The heterotic string and supersymmetric counterparts of the Lorentz Chern-Simons terms

The heterotic string three-point amplitude, which involves two fermionic and one bosonic state, determines some of the terms that must be added to the action of the N=1 supergravity coupled to N=1 supersymmetric Yang-Mills in ten dimensions to preserve supersymmetry, if the Lorentz Chern-Simons term is included in the definition of the field strength H_μνϱ for the cancellation of anomalies. Our calculation reveals an interesting structure, which suggests that the relevant H-Bianchi for the analysis of possible heterotic string compactifications involves a spin connection possibly with torsion.     

The supersymmetric one-dimensional string

We consider a supersymmetric discretized string. The full string theory is defined as the sum over the triangulations of the surface, which is imbedded in the superspace. In the continuum limit such a string theory is described by an appropriate Wess-Zumino model. We present an explicit computation of the properties of the string in the ID case: we find that supersymmetry is spontaneously broken.     

The heterotic string is a soliton

It is shown that the Type IIA superstring compactified on K3 has a smooth string soliton with the same zero mode structure as the heterotic string compactified on a four-torus, thus providing new evidence for a conjectured exact duality between the two six-dimensional string theories. The chiral worldsheet bosons arise as zero modes of Ramond-Ramond fields of the IIA string theory and live on a signature (20,4) even, self-dual lattice. Stable, finite loops of soliton string provide the charged Ramond-Ramond states necessary for enhanced gauge symmetries at degeneration points of the K3 surface. It is also shown that Type IIB strings toroidally compactified to six dimensions have a multiplet of string solutions with Type II worldsheets.     

Supersymmetric sigma models and the heterotic string

We define the (1 + 1)-dimensional supersymmetry algebra of type (p, q) to be that generated by p right-handed Majorana-Weyl supercharges and q left-handed ones. We construct the non-linear sigma models with supersymmetry of type (1,0) and (2,0) and discuss their geometry and their relevance to compactifications of the heterotic superstring. The sigma-model anomalies can be cancelled by a mechanism closely related to that used by Green and Schwarz to cancel gravitational and Yang-Mills anomalies for the superstring.     

Heterotic string theory: (II). The interacting heterotic string

The theory of interacting heterotic strings is presented. Vertex operators are derived in both the bosonic and fermionic formulations of the theory and are shown to be consistent with gauge invariance, Lorentz invariance, and supersymmetry. Three- and four-point amplitudes for the scattering of massless string states are calculated and used to derive the low-energy field theory limit of the heterotic string. Divergences in string theories are discussed and it is shown that one-loop heterotic string amplitudes are finite and modular invariant only for gauge group E₈×E₈ or spin (32)/Z₂.     

Seesaw neutrinos from the heterotic string

We study the possibility of realizing the neutrino seesaw mechanism in the E(8) x E(8) heterotic string. In particular, we consider its Z6 orbifold compactifications leading to the supersymmetric standard model gauge group and matter content. We find that these models possess all the necessary ingredients for the seesaw mechanism, including the required Dirac Yukawa couplings and large Majorana mass terms. We argue that this situation is quite common in heterotic orbifolds. In contrast with the conventional seesaw of grand unified theories (GUTs), no large GUT representations are needed to generate the Majorana mass terms. The total number of right-handed neutrinos can be very large, up to O(100).     

R parity from the heterotic string

In T-duality invariant effective supergravity with gaugino condensation as the mechanism for supersymmetry breaking, there is a residual discrete symmetry that could play the role of R parity in supersymmetric extensions of the standard model.     

Orbifold compactification of heterotic string theories

The internal degrees of freedom of twisted heterotic strings are discussed using the theory of Kac-Moody algebras.     

Topologically non-trivial gauge configurations and the heterotic string

The contribution to the heterotic string of topologically non-trivial gauge configurations is studied. In the σ-model approach, it is proved that this kind of gauge configuration does not contribute to gauge anomalies. The ß = 0 condition is also analyzed.     

Towards the quantization of the Green-Schwarz heterotic string

The quantization of the Green-Schwarz heterotic string is reviewed. An improved solution for the master equation is found. The problem of the quantization on a higher-genus Riemann surface is discussed, and a careful analysis of the cancellation of the conformal anomaly is presented.     

Supersymmetric standard model from the heterotic string

We present a [FORMULA: SEE TEXT] orbifold compactification of the E8xE8 heterotic string which leads to the (supersymmetric) standard model gauge group and matter content. The quarks and leptons appear as three 16-plets of SO(10), whereas the Higgs fields do not form complete SO(10) multiplets. The model has large vacuum degeneracy. For generic vacua, no exotic states appear at low energies and the model is consistent with gauge coupling unification. The top quark Yukawa coupling arises from gauge interactions and is of the order of the gauge couplings, whereas the other Yukawa couplings are suppressed.     

A two-dimensional superfield formulation of the heterotic string

The density superfield and Einstein action for two-dimensional (2,0) supergravity are derived. The irreducible superfields of the heterotic string are discussed, and they are coupled to (2,0) supergravity. The locally (2,0) supersymmetric action for the heterotic string is presented in both superfields and component fields. For flat world sheet geometry, the globally (2,0) supersymmetric non-linear sigma model, and the associated Virasoro constraints, are derived. This formalism is applicable to (p,0) supersymmetry for any positive integer p.     

Compactifications of the heterotic string with unitary bundles

We describe a large new class of four‐dimensional supersymmetric string vacua defined as compactifications of the E₈ × E₈ and the SO(32) heterotic string on smooth Calabi‐Yau threefolds with unitary gauge bundles and heterotic five‐branes. The conventional gauge symmetry breaking via Wilson lines is replaced by the embedding of non‐flat line bundles into the ten‐dimensional gauge group, thus opening up the way for phenomenologically interesting string compactifications on simply connected manifolds. After a detailed analysis of the four‐dimensional effective theory we exemplify the general framework by means of a couple of explicit examples involving the spectral cover construction of stable holomorphic bundles. As for the SO(32) heterotic string, the resulting vacua can be viewed, in the S‐dual Type I picture, as a generalisation of magnetized D9/D5‐brane models. In the case of the E₈ × E₈ string, we find a natural way to construct realistic MSSM‐like models, either directly or via a flipped SU(5) GUT scenario.     

Dilaton vertices of the closed superstring and the heterotic string

BRST - and conformally invariant dilaton vertices of the closed superstring and the heterotic string are constructed, whose counter terms are consistent with the dilaton terms introduced in the non-linear sigma model approach of string theory.     

Low energy supersymmetry from the heterotic string landscape

We study possible correlations between properties of the observable and hidden sectors in heterotic string theory. Specifically, we analyze the case of the Z6-II orbifold compactification which produces a significant number of models with the spectrum of the supersymmetric standard model. We find that requiring realistic features does affect the hidden sector such that hidden sector gauge group factors SU(4) and SO(8) are favored. In the context of gaugino condensation, this implies low energy supersymmetry breaking.     

Towards low energy physics from the heterotic string

We investigate orbifold compactifications of the heterotic string, addressing in detail their construction, classification and phenomenological potential. We present a strategy to search for models resembling the minimal supersymmetric extension of the standard model (MSSM) in ℤ₆‐II orbifold compactifications. We find several MSSM candidates with the gauge group and the exact spectrum of the MSSM, and supersymmetric vacua below the compactification scale. They also exhibit the following realistic features: R‐parity, seesaw suppressed neutrino masses, and intermediate scale of supersymmetry breakdown. In addition, we find that similar models also exist in other ℤ_N orbifolds and in the SO(32) heterotic theory.     

Loop corrections to the heterotic string effective lagrangian

We derive string-loop corrections (torus topology) to the quartic curvature term in the low-energy effective lagrangian for the heterotic string theory. The one-loop correction is found to give the relative weight of two tensor structures different from the tree level.