Four-dimensional String Theory 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

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.

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.

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.

CHIRAL N=1 4D ORIENTIFOLDS WITH D-BRANES AT ANGLES

D6-branes intersecting at angles allow for phenomenologically appealing constructions of four-dimensional string theory vacua. While it is straightforward to obtain non-supersymmetric realizations of the standard model, supersymmetric and stable models with three generations and no exotic chiral matter require more involved orbifold constructions. The T6/(ℤ4×ℤ2×Ωℛ) case is discussed in detail. Other orbifolds including fractional D6-branes are treated briefly.

Target-space duality in heterotic and type I effective Lagrangians

We study the implications of target-space duality symmetries for low-energy effective actions of various four-dimensional string theories. In the heterotic case such symmetries can be incorporated in simple orbifold examples. At present a similar statement cannot be made about the simplest type IIB orientifolds due to an obstruction at the level of gravitational anomalies. This fact confirms previous doubts concerning a conjectured heterotic–type IIB orientifold duality and shows that target-space symmetries can be a powerful tool in studying relations between various string theories at the level of the effective low-energy action. Contraints on effective Lagrangians from these symmetries are discussed in detail. In particular, we consider ways of extending T-duality to include additional corrections to the Kähler potential in heterotic string models with N=2 subsectors.

Gravitational instantons and black plane solutions in four-dimensional string theory.

We consider gauged Wess-Zumino models based on the non compact group $SU(2,1)$. It is shown that by vector gauging the maximal compact subgroup $U(2)$ the resulting backgrounds obey the gravity-dilaton one loop string vacuum equations of motion in four dimensional euclidean space. The torsionless solution is then interpreted as a pseudo-instanton of the $d=4$ Liouville theory coupled to gravity. The presence of a traslational isometry in the model allows to get another string vacuum backgrounds by using target duality that we identify with those corresponding to the axial gauging. We also compute the exact backgrounds. Depending on the value of $k$, they may be interpreted as instantons connecting a highly singular big bang like universe with a static singular or regular black plane geometry.

ON THE ANOMALOUS MAGNETIC MOMENT IN HETEROTIC SUPERSTRINGS

We address the problem of computing amplitudes with external space-time fermions in four-dimensional heterotic string theories. As a non-trivial example we consider the anomalous magnetic moment at one-loop level for an "electron" with mass of the order of the Planck mass. We check that the anomalous magnetic moment vanishes if the model is space-time supersymmetric, as required by the supersymmetric sum rules.

STRONG–WEAK COUPLING DUALITY IN FOUR-DIMENSIONAL STRING THEORY

We present several pieces of evidence for strong–weak coupling duality symmetry in the heterotic string theory, compactified on a six-dimensional torus. They include symmetry of the (1) low energy effective action, (2) allowed spectrum of electric and magnetic charges in the theory, (3) allowed mass spectrum of particles saturating the Bogomol'nyi bound, and (4) Yukawa couplings between massless neutral particles and massive charged particles saturating the Bogomol'nyi bound. This duality transformation exchanges the electrically charged elementary string excitations with the magnetically charged soliton states in the theory. It is shown that the existence of a strong–weak coupling duality symmetry in four-dimensional string theory makes definite predictions about the existence of new stable monopole and dyon states in the theory with specific degeneracies, including certain supersymmetric bound states of monopoles and dyons. The relationship between strong–weak coupling duality transformation in string theory and target space duality transformation in the five-brane theory is also discussed.

Production of Kaluza-Klein states at future colliders

Perturbative breaking of supersymmetry in four-dimensional string theories predict in general the existence of new large dimensions at the TeV scale. Such large dimensions lie in a domain of energies accessible to particle accelerators. Their main signature is the production of Kaluzu-Klein excitations which can be detected at future colliders. We study this possibility for hadron colliders (TEVATRON, LHC) and e + e − colliders (LEP-200, NCL-500).

Bardeen anomaly and Wess-Zumino term in the supersymmetric standard model

We construct the Bardeen anomaly and its related Wess-Zumino term in the supersymmetric standard model. In particular we show that it can be written in terms of a composite linear superfield related to supersummetrized Chern-Simons forms, in very much the same way as the Green-Schwarz term in four-dimensional string theory. Some physical applications, such as the contribution to the g−2 of gauginos when a heavy top is integrated out, are briefly discussed.

Limits on extra dimensions in orbifold compactifications of superstrings

Perturbative breaking of supersymmetry in four-dimensional string theories predict in general the existence of new large dimensions at the TeV scale. Such dimensions can be consistent with perturbative unification up to the Planck scale in a class of string models and open the exciting possibility of lowering a part of the massive string spectrum at energies accessible to future accelerators. The main signature is the production of Kaluza-Klein excitations which have a very particular structure, strongly correlated with the supersymmetry breaking mechanism. We present a model independent analysis of the physics of these states in the context of orbifold compactifications of the heterotic superstring. In particular, we compute the limits on the size of large dimensions used to break supersymmetry.

Constraints on discrete symmetries from anomaly cancellation in compactified superstring theories

Compactified string theories give rise to discrete symmetries which are essential if they are to provide a realistic low energy theory. We find that in a class of four-dimensional string theories these symmetries are constrained by similar conditions to those discrete anomaly cancellation conditions found in the case the discrete symmetry is a residue of a spontaneously broken gauge symmetry. Such conditions strongly constrain the allowed form of the low energy effective theory.

Gaugino condensation in 4D superstring models

We study the possibility that supersymmetry is broken via a gaugino condensate in four-dimensional string theories. We derive an effective low-energy theory describing the Goldstone mode associated with the R-symmetry breaking driven by gaugino condensation and show that this gives a description of gaugino condensation equivalent, at tree level, to other effective lagrangian approaches based on the symmetries of the theory. A study of the mass gap equation shows that non-perturbative effects favour the appearance of a gaugino condensate. By minimizing the effective potential describing both the condensate and the moduli determining the gauge coupling constant and radius of compactification we show that large hierarchy may occur between the gravitino mass and the Planck mass with the existence of only one gaugino condensate. Associated with this is a determination of the fine structure constant and the compactification scale.

Fractionally charged particles and supersymmetry breaking in 4D strings

Four-dimensional string theories predict in general the existence of light exotic particles with fractional electric charges. Such particles could escape present observations if they are confined by a gauge group of the “hidden” sector into integrally charged states. It is conceivable that the same gauge group is also responsible for dynamical supersymmetry breaking, via gaugino and scalar condensation. The communication of the breaking to the observable sector is not mediated by ordinary gauge interactions, implying that the confining scale can be in the TeV region. We study the main phenomenological implications of this possibility. In particular, we analyze the pattern of supersymmetry breaking and the mass-spectrum of the particles. We also show that this scenario can be consistent with the unification of all coupling constants at the string scale.

Quantum mechanics and black holes in four-dimensional string theory

In previous papers we have shown how strings in a two-dimensional target space reconcile quantum mechanics with general relativity, thanks to an infinite set of conserved quantum numbers, “W-hair”, associated with topological soliton-like states. In this paper we extend these arguments to four dimensions, by considering explicitly the case of string black holes with radial symmetry. The key infinite-dimensional W-symmetry is associated with the SU(1, 1)/U(1) coset structure of the dilaton-graviton sector that is a model-independent feature of spherically symmetric four-dimensional strings. Arguments are also given that the enormous number of string discrete (topological) states account for the maintenance of quantum coherence during the (non-thermal) stringy evaporation process, as well as quenching the large Hawking-Bekenstein entropy associated with the black hole. Defining the latter as the measure of the loss of information for an observer at infinity, who-ignoring the higher string quantum numbers-keeps track only of the classical mass, angular momentum and change of the black hole, one recovers the familiar quadratic dependence on the black-hole mass by simple counting arguments on the asymptotic density of string states in a linear-dilaton background.

Selection rules in low energy string effective lagrangians

Selection rules which restrict elementary particle interactions are derived as the low-energy limit of superstring theory. A general mechanism is demonstrated, in four-dimensional string tree-amplitudes, whereby the supersymmetric trilinear Yukawa-like couplings in the effective lagrangian which violate lepton number vanish, terms which otherwise occur naturally in supersymmetric versions of the standard model. Explicit expressions for the vertex operators, and all cubic bosonic couplings involving the Yang-Mills gauge bosons and the graviton, together with the scalar and anti-symmetric tensor components of gravity are given. There are no √2 α' corrections to the three-point string tree-amplitudes, a result which eliminates any higher derivative trilinear couplings among these fields in the effective action. In this four-dimensional string theory, expressions are derived for the gravitational coupling constant κ and the Yang-Mills coupling constant g YM in terms of the two string parameters: the universal Regge slope parameter which is the origin of the length scale √2 α', and the dimensionless string coupling constant g. We find κ = 1 2 g√2α' and g YM = g .

Confining phase of superstrings and axionic strings.

In the four-dimensional effective field theory of the heterotic superstring compactified on a C.alabi- Yau manifold, we find a new class of spacetime string instantons in the gravity sector that involves graviton, dilaton, and Kalb-Ramond (axion) fields. The instantons satisfy generalized (anti)self-duality equations, and saturate a Bogomolnyi bound provided by the underlying supersymmetry. The instantons lead to several intriguing nonperturbative phenomena to low-energy string theory. A mass gap is generated to the Kalb-Ramond gauge fields, and results in the confinement of superstrings into Kalb-Ramond domain walls below the compactification scale. More interestingly, they provide a new example of the nonperturbative breakdown of the superpotential nonrenormalization theorem. Together with the world-sheet string instantons, this implies that all would-be Peccei-Quinn symmetries that arise in four-dimensional string theories are completely broken around the string compactification scale. Being self-dual, the instantons provide precisely two gravitino zero modes, thus might induce dynamical supersymmetry breaking. We also point out an underlying analogy with the invisible-axionic domain walls bounded by axionic strings.