Standard Grand Unification from Superstrings

Recent developments about the construction of standard $SO(10)$ and $SU(5)$ grand unified theories from 4-dimensional superstrings are presented. Explicit techniques involving higher level affine Lie algebras, for obtaining such stringGUTs from symmetric orbifolds are discussed. Special emphasis is put on the different constraints and selection rules for model building in this string framework, trying to disentangle those which are generic from those depending on the orbifold construction proposed. Some phenomenological implications from such constraints are briefly discussed.Comment: 7 pages, Latex, no figures. Talk at Susy 95. Paris, May 199

Double Field Theory: A Pedagogical Review

Double Field Theory (DFT) is a proposal to incorporate T-duality, a distinctive symmetry of string theory, as a symmetry of a field theory defined on a double configuration space. The aim of this review is to provide a pedagogical presentation of DFT and its applications. We first introduce some basic ideas on T-duality and supergravity in order to proceed to the construction of generalized diffeomorphisms and an invariant action on the double space. Steps towards the construction of a geometry on the double space are discussed. We then address generalized Scherk-Schwarz compactifications of DFT and their connection to gauged supergravity and flux compactifications. We also discuss U-duality extensions, and present a brief parcours on world-sheet approaches to DFT. Finally, we provide a summary of other developments and applications that are not discussed in detail in the review.Comment: 121 pages, invited review for Class. Quantum Grav; v2: Updated reference

The gauge structure of Exceptional Field Theories and the tensor hierarchy

We address the construction of manifest U-duality invariant generalized diffeomorphisms. The closure of the algebra requires an extension of the tangent space to include a tensor hierarchy indicating the existence of an underlying unifying structure, compatible with E_{11} and Borcherds algebras constructions. We begin with four-dimensional gauged maximal supergravity, and build a generalized Lie derivative that encodes all the gauge transformations of the theory. A generalized frame is introduced, which accommodates for all the degrees of freedom, including the tensor hierarchy. The generalized Lie derivative defines generalized field-dependent fluxes containing all the covariant quantities in the theory, and the closure conditions give rise to their corresponding Bianchi Identities. We then move towards the construction of a full generalized Lie derivative defined on an extended space, analyze the closure conditions, and explore the connection with that of maximal gauged supergravity via a generalized Scherk-Schwarz reduction, and with 11-dimensional supergravity.Comment: 53 page

Physics beyond the standard model : theoretical and phenomenological aspects

Estudiaremos diversos aspectos relacionados con la teoría de cuerdas, la fenomenología de la física de partículas elementales a la escala TeV, la teoría de campos en espacios curvos y aspectos formales de las teorías de campos cuánticos no locales en dimensiones no enteras. Teoría e cuerdas: Analizaremos teorías de campos, como teoría Doble de Campos, que describan aspectos de las compactificaciones de teorías de cuerdas y que incluyan estados masivos de momento y de enrollamiento de manera consistente. Se estudiarán las simetrías subyacentes y aspectos fenomenológicos en compactificaciones con flujos. Se avanzará en el estudio de las limitaciones que impone un límite ultravioleta consistente a modelos de bajas energías (Landscape-Swampland)Fenomenología de las partículas en la escala TeV: se explorará el vínculo entre la teoría y el experimento en relación con la escala TeV, con énfasis en la física del LHC. Por un lado, intentaremos interpretar los resultados experimentales en términos de modelos de nueva física que eventualmente puedan revelar discrepancias con respecto a las predicciones de SM. Por otro lado, se analizarán las predicciones de estos modelos comparándolos con las medidas experimentales, de esta manera la construcción de la prueba observable podrá actuar como una guía en el diseño de los experimentos. Fenómenos críticos y teorías de campo no locales. Teorías de campo en espacios con dimensiones no enteras: Analizaremos sistemas críticos mediante teorías de campo no locales. Estas teorías pueden incluir términos cinéticos no locales y / o términos de interacción no locales, se prevé el estudio de ambas opciones. Los resultados también se compararán utilizando técnicas de decimación de Wilson en teorías de campos. Teoría cuántica de campos en espacios curvos: se analizará el problema de la contribución de las fluctuaciones cuánticas del vacío a la energía oscura, con especial énfasis en el rol gravitacional de las fluctuaciones del tensor de energía-impulso de los campos cuánticos alrededor de su valor medio. Se utilizará el formalismo de la gravitación estocástica, estudiando las soluciones a las ecuaciones de Einstein- Langevin. Por otra parte se continuará con el estudio del comportamiento infrarojo de las funciones de correlación para campos interactuantes en el espacio-tiempo de De Sitter, desarrollando métodos de cálculo no perturbativos, que son imprescindibles para campos livianos y no masivos en esta geometría.IWe propose to study various aspects that involve string theory, the phenomenology of elementary particle physics to the TeV scale, the theory of fields in curved spaces (semi-classical gravitation) and formal aspects of non local quantum field theories in non-integer dimensions.String theory: We will analyze field theories, such as Double Field Theory, that describe aspects of the compactifications of string theories and that include massive moment and winding states. The underlying symmetries and phenomenological aspects of compactifications with fluxes will be studied. I Progress will be made in the study of the limitations imposed by a consistent ultraviolet limit on low-energy models (Landscape-Swampland).Phenomenology of particles at the TeV scale: The link between theory and experiment in relation to the TeV scale, with emphasis on the physics of the LHC, will be explored. On the one hand, we will try to interpret experimental results in terms of models of new physics that may eventually reveal discrepancies with respect to SM predictions. On the other hand, the predictions of these models will be analyzed comparing them with the experimental measures, in this way the construction of observable test will be able to act as a guide in the design of the experiments.Critical phenomena and non-local field theories. Field theories in spaces with non-integer dimensions: The study of critical systems is proposed by means of non local field theories . These theories may include non-local kinetic terms and / or non-local interaction terms, the study of both options is foreseen. The results will also be compared using field theory techniques and Wilson's decimation technique.Quantum field theory in curved spaces: In the framework of the quantum field theory in curved spaces, the problem of the contribution of vacuum quantum fluctuations to dark energy will be analyzed, with special emphasis on the gravitational role of Stress-energy tensor fluctuations of the quantum fields around their mean value. The formalism of stochastic gravitation will be used, studying the solutions to the Einstein-Langevin equations. On the other hand, we will continue with the study of the infrared behavior of the correlation functions for interacting fields in De Sitter space-time of De Sitter, developing non-perturbative calculation methods, which are essential for light and non-massive fields in this geometry

The effective action of Double Field Theory

We perform a generalized Scherk-Schwarz dimensional reduction of Double Field Theory on a twisted double torus. The four dimensional effective action is shown to exactly reproduce the bosonic electric sector of gauged N = 4 supergravity. We present explicit expressions for the gaugings in terms of the twists, and analyze the associated string backgrounds. This framework provides a higher dimensional origin of the gaugings in terms of generalized fluxes.Comment: 45 pages, 1 figure; v2: minor corrections and references added; v3: published versio

On Susy Standard-like models from orbifolds of D=6 Gepner orientifolds

As a further elaboration of the proposal of Ref. [1] we address the construction of Standard-like models from configurations of stacks of orientifold planes and D-branes on an internal space with the structure ${(Gepner model)^{c=6} \times T^2}/Z_N$. As a first step, the construction of D=6 Type II B orientifolds on Gepner points, in the diagonal invariant case and for both, odd and even, affine levels is discussed. We build up the explicit expressions for B-type boundary states and crosscaps and obtain the amplitudes among them. From such amplitudes we read the corresponding spectra and the tadpole cancellation equations. Further compactification on a T^2 torus, by simultaneously orbifolding the Gepner and the torus internal sectors, is performed. The embedding of the orbifold action in the brane sector breaks the original gauge groups and leads to N=1 supersymmetric chiral spectra. Whenever even orbifold action on the torus is considered, new branes, with worldvolume transverse to torus coordinates, must be included. The detailed rules for obtaining the D=4 model spectra and tadpole equations are shown. As an illustration we present a 3 generations Left-Right symmetric model that can be further broken to a MSSM model.Comment: 40 pages, 2 figures, added references, table 3 correcte

On Type IIB moduli stabilization and N = 4, 8 supergravities

We analyze D = 4 compactifications of Type IIB theory with generic, geometric and non-geometric, dual fluxes turned on. In particular, we study N = 1 toroidal orbifold compactifications that admit an embedding of the untwisted sector into gauged N = 4, 8 supergravities. Truncations, spontaneous breaking of supersymmetry and the inclusion of sources are discussed. The algebraic identities satisfied by the supergravity gaugings are used to implement the full set of consistency constraints on the background fluxes. This allows to perform a generic study of N = 1 vacua and identify large regions of the parameter space that do not admit complete moduli stabilization. Illustrative examples of AdS and Minkowski vacua are presented.Comment: 48 pages, 1 figure. References added. Published in NP B 849 (2011) pp. 80-11

Stringy Tachyonic Instabilities of Non-Supersymmetric Ricci Flat Backgrounds

Superstring/M-theory compactified on compact Ricci flat manifolds have recently been conjectured to exhibit instabilities whenever the metrics do not have special holonomy. We use worldsheet conformal field theory to investigate instabilities of Type II superstring theories on compact, Ricci flat, spin 3-manifolds including a worldsheet description of their spin structures. The instabilities are signalled by the appearance of stringy tachyons at small radius and a negative (1-loop) vacuum energy density at large radius. We briefly discuss the extension to higher dimensions.Comment: 30+3p

Type IIB orientifolds on Gepner points

We study various aspects of orientifold projections of Type IIB closed string theory on Gepner points in different dimensions. The open string sector is introduced, in the usual constructive way, in order to cancel RR charges carried by orientifold planes. Moddings by cyclic permutations of the internal N=2 superconformal blocks as well as by discrete phase symmetries are implemented. Reduction in the number of generations, breaking or enhancements of gauge symmetries and topology changes are shown to be induced by such moddings. Antibranes sector is also considered; in particular we show how non supersymmetric models with antibranes and free of closed and open tachyons do appear in this context. A systematic study of consistent models in D=8 dimensions and some illustrative examples in D=6 and D=4 dimensions are presented.Comment: 67 pages, no figures References added, typos correcte

A second look at N=1 supersymmetric AdS_4 vacua of type IIA supergravity

We show that a class of type IIA vacua recently found within the N=4 effective approach corresponds to compactification on Ads_4 \times S^3 \times S^3/Z_2^3. The results obtained using the effective method completely match the general ten-dimensional analysis for the existence of N=1 warped compactifications on Ads_4 \times M_6. In particular, we verify that the internal metric is nearly-Kahler and that for specific values of the parameters the Bianchi identity of the RR 2-form is fulfilled without sources. For another range of parameters, including the massless case, the Bianchi identity is satisfied when D6-branes are introduced. Solving the tadpole cancellation conditions in D=4 we are able to find examples of appropriate sets of branes. In the second part of this paper we describe how an example with internal space CP^3 but with non nearly-Kahler metric fits into the general analysis of flux vacua.Comment: Latex file, 35 pages, no figures. Reference added, minor corrections adde