Fernando Quevedo

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 .

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.

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.

SUSY Breaking in Local String/F-Theory Models

We investigate bulk moduli stabilisation and supersymmetry breaking in local string/F-theory models where the Standard Model is supported on a del Pezzo surface or singularity. Computing the gravity mediated soft terms on the Standard Model brane induced by bulk supersymmetry breaking in the LARGE volume scenario, we explicitly find suppressions by M_s/M_P ~ V^{-1/2} compared to M_{3/2}. This gives rise to several phenomenological scenarios, depending on the strength of perturbative corrections to the effective action and the source of de Sitter lifting, in which the soft terms are suppressed by at least M_P/V^{3/2} and may be as small as M_P/V^2. Since the gravitino mass is of order M_{3/2} ~ M_P/V, for TeV soft terms all these scenarios give a very heavy gravitino (M_{3/2} >= 10^8 GeV) and generically the lightest moduli field is also heavy enough (m >= 10 TeV) to avoid the cosmological moduli problem. For TeV soft terms, these scenarios predict a minimal value of the volume to be V ~ 10^{6-7} in string units, which would give a unification scale of order M_{GUT} ~ M_s V^{1/6} ~ 10^{16} GeV. The strong suppression of gravity mediated soft terms could also possibly allow a scenario of dominant gauge mediation in the visible sector but with a very heavy gravitino M_{3/2} > 1 TeV.

Reducing the rank of the gauge group in orbifold compactifications of the heterotic string

Abstract Using the fact that the space group of an orbifold is non-abelian, we can reduce the rank of the four-dimensional gauge group obtained from orbifold compactification of the heterotic string. The embedding of the space group in the gauge degrees of freedom is performed by assigning shifts (Wilson lines) in the E 8 × E 8 lattice to the shifts in the six-dimensional lattice, and E 8 × E 8 Weyl rotations to the spatial discrete rotations. Reducing the rank of the gauge group is phenomenologically interesting for explaining the absence of extra low-energy gauge interactions.

Towards realistic string vacua from branes at singularities

We report on progress towards constructing string models incorporating both realistic D-brane matter content and moduli stabilisation with dynamical low-scale super- symmetry breaking. The general framework is that of local D-brane models embedded into the LARGE volume approach to moduli stabilisation. We review quiver theories on del Pezzo n (dPn) singularities including both D3 and D7 branes. We provide supersymmet- ric examples with three quark/lepton families and the gauge symmetries of the Standard, Left-Right Symmetric, Pati-Salam and Trinification models, without unwanted chiral ex- otics. We describe how the singularity structure leads to family symmetries governing the Yukawa couplings which may give mass hierarchies among the different generations. We outline how these models can be embedded into compact Calabi-Yau compactifications with LARGE volume moduli stabilisation, and state the minimal conditions for this to be possible. We study the general structure of soft supersymmetry breaking. At the singular- ity all leading order contributions to the soft terms (both gravity- and anomaly-mediation) vanish. We enumerate subleading contributions and estimate their magnitude. We also de- scribe model-independent physical implications of this scenario. These include the masses of anomalous and non-anomalous U(1)s and the generic existence of a new hyperweak force under which leptons and/or quarks could be charged. We propose that such a gauge boson could be responsible for the ghost muon anomaly recently found at the Tevatrons CDF detector.

Phases of antisymmetric tensor field theories

We study the different phases of field theories of compact antisymmetric tensors of rank h − 1 in arbitrary space-time dimensions D = d + 1. Starting in a ‘Coulomb’ phase, topological defects of dimension d − h − 1 ((d − h − 1)-branes) may condense leading to a generalized ‘confinement’ phase. If the dual theory is also compact the model may also have a third, generalized ‘Higgs’ phase, driven by the condensation of the dual (h − 2)-branes. Developing on the work of Julia and Toulouse for ordered solid-state media, we obtain the low energy effective action for these phases. Each phase has two dual descriptions in terms of antisymmetric tensors of different ranks, which are massless for the Coulomb phase but massive for the Higgs and confinement phases. We illustrate our prescription in detail for compact QED in 4D. Compact QED and O(2) models in 3D, as well as a periodic scalar field in 2D (strings on a circle), are also discussed. In this last case we show how T-duality is maintained if one considers both worldsheet instantons and their duals. We also unify various approaches to the problem of the axion mass in 4D string models. Finally we discuss possible implications of our results for non-perturbative issues in string theory.

Chains of N=2, D = 4 heterotic type II duals

Abstract We report on a search for N = 2 heterotic strings that are dual candidates of type II compactifications on Calabi-Yau threefolds described as K 3 fibrations. We find many new heterotic duals by using standard orbifold techniques. The associated type II compactifications fall into chains in which the proposed duals are heterotic compactifications related one another by a sequential Higgs mechanism. This breaking in the heterotic side typically involves the sequence SU (4) → SU (3) → SU (2) → ), while in the type II side the weights of the complex hypersurfaces and the structure of the K 3 quotient singularities also follow specific patterns. Some qualitative features of the relationship between each model and its dual can be understood by fiber-wise application of string-string duality.

Lectures on superstring phenomenology

The phenomenological aspects of string theory are briefly reviewed. Emphasis is given to the status of 4D string model building, effective Lagrangians, model independent results, supersymmetry breaking and duality symmetries.

Heterotic/heterotic duality in D = 6,4

Abstract We consider E 8 × E 8 heterotic compactifications on K 3 and K 3 × T 2 . The idea of heterotic/heterotic duality in D = 6 has difficulties for generic compactifications since for large dilaton values some gauge groups acquire negative kinetic terms. Recently Duff, Minasian and Witten (DMW) suggested a solution to this problem which only works if the compactification is performed assuming the presence of symmetric gauge embeddings on both E 8 s. We consider an alternative in which asymmetric embeddings are possible and the wrong sign of kinetic terms for large dilaton value is a signal of spontaneous symmetry breaking. Upon further toroidal compactification to D = 4, we find that the duals in the DMW case correspond to N = 2 models in which the β-function of the different group factors verify β α = 12 whereas the asymmetric solutions that we propose have β α = 24. We check the consistency of these dualities by studying the different large T , S limits of the gauge kinetic function. Dual N = 1, D = 4 models can also be obtained by the operation of appropriate freely acting twists, as shown in specific examples.