differential system satisfied by one form in the cotangent bundles on the four-manifolds. Based on this and other physical conditions, the three-geometries are restricted to be [Formula: see text], [Formula: see text] and [Formula: see text] with a boundary, which may be included in the quantum gravitational path integral over four-manifolds which are closed at initial times followed by an exponential expansion compatible with supersymmetry.

Quasi-Jacobi forms, elliptic genera and strings in four dimensions

We investigate the interplay between the enumerative geometry of Calabi-Yau fourfolds with fluxes and the modularity of elliptic genera in four-dimensional string theories. We argue that certain contributions to the elliptic genus are given by derivatives of modular or quasi-modular forms, which may encode BPS invariants of Calabi-Yau or non-Calabi-Yau threefolds that are embedded in the given fourfold. As a result, the elliptic genus is only a quasi-Jacobi form, rather than a modular or quasi-modular one in the usual sense. This manifests itself as a holomorphic anomaly of the spectral flow symmetry, and in an elliptic holomorphic anomaly equation that maps between different flux sectors. We support our general considerations by a detailed study of examples, including non-critical strings in four dimensions.For the critical heterotic string, we explain how anomaly cancellation is restored due to the properties of the derivative sector. Essentially, while the modular sector of the elliptic genus takes care of anomaly cancellation involving the universal B-field, the quasi-Jacobi one accounts for additional B-fields that can be present.Thus once again, diverse mathematical ingredients, namely here the algebraic geometry of fourfolds, relative Gromow-Witten theory pertaining to flux backgrounds, and the modular properties of (quasi-)Jacobi forms, conspire in an intriguing manner precisely as required by stringy consistency.

BKM Lie superalgebras from counting twisted CHL dyons – II

We revisit earlier work by one of us which lead to a periodic table of Borcherds-Kac-Moody algebras that appeared in the context of the refined generating function of quarter-BPS states (dyons) in N=4 supersymmetric four-dimensional string theory. We make new additions to the periodic table by making use of connections with generalized Mathieu moonshine as well as umbral moonshine. We show the modularity of some Siegel modular forms that appear in umbral moonshine associated with Niemeier lattices constructed from A-type root systems and further show that the same Siegel modular forms appear for generalized Mathieu moonshine in some cases. We argue for the existence of a new kind of BKM Lie superalgebras that arise from the dyon generating functions for the Z5 and Z6 CHL orbifolds.

Aspects of nonsupersymmetric string phenomenology

We consider a big class of chiral four-dimensional string models which bear [Formula: see text] gauge symmetry. Supersymmetry (SUSY) is spontaneously broken via the Scherk–Schwarz mechanism associated with two large internal dimensions. We study two central issues in nonsupersymmetric string phenomenology: the suppression of the cosmological constant and the decompactification problem. We identify a subclass of chiral nonsupersymmetric models with fermion–boson degeneracy leading to exponentially suppressed cosmological constant. In addition, we propose a novel solution to the decompactification problem related to the cancellation of the linear growth of the gauge part of the thresholds with a similar growth of the universal part. We show that the proposed mechanism resolves the decompactification problem related to the non-Abelian gauge couplings in approximately 40% of the models under consideration.

Magnetic Dilaton Rotating Strings in the Presence of Exponential Nonlinear Electrodynamics

In this paper, we construct a new class of four-dimensional spinning magnetic dilaton string solutions which produces a longitudinal nonlinear electromagnetic field. The Lagrangian of the matter field has the exponential form. We study the physical properties of the solution in ample details. Geometrical, causal and geodisical structures of the solutions are investigated, separately. We confirm that the spacetime is both null and geodesically complete. We find that these solutions have no curvature singularity and no horizon, but have a conic geometry. We investigate the effects of variation of charge and the intensity of the dilaton field, on the deficit angle. Due to the presence of the dilaton field, the asymptotic behavior of the solutions are neither flat nor (anti-) de Sitter [(A)dS]. Furthermore, we extend our study to the higher dimensions and obtain the (n+1)-dimensional magnetic rotating dilaton strings with k≤[n/2] rotation parameters and calculate conserved quantities of the solutions. Although these solutions are not asymptotically (A)dS, we use counterterm method to calculate conserved quantities. We also calculate electric charge and show that the net electric charge of the spinning string is proportional to the rotating parameter and the electric field only exists when the rotation parameter does not vanish.

Magnetic dilaton rotating strings in the presence of logarithmic nonlinear electrodynamics

We consider the Einstein-dilaton gravity in the presence of logarithmic nonlinear electrodynamics, and find a new class of four-dimensional spinning magnetic dilaton string solutions which produces a longitudinal nonlinear electromagnetic field. We find that these solutions have no curvature singularity and no horizon, but have a conic geometry. The net electric charge of the spinning string is proportional to the rotating parameter and the electric field only exists when the rotation parameter does not vanish. We investigate the effects of the nonlinearity as well as the dilaton field on the physical properties of the spacetime. Because of the presence of the dilaton field, the asymptotic behavior of the solutions are neither flat nor (anti)-de Sitter. We find the deficit angle of the spacetime and investigate the effects of dilaton and nonlinear electrodynamics on the value of the deficit angle. We use the counterterm method to calculate the conserved quantities of the solutions. Furthermore, we extend our study to the higher dimensions and obtain the $$(n+1)$$ -dimensional magnetic rotating dilaton strings with $$k\le [n/2]$$ rotation parameters and calculate electric charge and conserved quantities of the solutions.

Towards a nonsupersymmetric string phenomenology

Over the past three decades, considerable effort has been devoted to studying the rich and diverse phenomenologies of heterotic strings exhibiting spacetime supersymmetry. Unfortunately, during this same period, there has been relatively little work studying the phenomenologies associated with their nonsupersymmetric counterparts. The primary reason for this relative lack of attention is the fact that strings without spacetime supersymmetry are generally unstable, exhibiting large one-loop dilaton tadpoles. In this paper, we demonstrate that this hurdle can be overcome in a class of tachyon-free four-dimensional string models realized through coordinate-dependent compactifications. Moreover, as we shall see, it is possible to construct models in this class whose low-lying states resemble the Standard Model (or even potential unified extensions thereof)---all without any light superpartners, and indeed without supersymmetry at any energy scale. The existence of such models thus opens the door to general studies of nonsupersymmetric string phenomenology, and in this paper we proceed to discuss a variety of theoretical and phenomenological issues associated with such nonsupersymmetric strings. On the theoretical side, we discuss the finiteness properties of such strings, the general characteristics of their mass spectra, the magnitude and behavior of their one-loop cosmological constants, and their interpolation properties. By contrast, on the phenomenological side, the properties we discuss are more model-specific and include their construction techniques, their natural energy scales, their particle and charge assignments, and the magnitudes of their associated Yukawa couplings and scalar masses.

A DUAL FOUR-DIMENSIONAL SUPERSTRING

The 26-dimensional bosonic string, first suggested by Nambu and Goto, is reduced to a four-dimensional superstring by using two species of six and five Majorana fermions as proposed by Deo. These two species of fermions differ in their "neutrino-like" phase, and are vectors in the bosonic representation SO (d-1, 1). Using Polchinski's equivalence between operators and states, we can write the Virasoro generators for four-dimensional string theory. The theory is shown to give the same results as given by other superstrings and also reveals the well-known aspects of four-dimensional string theory. The bosons and the fermions are found to be the basis for constructing this string theory which includes gravity and exhibits strong–weak coupling duality as well as the usual electric–magnetic duality. This formalism is used to calculate the metric tensor as well as the entropy–area relation for a black hole.

Dark energy as an off-shell tachyon background in four-dimensional strings

We consider a time-dependent bosonic string in graviton, dilaton and tachyon backgrounds, for which it was already shown that conformal invariance is respected to all orders in α′ and in any space–time dimension. Assuming that the tachyon is off-shell, we show in this note that the specific time-homogeneity of the corresponding space–time effective action leads to a power-law expanding Universe, that can be interpreted as dark energy. We arrive at this result without requiring the knowledge of the structure of the string effective action, which is not known to all orders in α′. Moreover, in our approach, the background configurations are consistent in a four-dimensional space–time, without any need for extra dimensions.

(Unoriented) T-folds with few T's

We use the combined action of 2-chiral reflections (T-dualities) and shifts to build = 1,2 supersymmetric four-dimensional string compactifications with few moduli. In particular, we consider 24 asymmetric orbifolds of Type IIB on the maximal torus of SO(12) that mimic = 2 Calabi-Yau compactifications with small ``effective'' Hodge numbers starting from (h11,h21) = (1,1). We analyze possible unoriented projections, providing Type I examples with or without open strings. = 1 oriented asymmetric shift-orbifolds of Type IIB with few chiral multiplets are also presented.

Curvature-corrected dilatonic black holes and black hole—string transition

We investigate extremal charged black hole solutions in the four-dimensional string frame Gauss-Bonnet gravity with the Maxwell field and the dilaton. Without curvature corrections, the extremal electrically charged dilatonic black holes have singular horizon and zero Bekenstein entropy. When the Gauss-Bonnet term is switched on, the horizon radius expands to a finite value provided curvature corrections are strong enough. Below a certain threshold value of the Gauss-Bonnet coupling the extremal black hole solutions cease to exist. Since decreasing Gauss-Bonnet coupling corresponds to decreasing string coupling $g_s$, the situation can tentatively be interpreted as classical indication on the black hole -- string transition. Previously the extremal dilaton black holes were studied in the Einstein-frame version of the Gauss-Bonnet gravity. Here we work in the string frame version of this theory with the S-duality symmetric dilaton function as required by the heterotic string theory.

N-flation

The presence of many axion fields in four-dimensional string vacua can lead to a simple,radiatively stable realization of chaotic inflation.

Simple de Sitter solutions

We present a framework for de Sitter model building in type IIA string theory, illustrated with specific examples. We find metastable de Sitter (dS) minima of the potential for moduli obtained from a compactification on a product of two nil three-manifolds (which have negative scalar curvature) combined with orientifolds, branes, fractional Chern-Simons forms, and fluxes. As a discrete quantum number is taken large, the curvature, field strengths, inverse volume, and four-dimensional string coupling become parametrically small, and the de Sitter Hubble scale can be tuned parametrically smaller than the scales of the moduli, Kaluza Klein (KK), and winding mode masses. A subtle point in the construction is that although the curvature remains consistently weak, the circle fibers of the nilmanifolds become very small in this limit (though this is avoided in illustrative solutions at modest values of the parameters). In the simplest version of the construction, the heaviest moduli masses are parametrically of the same order as the lightest KK and winding masses. However, we provide a method for separating these marginally overlapping scales, and more generally the underlying supersymmetry of the model protects against large corrections to the low-energy moduli potential.

Antisymmetric-tensor and electromagnetic effects in an α′-non-perturbative four-dimensional string cosmology

Starting from an exact (in the Regge slope α′) functional method for a bosonic stringy σ-model, we investigate four-dimensional (4D) cosmological string solutions in graviton, dilaton and antisymmetric tensor backgrounds, compatible with world-sheet conformal invariance, and valid beyond perturbative expansions in powers of α′. The antisymmetric tensor field, playing the rôle of an axion in the 4D target space time, leads to spatial anisotropies of the emergent Robertson–Walker expanding Universe, and, upon coupling the system to the electromagnetic field, it results in nontrivial optical activity. Some estimates of the corresponding effects are made and their possible relevance to cosmology is briefly discussed. Probably the model can describe early Universe cosmology, where nontrivial dilaton effects, which necessarily characterize our solution, may be expected to be large.

Chiral family classification of fermionic Z2×Z2 heterotic orbifold models

Free fermionic construction of four-dimensional string vacua, are related to the Z2×Z2 orbifolds at special points in the moduli space, and yielded the most realistic three family string models to date. Using free fermionic construction techniques we are able to classify more than 1010 string vacua by the net family and anti-family number. Using a Monte Carlo technique we find a bell shaped distribution that peaks at vanishing net number of chiral families. We also observe that ∼15% of the models have three net chiral families. In addition to mirror symmetry we find that the distribution exhibits a symmetry under the exchange of (spinor plus anti-spinor) representations with vectorial representations.

Strings, black holes, the tripartite entanglement of seven qubits, and the Fano plane

Recently it has been observed that the group ${E}_{7}$ can be used to describe a special type of quantum entanglement of seven qubits partitioned into seven tripartite systems. Here we show that this curious type of entanglement is entirely encoded into the discrete geometry of the Fano plane. We explicitly work out the details concerning a qubit interpretation of the ${E}_{7}$ generators as representatives of tripartite protocols acting on the 56-dimensional representation space. Using these results we extend further the recently studied analogy between quantum information theory and supersymmetric black holes in four-dimensional string theory. We point out that there is a dual relationship between entangled subsystems containing three and four tripartite systems. This relationship is reflected in the structure of the expressions for the black hole entropy in the $N=4$ and $N=2$ truncations of the ${E}_{7(7)}$ symmetric area form of $N=8$ supergravity. We conjecture that a similar picture based on other qubit systems might hold for black hole solutions in magic supergravities.

More about soft terms and FCNC in realistic string constructions

In realistic four-dimensional string constructions the presence of anomalous U(1)'s is generic. In addition, the associated Fayet-Iliopoulos contribution to the D-term can break the extra gauge symmetries. As a consequence, physical particles can appear combined with other states. We show that even if a three-generation standard-like model has originally flavour-independent soft scalar masses, the particle mixing contribution may generate non-universality among them. Thus FCNC effects which were apparently absent reappear. We also discuss the size of these contributions in an explicit model, and how they can be suppressed.