Exact partition functions of Higgsed 5d TNT_N theories

We present a general prescription by which we can systematically compute exact partition functions of five-dimensional supersymmetric theories which arise in Higgs branches of the $T_N$ theory. The theories may be realized by webs of 5-branes whose dual geometries are non-toric. We have checked our method by calculating the partition functions of the theories realized in various Higgs branches of the $T_3$ theory. A particularly interesting example is the $E_8$ theory which can be obtained by Higgsing the $T_6$ theory. We explicitly compute the partition function of the $E_8$ theory and find the agreement with the field theory result as well as the enhancement of the global symmetry to $E_8$.Comment: 54 pages, 13 figures, v2. added an appendix and minor changes in the main text, version accepted on JHE

Topological vertex for Higgsed 5d TNT_N theories

We analyse the computation of the partition function of 5d $T_N$ theories in Higgs branches using the topological vertex. The theories are realised by a web of $(p,q)$ 5-branes whose dual description may be given by an M-theory compactification on a certain local non-toric Calabi-Yau threefold. We explicitly show how it is possible to directly apply the topological vertex to the non-toric geometry. Using this novel technique, which considerably simplifies the computation by the existing method, we are able to compute the partition function of the higher rank $E_6$, $E_7$ and $E_8$ theories. Moreover we show how in some specific cases similar results can be extended to the computation of the partition function of 5d $T_N$ theories in the Higgs branch using the refined topological vertex. These cases require a modification of the refined topological vertex.Comment: 60 pages, 23 figures. v2, corrected typos, version accepted on JHE

U(1) mixing and D-brane linear equivalence

Linear equivalence is a criterion that compares submanifolds in the same homology class. We show that, in the context of type II compactifications with D-branes, this concept translates to the kinetic mixing between U(1) gauge symmetries arising in the open and closed string sectors. We argue that in generic D-brane models such mixing is experimentally detectable through the existence of milli-charged particles. We compute these gauge kinetic functions by classifying the 4d monopoles of a compactification and analyzing the Witten effect on them, finding agreement with previous results and extending them to more general setups. In particular, we compute the gauge kinetic functions mixing bulk and magnetized D-brane U(1)'s and derive a generalization of linear equivalence for these objects. Finally, we apply our findings to F-theory SU(5) models with hypercharge flux breaking.Comment: 43 pages+appendices, 1 figure; v2: typos corrected and references adde

Flux Flattening in Axion Monodromy Inflation

String theory models of axion monodromy inflation exhibit scalar potentials which are quadratic for small values of the inflaton field and evolve to a more complicated function for large field values. Oftentimes the large field behaviour is gentler than quadratic, lowering the tensor-to-scalar ratio. This effect, known as flattening, has been observed in the string theory context through the properties of the DBI+CS D-brane action. We revisit such flattening effects in type IIB flux compactifications with mobile D7-branes, with the inflaton identified with the D7-brane position. We observe that, with a generic choice of background fluxes, flattening effects are larger than previously observed, allowing to fit these models within current experimental bounds. In particular, we compute the cosmological observables in scenarios compatible with closed-string moduli stabilisation, finding tensor-to-scalar ratios as low as r ~ 0.04. These are models of single field inflation in which the inflaton is much lighter than the other scalars through a mild tuning of the compactification data.Comment: 56 pages, 11 plot

Open string multi-branched and Kahler potentials

We consider type II string compactifications on Calabi-Yau orientifolds with fluxes and D-branes, and analyse the F-term scalar potential that simultaneously involves closed and open string modes. In type IIA models with D6-branes such potential can be directly computed by integrating out Minkowski three-forms. The result shows a multi-branched structure along the space of lifted open string moduli, in which discrete shifts in special Lagrangian and Wilson line deformations are compensated by changes in the RR flux quanta. The same sort of discrete shift symmetries are present in the superpotential and constrain the Kahler potential. As for the latter, inclusion of open string moduli breaks the factorisation between complex structure and Kahler moduli spaces. Nevertheless, the 4d Kahler metrics display a set of interesting relations that allow to rederive the scalar potential analytically. Similar results hold for type IIB flux compactifications with D7-brane Wilson lines.Comment: 60 pages, one figure. v2 minor corrections and references adde

From F-theory to brane webs: Non-perturbative effects in type IIB String Theory

Tesis doctoral inédita leída en la Universidad Autónoma de Madrid, Facultad de Ciencias, Departamento de Física Teórica. Fecha de lectura: 13-06-2016We analyse the flavour sector of SU(5) Grand Unified Theories in F–theory. Two classes of local models are formulated, one with enhancement to E6 where the masses of the up–type quarks are generated, and one with enhancement to either E7 or E8 where the masses for all fermions of the Standard Model are generated. A full rank 3 Yukawa matrix is attained only after the inclusion of non–perturbative effects in the compactification space. By performing a scan over the parameters defining the local models we check whether realistic masses for the fermions may be attained. Secondly we present two example of the appearance of linear equivalence between cycles in D–brane models. In the first case we show how linear equivalence is tied with kinetic mixing between open and closed string massless U(1)’s and discuss potential phenomenological implications for dark matter and unification of gauge couplings. Secondly we show how taking into account the coupling with closed string moduli some of the brane moduli may acquire a mass. We clarify the microscopic origin of this effect and its connection with linear equivalence of cycles, and finally match it with the 4d supergravity description. Finally we discuss the application of topological string techniques for the computation of the Nekrasov partition function for theories in the Higgs branch. We formulate a general algorithm for the computation of the Nekrasov partition function of the 5d TN theory in a generic point of the Higgs branch. Afterwards we present a generalisation of the topological vertex applicable to a wide class of non– toric varieties. In both cases we provide some explicit examples of the application of the new rules formulatedSe analiza el sector de sabor en teorías SU(5) de Gran Unificación en Teoría F. Se construyen dos clases de modelos locales, una con aumento del grupo gauge a E6 donde se generan las masas de los quarks de tipo up, y una con aumento del grupo gauge a E7 o E8 donde se generan las masas de todos los fermiones del Modelo Estándar. Solamente después de haver incluido efectos no perturbativos en el espacio de compactificación se consigue una matriz de Yukawa de rango 3. Haciendo una búsqueda en los valores de los parámetros que definen los modelos locales se comprueba si es posible conseguir masas realistas para los fermiones. En segundo lugar se presentan dos ejemplos de cómo la equivalencia lineal entre ciclos aparece en modelos de D–branas. En el primer caso se demuestra cómo la equivalencia lineal está conectada con la mezcla cinética entre U(1)’s sin masa de cuerda abierta y cerrada y se discuten implicaciones fenomenológicas para materia oscura y unificación de los acoplos de gauge. Después se demuestra cómo algunos de los módulos de brana reciben masa al tener en cuenta el acoplo con los módulos de cuerda cerrada. Se aclara el origen microscópico de este efecto y su conexión con la equivalencia lineal de ciclos, comparandolo por último con la descripción en supergravedad en 4d. Finalmente se discute la aplicación de técnicas de cuerda topológica para el cálculo de funciones de partición de Nekrasov para teoría en la rama de Higgs. Se formula un algoritmo general para el cálculo de la función de partición de Nekrasov de la teoría TN en 5d en un punto genérico de la rama de Higgs. Después se presenta una generalización del vértice topológico que se puede aplicar a una amplia clase de variedades no tóricas. En ambos casos se presentan algunos ejemplos de la aplicación de las nuevas reglas que se han formulad

Fitting fermion masses and mixings in F-theory GUTs

Journal of High Energy Physics 2016.3 (2016): 126 reproduced by permission of Scuola Internazionale Superiore di Studi Avanzati (SISSA)We analyse the structure of Yukawa couplings in local SU(5) F-theory models with E7 enhancement. These models are the minimal setting in which the whole flavour structure for the MSSM charged fermions is encoded in a small region of the entire compactification space. In this setup the E7 symmetry is broken down to SU(5) by means of a 7-brane T-brane background, and further to the MSSM gauge group by means of a hypercharge flux that also implements doublet-triplet splitting. At tree-level only one family of quarks and charged leptons is massive, while the other two obtain hierarchically smaller masses when stringy non-perturbative effects are taken into account. We find that there is a unique E7 model with such hierarchical flavour structure. The relative simplicity of the model allows to perform the computation of Yukawa couplings for a region of its parameter space wider than previous attempts, obtaining realistic fermion masses and mixings for large parameter regions. Our results are also valid for local models with E8 enhancement, pointing towards a universal structure to describe realistic fermion masses within this frameworkThis work has been partially supported by the grant FPA2012-32828 from the MINECO, the REA grant agreement PCIG10-GA-2011-304023 from the People Programme of FP7 (Marie Curie Action), the ERC Advanced Grant SPLE under contract ERC-2012-ADG-20120216-320421 and the grant SEV-2012-0249 of the “Centro de Excelencia Severo Ochoa” Programme. F.C. is supported through a fellowship of the international programme “La Caixa-Severo Ochoa”. F.M. is supported by the Ram´on y Cajal programme through the grant RYC-2009-05096. G.Z. is supported through a grant from “Campus Excelencia Internacional UAM+CSIC”. F.M. would like to thank HKUST IAS, the CERN TH Division, the Aspen Center for Theoretical Physics (supported through the NSF grant PHY-1066293) and UW-Madison for hospitality and support during the completion of this wor