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.     

Spinor-vector duality in heterotic string vacua

Classification of the N=1 space–time supersymmetric fermionic Z₂×Z₂ heterotic-string vacua with symmetric internal shifts, revealed a novel spinor-vector duality symmetry over the entire space of vacua, where the S_t↔V duality interchanges the spinor plus anti-spinor representations with vector representations. In this paper we demonstrate that the spinor-vector duality exists also in fermionic Z₂ heterotic string models, which preserve N=2 space–time supersymmetry. In this case the interchange is between spinorial and vectorial representations of the unbroken SO(12) GUT symmetry. We provide a general algebraic proof for the existence of the S_t↔V duality map. We present a novel basis to generate the free fermionic models in which the ten-dimensional gauge degrees of freedom are grouped into four groups of four, each generating an SO(8) modular block. In the new basis the GUT symmetries are produced by generators arising from the trivial and non-trivial sectors, and due to the triality property of the SO(8) representations. Thus, while in the new basis the appearance of GUT symmetries is more cumbersome, it may be more instrumental in revealing the duality symmetries that underly the string vacua.     

Orbifold compactification of heterotic string theories

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

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.     

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.     

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.     

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.     

Spacetime supersymmetry breaking in heterotic string theory

A simple mechanism for spacetime supersymmetry breaking in the ten-dimensional heterotic string theory is proposed. We present a heterotic string model with a hidden two-dimensional sigma-model sector which can induce desirably small supersymmetry breaking, without upsetting the zero value of the cosmological constant, through a topological instanton effect due to an abelian gauge field on the string world sheet. We find that the consistency condition of the gravitino field equation is satisfied for some configurations even after supersymmetry breaking.     

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.     

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.     

On a possible Wess-Zumino term in the heterotic string

We examine the low-energy limits of the one-particle irreducible one-loop amplitudes in the heterotic superstring for five gravitons, for three gravitons and two gauge bosons, and for one graviton and four gauge bosons. In agreement with general arguments, explicit calculation shows that there is a Wess-Zumino term in the low-energy effective action for D = 10 supergravity.     

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.     

Two-loop computation of the four-particle amplitude in heterotic string theory

By using the hyperelliptic formalism we obtain an explicit integral formulafor the four-massless-particle scattering amplitude at two loops in heterotic string theory. We verify the main properties and in particular its finiteness. The corresponding expression for type II superstrings is also given.     

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.     

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.