Four-dimensional Superstring Research Articles

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.

PATH INTEGRAL QUANTIZATION OF SUPERSTRING

Motivated by the Hamilton–Jacobi approach of constrained systems, we analyze the classical structure of a four-dimensional superstring. The equations of motion for a singular system are obtained as total differential equations in many variables. The path integral quantization based on Hamilton–Jacobi approach is applied to quantize the system, and the integration is taken over the canonical phase space coordinates.

THREE GENERATIONS OF SUSY STANDARD MODEL OF NAMBU–GOTO STRING

A four-dimensional superstring have been constructed starting from a 26-dimensional bosonic string. Fermions are introduced by noting the Mandelstam's proof of equivalence of two fermions to one boson in 1+1 dimensions. The action of the superstring is invariant under SO (6) ⊗ SO (5) in the worldsheet. It has four bosonic coordinates and 44 Majorana fermions of SO (3, 1). Here the superstring action is shown to be invariant under conformal and superconformal transformations with the usual conformal and superconformal ghosts of the ten-dimensional superstrings. The massless spectrum obtained by quantizing the action, contain vector mesons which are generators of the SO (6) ⊗ SO (5). Using Wilson loops, this product group is proven to descend to Z3 ⊗ SU (3) ⊗ SU (2) ⊗ U (1) without breaking supersymmetry. Thus there are just three generations of quarks and leptons.

Sum rules in the superpartner spectrum of the minimal supersymmetric standard model

Assuming that the universal sum rules for soft supersymmetry-breaking terms, which have been recently found both in four-dimensional superstring models and in supersymmertic gauge-Yukawa unified gauge models, are satisfied above and at the grand unification scale, we investigate their low energy consequences and derive sum rules in the superpartner spectrum of the minimal supersymmetric standard model (MSSM). These sum rules contain only observable parameters of the MSSM, and could be experimentally verified in future.

The Unification in the String Theories with the G × G Gauge Groups

In the framework of the four-dimensional heterotic superstring with free fermions we discuss the rank eight and/or 16 Grand Unified String Theories (GUSTs) which contain the SU (3)H-gauge family symmetry. We explicitly investigate the paths of the unification in the GUST with gauge symmetry G × G = [ SU (5)× U (1)×( SU (3)× U (1))H]⊗2. We show that the GUSTs with the G × G gauge group allow one to make the scale of unification to be consistent with the string scale M SU ~ g str ×5×1017 GeV.

THE FERMION GENERATION PROBLEM IN THE GUST’S OF THE FREE WORLD SHEET FERMION FORMULATION

In the framework of the four-dimensional heterotic superstring with free fermions, we investigate the rank 8 grand unified string theories (GUST’s) which contain the SU (3)H gauge family symmetry, and develop some methods for building corresponding string models. We explicitly construct GUST’s with gauge symmetry G= SU (5)× U (1) × [ SU (3)× U (1)]H and G= SO (10)×[ SU (3)× U (1)]H ⊂ SO (16) or E(6)× SU (3)H ⊂ E(8), and consider the full massless spectrum for our string models. As the GUST’s originating from level 1 Kac–Moody algebra (KMA) contain only low-dimensional representations, we consider for the observable gauge symmetry the diagonal subgroup G sym of the rank 16 group G×G ⊂ SO (16)× SO (16) or ⊂ E(8)×E(8). We discuss the possible fermion matter and Higgs sectors in these theories. There has to exist “superweak” light chiral matter [Formula: see text] in the GUST’s under consideration. The understanding of quark and lepton mass spectra and family mixing leaves a possibility for the existence of an unusually low mass breaking scale of the SU (3)H family gauge symmetry (some TeV).

Possible dynamical determination of mt, mb and mτ

Motivated by four-dimensional superstring models, we consider the possibility of treating the Yukawa couplings of the Minimal Supersymmetric Standard Model (MSSM) as dynamical variables of the effective theory at the electroweak scale. Assuming bottom-tau unification, we concentrate on the top and bottom Yukawa couplings, and find that minimizing the effective potential drives them close to an effective infrared fixed line. Requiring an acceptable bottom-top mass ratio leads in principle to an additional constraint on the MSSM parameter space. As a by-product, we give new approximate analytical solutions of the renormalization group equations for the MSSM parameters.

Naturalness of scales and quadratic divergences in N=1 supergravity

Some conditions for the hierarchy m3/2 ≪ MP to naturally occur in a generic effective supergravity theory are discussed. In particular cancellation of quadratic divergences in the one-loop effective potential are studied in supergravity theories derived from four-dimensional superstring models with supersymmetry broken either at the tree level via compactification or by non-perturbative effects such as gaugino condensation.

STRING-MOTIVATED GRAND UNIFIED THEORIES WITH HORIZONTAL GAUGE SYMMETRY

In the framework of four-dimensional heterotic superstring with free fermions, we investigate the rank 8 grand unified string theories (GUST’s) which contain the SU(3) H gauge family symmetry. GUST’s of this type accommodate naturally the three fermion families presently observed and, moreover, can describe the fermion mass spectrum without high-dimensional representations of conventional unification groups. We explicitly construct GUST’s with gauge symmetry G= SU(5) × U(1) ×[ SU(3) × U(1) ]H ⊂ SO (16) in free complex fermion formulation. As the GUST’s originating from Kac-Moody algebras (KMA’s) contain only low-dimensional representations, it is usually difficult to break the gauge symmetry. We solve this problem by taking for the observable gauge symmetry the diagonal subgroup G sym of the rank 16 group G×G ⊂ SO(16) × SO(16) ⊂ E(8)×E(8). Such a construction effectively corresponds to a level 2 KMA, and therefore some higher-dimensional representations of the diagonal subgroup appear. This (due to G×G tensor Higgs fields) allows one to break GUST symmetry down to SU (3c)× U(1) em . In this approach the observed electromagnetic charge Q em can be viewed as a sum of two Q I and Q II charges of each G group. In this case, below the scale where G×G breaks down to G sym the spectrum does not contain particles with exotic fractional charges.

Mass formulae and natural hierarchy in string effective supergravities

We study some conditions for the hierarchy m 3 2 ⪡ M P to occur naturally in a generic effective supergravity theory. Absence of fine-tunuinf and perturbative calculabilty require that the effective potential has a sliding gravitino mass and vanishing cosmological constant, up to O(m 3 2 4) corrections. In particular, cancellation of quadratically divergent contributions to the one-loop effective potential should take place, including the ‘hidden sector’ of the theory. We show that these conditions can be met in the effective supergravities derived from four-dimensional superstrings, with supersymmetry broken either at the string tree-level via compactification, or by non-perturbative effects such as gaugino condensation. A crucial role is played by some approximate scaling symmetries, which are remnants of discrete target-space dualities in the large moduli limit. We derive explicit formulae for the soft breaking terms arising from this class of ‘large hierarchy compatible’ (LHC) supergravities.

Towards a dynamical determination of parameters in the minimal supersymmetric standard model

In the Minimal Supersymmetric Standard Model (MSSM), the scale M SUSY of soft supersymmetry breaking is usually assumed to be of the order of the electroweak scale. We reconsider here the possibility of treating M SUSY as a dynamical variable. Its expectation value should be determined by minimizing the vacuum energy, after including MSSM quantum corrections. We point out the crucial role of the cosmological term for a dynamical generation of the desired hierarchies m z , M SUSY ⪡ M p . Inspired by four-dimensional superstring models, we also consider the Yukawa couplings as dynamical variables. We find that the top Yukawa coupling is attracted close to its effective infrared fixed point, corresponding to a top-quark mass in the experimentally allowed range. As an illustrative example, we present the results of explicit calculations for a special case of the MSSM.

Physical properties of four-dimensional superstring gravity black hole solutions

We consider the physical properties of four-dimensional black hole solutions to the effective action describing the low energy dynamics of the gravitational sector of heterotic superstring theory. We compare the properties of the external field strengths in the perturbative solution to the full O(α′) string effective action equations, to those of exact solutions in a truncated action for charged black holes, and to the Kerr-Newman family of solutions of Einstein-Maxwell theory. We contrast the numerical results obtained in these approaches, and discuss limitations of the analyses. Finally we discuss how the new features of classical string gravity affect the standard tests of general relativity.

Moduli corrections to gauge and gravitational couplings in four-dimensional superstrings

We study one-loop, moduli-dependent corrections to gauge and gravitational couplings in supersymmetric vacua of the heterotic string. By exploiting their relation to the integrability condition for the associated CP-odd couplings, we derive general expressions for them, both for (2, 2) and (2, 0) models, in terms of tree-level four-point functions in the internal N = 2 superconformal theory. The (2, 2) case, in particular symmetric orbifolds, is discussed in detail.

N = 2 superconformal algebras and Jordan triple systems

We give a construction of N = 2 superconformal algebras over hermitian Jordan triple systems (JTS). The N = 2 superconformal algebras obtained by this method correspond to realizations over hermitian symmetric spaces, which can be compact or non- compact. Over the hermitian JTS's one can construct a large class of N = 2 superconformal algebras with central charge c = 9, which characterize the “internal sector” of the four-dimensional superstring or heterotic string theories with N = 1 space-time supersymmetry.

Spontaneous gauge symmetry breaking in conformal theories of a four-dimensional superstring

We formulate a mechanism of spontaneous gauge symmetry breaking with continuous parameters, in the superconformal theory approach to four-dimensional superstring theories. As an example, we inspect the 1 9-model with the breaking of the gauge group SO(26). Supersymmetry is unbroken, maintaining the zero cosmological constant, and realistic gauge groups such as E 8⊗ SU(3) ⊗ SU(2) ⊗ U(1) 11 are obtained after the gauge breaking for the 1 × 16 3-model with three generations.

Extended supersymmetry in four-dimensional type II strings

We construct models with N = 3, 4, 5, 6 and 8 space-time supersymmetry in type II four-dimensional superstrings and analyze their moduli space. These models are obtained in the fermionic formulation and most of them can be reformulated as asymmetric orbifold compactifications. The massless sector of these theories is shown to be compatible with the symmetries of the extended supergravity lagrangians.

Cosmological implications of an anomalous U(1): Inflation, cosmic strings and constraints on superstring parameters

A string-loop generated Fayet-Iliopoulos term can trigger, in four-dimensional superstring models with an anomalous U(1), the presence of global and local cosmic strings and, depending on the values of the string parameters M s (string scale) and M c (compactification scale), a period of inflationary expansion of the universe. The observational effects of inflation (density inhomogeneities) and cosmic strings (gravitational radiation, etc.) put severe bounds on the values of M s and M c.

Cosmic strings from superstrings

In the low-energy theory of four-dimensional superstrings the spontaneous breakdown of a pseudo-anomalous U(1) can trigger (but not necessarily) the formation of global and/or local cosmic strings. When cosmic strings are formed, supersymmetry is broken inside the string cores with a positive cosmological constant and an exponential growth of the cosmic scale factor. Strings are conformally stretched with the inflationary expansion, never enter the physics horizon and can have no observable (e.g. optical) effects. Off-string regions are in a (radiation-dominated) FRW universe. Most of our observable universe would still be inflating today unless a late (conventional) period of inflation transforms an off-string region into our present universe. The required amount of inflation coincides with the one needed to solve the usual flatness and horizon problems of the standard cosmological model. We consider, as an example, the chaotic inflation associated with the low-energy breaking (∼1 TeV) of supersymmetry.

World-sheet versus spectrum symmetries in heterotic and type II superstrings

We discuss the relation between world-sheet symmetries of general four-dimensional superstring theories and the classification of their massless and massive excitations. This follows from the connection between extended superconformal algebras on the world-sheet and extended space-time supersymmetry algebras. In particular we show that the relevant Kac-Moody symmetries are extended to the spectrum symmetries of the supermultiplets of states. This analysis reproduces results for the field theory limit of superstring compactifications.

On non-renormalization theorems for four-dimensional superstrings

For d=4, N=1 supersymmetric string theories we compute the quantum corrections to the superpotential to two-loop order. The vanishing of the amplitudes relies crucially on generalized Riemann identities. Beyond genus one, these map to non-trivial zeroes of theta functions implied by the Riemann vanishing theorem.