Radu Tatar

Codimension-3 singularities and Yukawa couplings in F-theory

Abstract F-theory is one of the frameworks where all the Yukawa couplings of grand unified theories are generated and their computation is possible. The Yukawa couplings of charged matter multiplets are supposed to be generated around codimension-3 singularity points of a base complex 3-fold, and that has been confirmed for the simplest type of codimension-3 singularities in recent studies. However, the geometry of F-theory compactifications is much more complicated. For a generic F-theory compactification, such issues as flux configuration around the codimension-3 singularities, field-theory formulation of the local geometry and behavior of zero-mode wavefunctions have virtually never been addressed before. We address all these issues in this article, and further discuss nature of Yukawa couplings generated at such singularities. In order to calculate the Yukawa couplings of low-energy effective theory, however, the local descriptions of wavefunctions on complex surfaces and a global characterization of zero-modes over a complex curve have to be combined together. We found the relation between them by re-examining how chiral charged matters are characterized in F-theory compactification. An intrinsic definition of spectral surfaces in F-theory turns out to be the key concept. As a biproduct, we found a new way to understand the Heterotic–F theory duality, which improves the precision of existing duality map associated with codimension-3 singularities.

New aspects of Heterotic–F-theory duality

Abstract In order to understand both up-type and down-type Yukawa couplings, F-theory is a better framework than the perturbative Type IIB string theory. The duality between the Heterotic and F-theory is a powerful tool in gaining more insights into F-theory description of low-energy chiral multiplets. Because chiral multiplets from bundles ∧ 2 V and ∧ 2 V × as well as those from a bundle V are all involved in Yukawa couplings in Heterotic compactification, we need to translate descriptions of all those kinds of matter multiplets into F-theory language through the duality. We find that chiral matter multiplets in F-theory are global holomorphic sections of line bundles on what we call covering matter curves. The covering matter curves are formulated in Heterotic theory in association with normalization of spectral surface, while they are where M2-branes wrapped on a vanishing two-cycle propagate in F-theory. Chirality formulae are given purely in terms of primitive four-form flux. In order to complete the translation, the dictionary of the Heterotic–F-theory duality has to be refined in some aspects. A precise map of spectral surface and complex structure moduli is obtained, and with the map, we find that divisors specifying the line bundles correspond precisely to codimension-3 singularities in F-theory.

Orientifold, geometric transition and large N duality for SO / Sp gauge theories

We extend the large N duality of four dimensional = 1 supersymmetric Yang-Mills theory with additional chiral fields and arbitrary superpotential recently proposed by Cachazo, Intriligator and Vafa to the case of SO/Sp gauge groups. By orientifolding the geometric transition, we investigate a large N duality between = 1, SO/Sp supersymmetric theories with arbitrary superpotential and an abelian = 2 theory with supersymmetry broken to = 1 by electric and magnetic Fayet-Iliopoulos terms.

Lumps and p branes in open string field theory

Abstract We describe numerical methods for constructing lump solutions in open string field theory. According to Sen, these lumps represent lower dimensional Dp branes and numerical evaluation of their energy can be compared with the expected value for the tension. We take particular care of all higher derivative terms inherent in Wittens version of open string field theory. The importance of these terms for off shell phenomena is argued in the text. Detailed numerical calculations done for the case of general p brane show very good agreement with Sens conjectured value. This gives credence to the conjecture itself and establishes further the usefulness of Wittens version of SFT.

Geometric transition, large N dualities and MQCD dynamics

Abstract We study Vafas geometric transition from a brane setup in M-theory. In this transition D5 branes wrapped on P 1 cycles of a resolved conifold disappear and are replaced by fluxes on a deformed conifold. In the limit of small sized P 1 , we describe this mechanism as a transition from curved M5 branes to plane M5 branes which replaces SU(N) MQCD by U(1) theories on the bulk. This agrees with the results expected from the geometric transition. We also discuss the reduction to ten dimensions and a brane creation mechanism in the presence of fluxes.

Open/Closed String Dualities and Seiberg Duality from Geometric Transitions in M-theory

We propose a general method to study open/closed string dualities from transitions in M theory which is valid for a large class of geometrical configurations. By T-duality we can transform geometrically engineered configurations into = 1 brane configurations and study the transitions of the corresponding branes by lifting the configurations to M-theory. We describe the transformed degenerated M5 branes and extract the field theory information on gluino condensation by factorization of the Seiberg-Witten curve. We also include massive flavors and orientifolds and discuss Seiberg duality which appears in this case as a birational flop. After the transition, the Seiberg duality becomes an abelian electric-magnetic duality.

Geometric transition versus cascading solution

We study Vafas geometric transition and Klebanov-Strassler solution from various points of view in M-theory. In terms of brane configurations, we show the detailed equivalences between the two models. In some limits, both models have an alternative realization as fourfolds in M-theory with appropriate G-fluxes turned on. We discuss some aspects of the fourfolds including how to see the transition and a possible extension to the non-supersymmetric case.

Right-handed Neutrinos in F-theory Compactifications

Abstract F-theory is one of the frameworks where up-type Yukawa couplings of SU(5) unified theories are naturally generated. As charged matter fields have localized zero modes in F-theory, a study of flavor structure could be easier in F-theory than in Heterotic string theory. In a study of flavor structure in the lepton sector, however, an important role is played by right-handed neutrinos, which are not charged under the SU(5) unified gauge group. It is therefore solicited to find out what right-handed neutrinos are in F-theory compactifications and how their Majorana mass terms are generated together with developing a theoretical framework where effective Yukawa couplings involving both SU(5)-neutral and charged fields can be calculated. We find that the complex structure moduli chiral multiplets of F-theory compactifications are good candidates to be right-handed neutrinos, and that their Majorana masses are automatically generated in flux compactifications. The mass scale is predicted to be somewhat below the GUT scale, which is in nice agreement with the Δ m 2 of the atmospheric neutrino oscillation through the see-saw mechanism. We also discuss various scenarios of solving the dimension-4 proton decay problem in supersymmetric F-theory compactifications, along with considering the consequences of those scenarios in the nature of right-handed neutrinos.

Proton decay, yukawa couplings and underlying gauge symmetry in string theory

In string theory, massless particles often originate from a symmetry breaking of a large gauge symmetry G to its subgroup H. The absence of dimension-4 proton decay in supersymmetric theories suggests that ({bar D},L) are different from {bar H}({bar 5}) in their origins. In this article, we consider a possibility that they come from different irreducible components in g/h. Requiring that all the Yukawa coupling constants of quarks and leptons be generated from the super Yang-Mills interactions of G, we found in the context of Georgi-Glashow H = SU(5) unification that the minimal choice of G is E{sub 7} and E{sub 8} is the only alternative. This idea is systematically implemented in Heterotic String, M theory and F theory, confirming the absence of dimension 4 proton decay operators. Not only H = SU(5) but also G constrain operators of effective field theories, providing non-trivial information.

Geometric transitions, flops and non-Kähler manifolds: II

Abstract We continue our study of geometric transitions in type II and heterotic theories. In type IIB theory we discuss an F-theory setup which clarifies many of our earlier assumptions and allows us to study gravity duals of N = 1 gauge theories with arbitrary global symmetry group G . We also point out the subtle differences between global and local metrics, and show that in many cases the global descriptions are far more complicated than discussed earlier. We determine the full global description in type I/heterotic theory. In type IIA, our analysis gives rise to a local non-Kahler metric whose global description involves a particular orientifold action with gauge fluxes localised on branes. We are also able to identify the three form fields that allow for a smooth flop in the M-theory lift. We briefly discuss the issues of generalized complex structures in type IIB theory and possible half-twisted models in the heterotic duals of our type II models. In a companion paper we will present details on the topological aspects of these models.