Luis E. Ibanez

On the Low Energy d = 4, N = 1 Supergravity Theory Extracted from the d = 10, N = 1 Superstring*

We extract some general features of the N = 1 supergravity, d = 4 theory which could be obtained as a low energy limit of the recently proposed anomaly-free superstring theories. One finds that after the breaking of the residual d = 4 supersymmetry the gravitino and gaugino masses are equal. Soft scalar couplings are also obtained, including trilinear terms as well as common scalar masses m ˜ m 3/2 . It is argued that a possible source of supersymmetry breaking may be the condensation of fermions in the Yang-Mills sector and we discuss this possibility in the context of the E 8 × E 8 model. Finally, we discuss some implications for the low energy supersymmetric spectrum, particularly squark and gluino masses.

Orbifolds and Wilson lines

We study the consequences of the presence of gauge background fields on the torus underlying orbifold compactification of the heterotic string. It is pointed out that such Wilson lines provide us with a mechanism for controlling the number of chiral matter states both from twisted and untwisted sectors, as well as breaking the symmetry group. Starting from the Z orbifold, we can construct a variety of four-dimensional string models with three families of quarks and leptons and different gauge groups such as E 6 , SU(3) 3 , SU(6)×U(1) or SU(5)×[SU(2)×U(1)] 2 .

Duality-anomaly cancellation, minimal string unification and the effective low-energy lagrangian of 4D strings

We present a systematic study of the constraints coming from targetspace duality and the associated duality anomaly cancellations on orbifoldlike 4-D strings. A prominent role is played by the modular weights of the massless fields. We present a general classification of all possible modular weights of massless fields in Abelian orbifolds. We show that the cancellation of modular anomalies strongly constrains the massless fermion content of the theory, in close analogy with the standard ABJ anomalies. We emphasize the validity of this approach not only for (2,2) orbifolds but for (0,2) models with and without Wilson lines. As an application one can show that one cannot build a Z3 or Z7 orbifold whose massless charged sector with respect to the (level one) gauge group SU(3) × SU(2) × U(1) is that of the minimal supersymmetric standard model, since any such model would necessarily have duality anomalies. A general study of those constraints for Abelian orbifolds is presented. Duality anomalies are also related to the computation of string threshold corrections to gauge coupling constants. We present an analysis of the possible relevance of those threshold corrections to the computation of sin 2 θW and α3 for all Abelian orbifolds. Some particular minimal scenarios, namely those based on all ZN orbifolds except Z6 and Z ′ , are ruled out on the basis of these constraints. Finally we discuss the explicit dependence of the SUSY-breaking soft terms on the modular weights of the physical fields. We find that those terms are in general not universal. In some cases specific relationships for gaugino and scalar masses are found.

Discrete gauge symmetries and the origin of baryon and lepton number conservation in supersymmetric versions of the standard model

In the supersymmetric standard model operators of dimension 4 and 5 generically violate B and L number. One usually assumes the presence of some discrete symmetry (“matter parities”) in order to forbid dangerous operators which may lead otherwise to unacceptable violations of B and L. We give a general classification of such discrete ZN symmetries (and R-symmetries) and show that the number of independent possibilities is substantially reduced by equivalences. We argue that normal discrete symmetries may be expected to be violated by quantum gravity effects and hence are not enough to inhibit nucleon decay. On the other hand, gauge (either discrete or continuous) symmetries are stable under quantum gravity effects and we discuss how such symmetries may eliminate the dangerous B- or L-violating operators. We find that the massless fermion content of modeld with discrete “gauge” symmetries is strongly constrained by the cancellation of “discrete gauge anomalies”. We show that there are two preferred ZN symmetries which are discrete anomaly free with the minimal light matter content. One of them is the standard R-parity whereas the other is a unique Z3 symmetry allowing for lepton number violation. We argue that from the point of view of arranging for proton stability without fine-tuning the second option should be preferred. The differences in the phenomenology of the various sypersymmetric models dictated by the different symmetries are discussed.

Heterotic strings in symmetric and asymmetric orbifold backgrounds

We present a general formalism for constructing four-dimensional string models from ZN orbifolds. An explicit form for the generalized GSO projector in the construction of twisted and untwisted states is provided, allowing then the computation of the massless spectrum for any embedding of the point group in the gauge degrees of freedom. Constant background fields, in particular Wilson lines, are considered, and the general constraints on them are presented for both symmetric and asymmetric orbifolds. Several examples are provided, including a general classification of the Z3 orbifold models with one Wilson line, a systematic search for SU(3) × SU(2) × U(1)n models with three generations, models with tontinuous symmetry breaking and lower rank, and asymmetric orbifold models with and without Wilson lines.

Strong-weak coupling duality and non-perturbative effects in string theory

Abstract We conjecture the existence of a new discrete symmetry of the modular type relating weak and strong coupling in string theory. The existence of this symmetry would strongly constrain the non-perturbative behaviour in string partition functions and introduces the notion of a maximal (minimal) coupling constant. An effective lagrangian analysis suggests that the dilaton vacuum expectation value is dynamically fixed to be of order one. In supersymmetric heterotic strings, supersymmetry (as well as this modular symmetry itself) is generically spontaneously broken.

Low-energy predictions in supersymmetric grand unified theories

Abstract Globally supersymmetric theories provide a solution to the gauge hierarchy problem without the need for a strongly interacting sector. We consider various such theories which generalise the standard SU(3) × SU(2) × U(1) model and compute their predictions for the unification scale M X , sin 2 θ W and fermion mass ratios.

Locally Supersymmetric SU(5) Grand Unification

We consider the coupling of the SU(5) GUT to N = 1 supergravity. A general strategy to obtain a reasonable low-energy phenomenology is discussed. Very simple superpotentials naturally lead to large (∼mp) vacuum expectation values for the Higgses breaking SU(5) but no large expectation values for the scalar quarks and leptons. Various schemes for obtaining naturally massless Higgs doublets are discussed. Local supersymmetry is broken at a scale ∼1011 GeV and the weak interaction scale is generated from the soft terms breaking global supersymmetry which are left after the breakdown of supergravity. The 24-Higgs scalar potential is very flat and may have cosmological relevance.

N = 1 supergravity, the weak scale and the low-energy particle spectrum

Abstract We consider in detail the radiative SU(2) × U(1) breaking induced by broken N = 1 supergravity. We include in this study some parameters (b-quark Yukawas, mixed Higgs mass terms) neglected in a previous analysis. We show that there are essentially two types of mechanisms leading to radiative SU(2) × U(1) breaking. The first of them occurs for a t-quarks mass m t ⪆60 GeV. The second one appears for arbitrary small values of mt (without using a large A). These two mechanism correspond to two different classes of local SUSY GUTs. We present results for the low-energy supersymmetric particle spectrum. In some of the possible scenarios presented, squarks, sleptons and/or gauginos are accessible to present accelerator energies. In other scenarios, the scalar neutrinos may be the lightest R-odd particles. We finally remark that the SU(5) prediction for mb/mt is substanially suppressed for a heavy t-quark.

Orbifold compactifications with three families of Su(3) ×Su(2) ×U(1)n

Abstract We construct several N = 1 supersymmetric three-generation models with SU(3)×SU(2)×U(1)n gauge symmetry, obtained from orbifold compactification of the heterotic string in the presence of constant gauge-background fields. This Wilson-line mechanism also allows us to eliminate extra colour triplets which could mediate fast proton decay.