We further study the cancellation of the one-loop corrections to the scalar mass in a six dimensional SU(2) gauge theory with higher dimensional operators, which is compactified on a torus with magnetic flux. Higher dimensional operators also contribute to the corrections to the scalar mass nontrivially. We explicitly show by the diagrammatic calculations that the corrections are exactly cancelled even with the leading terms of the higher dimensional operators.
We calculate one-loop corrections to the mass for the zero mode of scalar field in a six-dimensional Yang-Mills theory compactified on a torus with magnetic flux. It is shown that these corrections are exactly cancelled thanks to a shift symmetry under the translation in extra spaces. This result is expected from the fact that the zero mode of scalar field is a Nambu-Goldstone boson of the translational invariance in extra spaces.
This paper proposes a concrete model of nonuniversal gaugino masses on the basis of higher-dimensional supersymmetric Yang-Mills theories compactified on a magnetized factorizable torus, and we estimate the gauge coupling constants and gaugino masses in the model. In the magnetized toroidal compactifications, the four-dimensional effective action can be obtained analytically identifying its dependence on moduli fields, where the magnetic fluxes are able to yield the flavor structure of the minimal supersymmetric standard model (MSSM). The obtained gauge kinetic functions contains multi moduli …
We study in detail how four-dimensional local anomalies manifest themselves when the theory is compactified on a circle. By integrating out the Kaluza-Klein modes in a way that preserves the four-dimensional symmetries in the UV, we show that the three-dimensional theory contains field-dependent Chern-Simons terms that appear at one-loop. These vanish if and only if the four-dimensional anomaly is canceled, so the anomaly is not lost upon compactification. We extend this analysis to situations where anomalies are canceled through a Green-Schwarz mechanism. We then use these results to show aut…
A multiplicity of quark-lepton families can naturally arise as zero-modes in flux compactifications. The flavour structure of quark and lepton mass matrices is then determined by the wave function profiles of the zero-modes. We consider a supersymmetric $SO(10)\times U(1)$ model in six dimensions compactified on the orbifold $T^2/{\mathbb Z_2}$ with Abelian magnetic flux. A bulk $\mathbf{16}$-plet charged under the $U(1)$ provides the quark-lepton generations whereas two uncharged $\mathbf{10}$-plets yield two Higgs doublets. Bulk anomaly cancellation requires the presence of additional $\math…
We consider type IIB large volume compactifications involving orientifolds of the Swiss-Cheese Calabi-Yau WCP^4[1; 1; 1; 6; 9] with a single mobile space-time filling D3-brane and stacks of D7-branes wrapping the "big" divisor (as opposed to the "small" divisor usually done in the literature thus far) as well as supporting D7-brane fluxes. After reviewing our proposal of [1] for resolving a long-standing tension between large volume cosmology and phenomenology pertaining to obtaining a 10^12 GeV gravitino in the inflationary era and a TeV gravitino in the present era, and summarizing our resul…
We consider flux vacua for type IIB orientifold compactifications and study their interplay with the tadpole-cancellation condition. As a concrete example we focus on $\mathbb T^6/\mathbb Z_2\times \mathbb Z_2$, for which we find that solutions to the F-term equations at weak coupling, large complex structure and large volume require large flux contributions. Such contributions are however strongly disfavored by the tadpole-cancellation condition. We furthermore find that solutions which stabilize moduli in this perturbatively-controlled regime are only a very small fraction of all solutions, …
We investigate the interplay between the string scale and phenomenological scales in orientifold compactifications. Specifically, we discuss in generality the tension that often arises in accounting for neutrino masses, Yukawa couplings, and a mu-term of the correct order and show that it often constrains the string scale M_s. The discussion focuses on two scenarios where, (1) the observed order of the neutrino masses are accounted for by a D-instanton induced "stringy" Weinberg operator, or (2) effectively via the type I seesaw mechanism with an instanton induced Majorana mass term. In both s…
We study 4D F-theory compactifications on singular Calabi-Yau fourfolds with fluxes. The resulting N=1 effective theories can admit non-Abelian and U(1) gauge groups as well as charged chiral matter. In these setups we analyze anomaly cancellation and the generalized Green-Schwarz mechanism. This requires the study of 3D N=2 theories obtained by a circle compactification and their M-theory duals. Reducing M-theory on resolved Calabi-Yau fourfolds corresponds to considering the effective theory on the 3D Coulomb branch in which certain massive states are integrated out. Both 4D gaugings and 3D …
Chern-Simons couplings, modular duality, and anomaly cancellation in abelian F-theory
Irving K. Barber School of Arts and Sciences, University of British Columbia Okanagan（不列颠哥伦比亚大学奥肯那根分校欧文K.巴伯艺术与理学院）；Canadian Quantum Research Center（加拿大量子研究中心）；Department of Mathematical Sciences, Durham University（杜伦大学数学科学系）；Computational Mathematics Group, Faculty of Sciences, Hasselt University（哈瑟尔特大学理学院计算数学组）
We address the issue of radiative corrections to Kaluza-Klein (KK) masses in five-dimensional QED supplemented by aether Lorentz-violating terms. Specifically, we compute the corrections to the KK photon masses from one fermion loop. In general, the KK masses receive radiative corrections due to breaking the five-dimensional Lorentz invariance by compactification. As we show, the presence of the additional Lorentz violating factor - an aether background, leads to the non-trivial modification of these corrections. This model may be of interest in addressing important phenomenological issues suc…
We discuss effects of the brane-localized mass terms on the fixed points of the toroidal orbifold $T^2/Z_2$ under the presence of background magnetic fluxes, where multiple lowest and higher-level Kaluza-Klein (KK) modes are realized before introducing the localized masses in general. Through the knowledge of linear algebra, we find that, in each KK level, one of or more than one of the degenerate KK modes are almost inevitably perturbed, when single or multiple brane-localized mass terms are introduced. When the typical scale of the compactification is far above the electroweak scale or the T…
We study proton decay in a six-dimensional orbifold GUT model with gauge group $SO(10)\times U(1)_A$. Magnetic $U(1)_A$ flux in the compact dimensions determines the multiplicity of quark-lepton generations, and it also breaks supersymmetry by giving universal GUT scale masses to scalar quarks and leptons. The model can successfully account for quark and lepton masses and mixings. Our analysis of proton decay leads to the conclusion that the proton lifetime must be close to the current experimental lower bound. Moreover, we find that the branching ratios for the decay channels $p \rightarrow e…
The gravitino mass is expected not to be much smaller than the Planck scale for a large fraction of vacua in flux compactifications. There is no continuous parameter to tune even by hand, and it seems that the gravitino mass can be small only as a result of accidental cancellation among period integrals weighted by integer-valued flux quanta. DeWolfe et.al. (2005) proposed to pay close attention to vacua where the Hodge decomposition is possible within a number field, so that the precise cancellation takes place as a result of algebra. We focus on a subclass of those vacua---those with complex…
We investigate the vacuum structure of four-dimensional effective theory arising from Type IIB flux compactifications on a mirror of the rigid Calabi-Yau threefold, corresponding to a T-dual of the DeWolfe-Giryavets-Kachru-Taylor model in Type IIA flux compactifications. By analyzing the vacuum structure of this interesting corner of string landscape, it turns out that there exist perturbatively unstable de Sitter (dS) vacua in addition to supersymmetric and non-supersymmetric anti-de Sitter vacua. On the other hand, the stable dS vacua appearing in the low-energy effective action violate the …
We use Pauli-Villars regularization to evaluate the conformal and chiral anomalies in the effective field theories from Z3 and Z7 compactifications of the heterotic string without Wilson lines. We show that parameters for Pauli-Villars chiral multiplets can be chosen in such a way that the anomaly is universal in the sense that its coefficient depends only on a single holomorphic function of the three diagonal moduli. It is therefore possible to cancel the anomaly by a generalization of the four-dimensional Green-Schwarz mechanism. In particular we are able to reproduce the results of a string…
We examine the structure of lower-dimensional standard model vacua for two-dimensional compactifications (on a 2D torus and on a 2D sphere). In the case of the torus we find a new standard model vacuum for a large range of neutrino masses consistent with experiment. Quantum effects play a crucial role in the existence of this vacuum. For the compactification on a sphere the classical terms dominate the effective potential for large radii and a stable vacuum is achieved only by introducing a large magnetic flux. We argue that there are no two-dimensional standard model vacua for compactificatio…
We study soft supersymmetry breaking terms for anisotropic LARGE volume compactifications, where the bulk volume is set by a fibration with one small four-cycle and one large two-cycle. We consider scenarios where D7s wrap either a blow-up cycle or the small fibre cycle. Chiral matter can arise either from modes parallel or perpendicular to the brane. We compute soft terms for this matter and find that for the case where the D7 brane wraps the fibre cycle the scalar masses can be parametrically different, allowing a possible splitting of third-generation soft terms.
The 102581 flat toric elliptic fibrations over P^2 are identified among the Calabi-Yau hypersurfaces that arise from the 473800776 reflexive 4-dimensional polytopes. In order to analyze their elliptic fibration structure, we describe the precise relation between the lattice polytope and the elliptic fibration. The fiber-divisor-graph is introduced as a way to visualize the embedding of the Kodaira fibers in the ambient toric fiber. In particular in the case of non-split discriminant components, this description is far more accurate than previous studies. The discriminant locus and Kodaria fibe…
The compactification from the 11-dimensional Horava-Witten orbifold to 5-dimensional heterotic M-theory on a Schoen Calabi-Yau threefold is reviewed, as is the specific $SU(4)$ vector bundle leading to the "heterotic standard model" in the observable sector. A generic formalism for a consistent hidden sector gauge bundle, within the context of strongly coupled heterotic M-theory, is presented. Anomaly cancellation and the associated bulk space 5-branes are discussed in this context. The further compactification to a 4-dimensional effective field theory on a linearized BPS double domain wall is…
We compute the effective Kahler potential for matter fields in warped compactifications, starting from five dimensional gauged supergravity, as a function of the matter fields localization. We show that truncation to zero modes is inconsistent and the tree-level exchange of the massive gravitational multiplet is needed for consistency of the four-dimensional theory. In addition to the standard Kahler coming from dimensional reduction, we find the quartic correction coming from integrating out the gravity multiplet. We apply our result to the computation of scalar masses, by assuming that the S…
We initiate the construction of gauge fluxes in F-theory compactifications on genus-one fibrations which only have a multi-section as opposed to a section. F-theory on such spaces gives rise to discrete gauge symmetries in the effective action. We generalize the transversality conditions on gauge fluxes known for elliptic fibrations by taking into account the properties of the available multi-section. We test these general conditions by constructing all vertical gauge fluxes in a bisection model with gauge group SU(5) x Z2. The non-abelian anomalies are shown to vanish. These flux solutions ar…
We construct a set of chirality inducing G_4-fluxes in global F-theory compactifications on Calabi-Yau four-folds. Special emphasis is put on models with gauge group SU(5) x U(1)_X relevant in the context of F-theory GUT model building, which are described in terms of a U(1)-restricted Tate model. In this type of constructions, the G_4-flux arises in a manner completely analogous to the U(1)_X gauge potential. We describe in detail the resolution by blow-up of the various singularities responsible for the U(1)_X factor and the standard SU(5) gauge group and match the result with techniques app…
We examine the large volume compactification of Type IIB string theory or its F theory limit and the associated supersymmetry breakdown and soft terms. It is crucial to incorporate the loop-induced moduli mixing, originating from radiative corrections to the Kahler potential. We show that in the presence of moduli mixing, soft scalar masses generically receive a D-term contribution of the order of the gravitino mass m_{3/2} when the visible sector cycle is stabilized by the D-term potential of an anomalous U(1) gauge symmetry, while the moduli-mediated gaugino masses and A-parameters tend to b…
It has been shown that non-Abelian solitonic vortex strings supported in four-dimensional (4D) ${\mathcal N}=2\;$ supersymmetric QCD (SQCD) with the U($N=2$) gauge group and $N_f=4$ quark flavors behave as critical superstrings. In addition to four translational moduli non-Abelian strings under consideration carry six orientational and size moduli. Together they form a ten-dimensional space required for a superstring to be critical. The target space of the string sigma model is a product of the flat four-dimensional space $\mathbb{R}^4$ and a Calabi-Yau non-compact threefold $Y_6$, namely, the…
Closed string fluxes induce generically SUSY-breaking soft terms on supersymmetric type IIB orientifold compactifications with D3/D7 branes. This was studied in the past by inserting those fluxes on the DBI+CS actions for adjoint D3/D7 fields, where D7-branes had no magnetic fluxes. In the present work we generalise those computations to the phenomenologically more relevant case of chiral bi-fundamental fields laying at 7-brane intersections and F-theory local matter curves. We also include the effect of 7-brane magnetic flux as well as more general closed string backgrounds, including the eff…
We discuss the structure of 4D gauged supergravity algebras corresponding to globally non-geometric compactifications of F-theory, admitting a local geometric description in terms of 10D supergravity. By starting with the well known algebra of gauge generators associated to non-geometric type IIB fluxes, we derive a full algebra containing all, closed RR and NSNS, geometric and non-geometric dual fluxes. We achieve this generalization by a systematic application of SL(2,Z) duality transformations and by taking care of the spinorial structure of the fluxes. The resulting algebra encodes much in…
In this thesis, we consider heterotic string vacua based on a warped product of a four-dimensional domain wall and a six-dimensional internal manifold preserving only two supercharges. Thus, they correspond to half-BPS states of heterotic supergravity. The constraints on the internal manifolds with SU(3) structure are derived. They are found to be a generalization of half-flat manifolds with a particular pattern of torsion classes and they include half-flat manifolds and Strominger's complex non-Kahler manifolds as special cases. We also verify that heterotic compactifications on half-flat mir…
We present exact solutions of four-dimensional Einstein's equations related to Minkoswki vacuum constructed from Type IIB string theory with non-trivial fluxes. Following recent works, we study a non-trivial flux compactification on a fibered product by a four-dimensional torus and a two-dimensional sphere punctured by 5- and 7-branes. By considering only 3-form fluxes and the dilaton, as functions on the internal sphere coordinates, we show that these solutions correspond to a family of supersymmetric solutions constructed by the use of G-theory. Meromorphicity on functions constructed in ter…
