Four-dimensional String Theory Research Articles

Spectral flow and supersymmetry operators in coset construction of N=2 superconformal field theory.

For {ital N}=2 superconformal coset {ital G}/{ital H} models, supersymmetry operators are constructed in accordance with the spectral flow. Gauge representation operators are also discussed. These are very powerful in the analysis of spectra in string models. In four-dimensional string theories, which are constructed via compactifications using {ital N}=2 superconformal models, one can use these operators to obtain all the other massless spectra, once canonical states are calculated.

On the NSR and GS formulations of twisted strings

The relationship between the Neveu-Schwarz-Ramond and Green-Schwarz formulations of four-dimensional string theories with twisted, orbifold-like boundary conditions is discussed.

Duality rotations in string theory

Global non-compact symmetries of four-dimensional string theories have their origin in duality transformations on the world-sheet which rotate field equations into Bianchi identities. Starting from a σ-model with target space coordinates x μ ( μ = 1,…, n), we introduce a dual σ-model with coordinates y α ( α = 1,…, n) for which the roles of field equations and Bianchi identities are interchanged. The hidden symmetries are then made manifest by considering a target space of double the dimension with coordinates Z M = ( x μ , y α ).

A new approach to supersymmetry breaking in superstring models

We re-examine supersymmetry breaking in effective four-dimensional field theories derived from the superstring, noting three features of modern four-dimensional string theories that were absent in the earlier compactifications of ten-dimensional string theories. These features are: the replacement of gauge-singlet moduli fields by gauge non-singlet chiral supermultiplets, vector-like matter fields in the hidden sector, and extra U(1) gauge symmetries under which both hidden and observable matter fields transform. We point out that an anomalous U(1) gauge symmetry can fix the magnitudes of the ersatz moduli fields. We propose a new scenario in which composite chiral supermultiplets in the hidden sector break global supersymmetry, and the extra massive U(1) gauge supermultiplets communicate this breaking to the observable sector via radiative corrections in the renormalizable effective field theory.

Chern-Simons terms in four-dimensional heterotic string theory.

We consider a four-dimensional heterotic string theory whose massless states are the {ital N}=4 supergravity multiplet and the gauge multiplet of SO(44). The string is coupled to the gauge background maintaining the world-sheet supersymmetry. It is found that the non-Abelian gauge current conservation becomes anomalous at the quantum level. The anomalies, however, can be eliminated by requiring the antisymmetric tensor field to transform nontrivially under the gauge transformation. This, in turn, introduces a Chern-Simons term in the definition of the corresponding field strength for it to be gauge invariant.

Yukawa couplings in four-dimensional fermionic string models

Yukawa couplings are studied in four-dimensional string theories formulated in terms of free fermionic degrees of freedom, with particular reference to flipped SU(5) × U(1) models.

Vacuum degeneracy in four-dimensional string theories

Vacuum degeneracy in four-dimensional string theories

New approach to one-loop calculations in gauge theories.

We propose using the technology of four-dimensional string theories to calculate amplitudes in gauge theories. Strings make such calculations much more efficient by summing a large number of Feynman diagrams all at once. We check the idea by constructing a string model reducing to a pure non-Abelian gauge theory in the infinite-tension limit and computing its \ensuremath{\beta} function with these techniques.

Ward identities in four-dimensional string theory

A four-dimensional heterotic string theory is envisaged in the background of its massless gauge Ward identities are derived. The spontaneous generating functional is constructed in the hamiltonian phase space and gauge Ward identities are derived. The spontaneous breaking of gauge symmetry is discussed in this approach.

Degenerate orbifolds

We present evidence for the existence of new four-dimensional string theories, obtained from a smooth variation of background fields in the twisted sectors of symmetric and asymmetric orbifolds. Flat directions only in the untwisted sector are shown to reproduce previously constructed models in terms of Wilson lines, exhibiting a Three-Higgs-Rule (THR). The new models provide a mechanism to lower the rank of the gauge group, lead to more flexible Yukawa couplings and give a strict separation of hidden and observable sectors, which are usually mixed in (2, 0)-models. Even though Fayet-Iliopoulos terms are induced in some of the models due to the presence of anomalous U(1)'s supersymmetry remains, in general, unbroken. Particular examples of the new models correspond to “blown up” versions of (2, 0)-orbifolds.

Logarithmic divergence in four-dimensional string theory

Logarithmic divergences in the one-loop scattering amplitude of the heterotic string compactified on the Zn-orbifold are investigated. The coefficient of these divergences is shown to be a function of the indices of the representations to which the massless states of the model belong.

4d fermionic superstrings with arbitrary twists

We present the rules for systematically constructing all consistent four-dimensional string theories, using free world-sheet fermions which pick up arbitrary phases when parallel transported around the string. These rules are necessary and sufficient for multi-loop modular invariance. They lead to theories with general Z N (GSO-type) projections, whose merits for model-building we discuss. We classify all boundary conditions yielding massless space-time spinors. We show that, in contrast to the case of only real 2d fermions, all possible realizations of world-sheet supersymmetry are now allowed. This opens the way for the construction of a new class of supersymmetric string models.

Higgs phenomenon in string theories

We show how to construct consistent four-dimensional string theories in the spontaneously broken, Higgs phase. The symmetry breaking scale is a free, classically undetermined parameter, due to the existence of flat directions in the scalar potential.

Gauge and gravitational couplings in four-dimensional string theories

We reconsider the relation between the string scale ms = 2α′ and the Planck scale mPl = 1GN in lower-dimensional string theories that do not necessarily admit an interpretation as compactified higher-dimensional theories. Assuming that the spacetime gauge symmetry is the reflection of a non-abelian affine Kac-Moody algebra on the world sheet, we point out that the string scale is generally given by ms2mPl2=(g24π)k, where g is the spacetime gauge coupling and k is the integrally quantized level of the affine algebra.

Four-dimensional string theory from the K3 lattice

The intersection form on K3 defines an even self-dual lorentzian lattice of signature (19, 3). This yields a heterotic string with gauge group E 8×E 8×SU(2)×SU(2)×SU(2) and uniquely seven uncompactified space-time dimensions. More interestingly, the lattice defined by K3× K3 has signature (22, 22) and yields a bosonic string with gauge group [E 8×E 8×SU(2) 6] 2 and uniquely four space-time dimensions. It is speculated on how a realistic four-dimensional theory may be obtained.