Four-dimensional Superstring Research Articles

Quantum supersymmetry and the supergeometry of four-dimensional superstrings

The origin of world-sheet supersymmetry in the free-fermion models used in many constructions of four-dimensional heterotic strings and superstrings is shown to be due to the quantum-mechanical effect of an anomaly. A component action which may be used as the basis for studying supermodular invariance on an arbitrary genus Riemann surface and a superspace formulation are given.

Light neutrinos with large magnetic moments and the solar neutrino problem

We analyze the question of having a large enough neutrino magnetic moment in order to implement the VVO mechanism in the framework of an SU(4)×SU(2) L×SU(2) R model, derivable from four-dimensional superstrings. We find that the radiative corrections to the seesaw type neutrino mass matrix can generate an appreciable magnetic moment without any seesaw type suppression.

Fermionic realizations of superstrings on orbifolds

Free fermion representations of four-dimensional superstrings compactified on T 6/ Z 4 and T 6/ Z 8 orbifolds are constructed. The underlying boson-fermion equivalence reduces to identities for products of Jacobi θ-functions with rational arguments which are derived. Some obstacles to construct the fermionic realizations of the remaining orbifolds consistent with superstring compactification are pointed out.

Unitarity and modular invariance as constraints on four-dimensional superstrings

It is shown that the requirements of space-time factorization for vertices and one-loop modular invariance guarantee higher-loop modular invariance (as it is presently understood) in the context of string models built out of free fermion fields, either twisted or untwisted. The general solution satisfying these requirements is derived and their relation to the conservation of quantum numbers at general fermionic vertices is discussed. A number of models are discussed using a diagrammatic notation. The natural occurrence in such models of spinor representations which have features in common with the observed quark-lepton multiplets is noted.

Mechanisms of spontaneous symmetry breaking in the fermionic construction of superstring models.

Mechanisms for spontaneous gauge symmetry breaking are presented in the context of the four-dimensional superstring models. Some phenomenologically interesting models are constructed to highlight the simplicity of the procedure.

Four-dimensional superstrings live on group manifolds

There exist a few non-abelian group manifolds, with twisted boundary conditions, where 4D superstrings with their massless fermionic excitations, including gravitinos, can propagate freely. It turns out that the associated Wess-Zumino-Witten action is fermionizable and puts severe restrictions on the possible modular-invariant string models built up with world-sheet fermions.

A custodial symmetry for the cosmological constant in the effective theories of four-dimensional superstrings

We discuss supersymmetry breaking in the effective supergravity theories of four-dimensional N = 1 superstrings. Improving a recent suggestion, we introduce a superpotential modification that describes spontaneous supersymmetry breaking with vanishing cosmological constant and Str M2 = 0 at any minimum of the tree level potential. We prove that in a class of models there are classical minima at which also Str f(M2 = 0 for any function f. In particular, the whole one-loop cosmological constant vanishes. We propose a new boson-fermion symmetry of the spectrum, relating the graviton and the “dilatino”, which explains these remarkable properties.

Comment on the non-renormalization theorem in the four-dimensional superstrings

We discuss the non-renormalization theorem in the context of the four-dimensional superstrings. We explicitly demonstrate that the graviton three-point one-loop amplitude does not vanish in contrast to the ten-dimensional superstring theories.

Multiloop modular invariance in spontaneously broken superstrings

The proof of modular invariance for a recently constructed class of four-dimensional superstrings exhibiting spontaneous breakdown of space-time supersymmetry is extended to any loop order.

On the vanishing of the cosmological constant in four-dimensional superstring models

In the general framework of the recently constructed fermionic superstring models, which can live in any spacetime dimension below ten and including four, we prove that the cosmological constant vanishes to all orders in the loop expansion if: (i) the free string spectrum contains at least one massless spin 3 2 particle, and (ii) a simple conjecture on the spin-structure dependence of the superghost and supermoduli contribution to the amplitudes holds. This conjecture, which arises naturally in the context of four-dimensional N = 1 superstrings, is the simplest one compatible with multiloop modular invariance.

The effective interactions of chiral families in four-dimensional superstrings

The low-energy effective interactions in four-dimensional superstrings with N = 2 and N = 1 space-time supersymmetry and massless twisted (family) sector are obtained. Our results rely on some general symmetry properties of superstring particle states and on tensor-calculus techniques for supergravity couplings. The novel feature is that the N = 2 quaternionic manifold and N = 1 Kähler space of the scalar superpartners of family multiplets are non-symmetric spaces whose structure can be obtained by “integrating out” the massive superstring modes.

Effective lagrangians for four-dimensional superstrings

We derive effective supergravity lagrangians for the massless sector of new four-dimensional superstrings. The untwisted sector is obtained by suitable Z 2 or Z 2 ⊗ Z 2 ′ truncations of N = 4, D = 4 lagrangians. For the N = 1 “minimal” models, related to the N = 4, SO(44) superstrings, we derive the Kähler potential, the superpotential and the ƒ gauge kinetic function. The underlying nonlinear sigma model is based on the Kähler manifold [SU(1,1)/U(1)] ⊗ Π i = 1 3 {SO(2, n i )/[SO(2) ⊗ SO( n i )]}. For models without massless twisted sector, this result provides the full superstring low-energy effective action. For models with massless twisted sector, the N = 1 theory may be obtained once the quaternionic manifold of the corresponding N = 2 hypermultiplets is specified.

The low-energy effective field theory from four-dimensional superstrings

We derive the low-energy effective supergravity field theory obtained from a fermionic formulation of four-dimensional superstrings. It contains a single dilaton supermultiplet parametrizing an SU(1, 1)/U(1) manifold, three self-conjugate sets of matter supermultiplets parametrizing SO( m, 2)/SO( m)×SO(2) manifolds, and chiral matter supermultiplets parametrizing a product of SU( M, 1)/SU( M)×U(1) manifolds. We derive the Yukawa couplings of the theory and identify some of the self-conjugate matter fields as Higgses. We also discuss the possible pattern of supersymmetry breaking.