No-go for tree-level R-symmetry breaking

We show that in gauge mediation models with tree-level R-symmetry breaking where supersymmetry and R-symmetries are broken by different fields, the gaugino mass either vanishes at one loop or finds a contribution from loop-level R-symmetry breaking. Thus tree-level R-symmetry breaking for phenomenology is either no-go or redundant in the simplest type of models. Including explicit messenger mass terms in the superpotential with a particular R-charge arrangement is helpful to bypass the no-go theorem, and the resulting gaugino mass is suppressed by the messenger mass scale.Comment: 8 pages, 7 figures; v2: discussion on Driac gauginos and references added; v3: a section on bypassing the no-go added, R-charge notation changed; v4: typos, EPJC pre-published versio

A Quadrillion Standard Models from F-theory

We present an explicit construction of ${\cal O}(10^{15})$ globally consistent string compactifications that realize the exact chiral spectrum of the Standard Model of particle physics with gauge coupling unification in the context of F-theory. Utilizing the power of algebraic geometry, all global consistency conditions can be reduced to a single criterion on the base of the underlying elliptically fibered Calabi--Yau fourfolds. For toric bases, this criterion only depends on an associated polytope and is satisfied for at least ${\cal O}(10^{15})$ bases, each of which defines a distinct compactification.Comment: 7 pages, double column; v3: improved and expanded discussion, technical details deferred to an added appendi

F-Theory Realizations Of Exact Mssm Matter Spectra

F-theory is remarked by its powerful phenomenological model building potential due to geometric descriptions of compactifications. It translates physics quantities in the effective low energy theory to mathematical objects extracted from the geometry of the compactifications. The connection is built upon identifying the varying axio-dilaton field in type IIB supergravity theory with the complex structure modulus of an elliptic curve, that serves as the fiber of an elliptic fibration. This allows us to capture the non-perturbative back-reactions of seven branes onto the compactification space $B_3$ of an elliptically fibered Calabi--Yau fourfold $Y_4$. The ingredients of Standard model physics, including gauge symmetries, charged matter, and Yukawa couplings, are then encoded beautifully by $Y_4$\u27s singularity structures in codimensions one, two, and three, respectively. Moreover, many global consistency conditions, including the D3-tadpole cancellation, can be reduced to simple criteria in terms of the intersection numbers of base divisors. In this thesis, we focus on searching for explicit models in the language of F-theory geometry that admit exact Minimal Supersymmetric Standard Model (MSSM) matter spectra. We first present a concrete realization of the Standard Model (SM) gauge group with $\mathbb{Z}_2$ matter parity, which admits three generations of chiral fermions. The existence of this discrete symmetry beyond the SM gauge group forbids proton decay. We then construct a family of $\mathcal{O}(10^{15})$ F-theory vacua. These are the largest currently known class of globally consistent string constructions that admit exactly three chiral families and gauge coupling unification. We advance to study the vector-like spectra in 4d F-theory SMs. The 4-form gauge background $G_4$ controls the chiral spectra. This is the field strength of 3-form gauge potential $C_3$, which impacts the vector-like spectra. It is well known that these massless zero modes are counted by line bundle cohomologies over matter curves induced by the F-theory gauge background. In order to understand the line bundle cohomology\u27s dependence on the moduli of the compactification geometry, we pick a simple geometry and create the database consisted of matter curves, the line bundles and the vector-like spectra. We analyze this database by machine learning techniques and ugain full understanding it via the Brill-Nother theory. Subsequently, we present the appearance of root bundles and how they enter as significant ingredients of realistic F-theory geometries. The algebraic geometry approaches to root bundles allow combinatoric descriptions, which facilitate the analyze of statistics on the vector-like spectra at the end of this thesis

6D Heterotic Little String Theories and F-theory Geometry: An Introduction

We review here some aspects of our recent works about the geometric engineering of heterotic little string theories using F-theory. Building on the seminal work by Aspinwall and Morrison as well as Intrilligator and Blum, we solve some longstanding open questions thanks to recent progress in our understanding of 6D (1,0) theories and their generalized symmetries. On the geometry side, these systems correspond to non-compact elliptically fibered Calabi-Yau varieties that must admit the structure of an elliptic K3 fibration. From fiberwise F-theory/Heterotic duality the K3 plays a central role - it determines the 6D flavor group, as well as different T-dual LSTs via inequivalent elliptic fibration structures. The geometries we obtain are some finer versions of Kulikov degenerations: the point where the K3 fiber degenerates is the locus where the LST arises. This structure serve on one hand to check our field theory predictions on LST dualities via the match of Coulomb branch dimension, flavor symmetries, and 2-group structure constants, and also on the other hand to deduce novel LST models and their networks of dualities, thus allowing exploring non-geometric Heterotic regimes.Comment: Contribution to the proceedings of String Math 202

Back to Heterotic Strings on ALE Spaces: Part I -- Instantons, 2-groups and T-duality

In this paper we begin revisiting the little string theories (LSTs) which govern the dynamics of the instantonic heterotic $E_8 \times E_8$ five-branes probing ALE singularities, building on and extending previous results on the subject by Aspinwall and Morrison as well as Blum and Intriligator. Our focus are the cases corresponding to choices of non-trivial flat connections at infinity. The latter are in particular interesting for the exceptional ALE singularities, where a brane realization in Type I$'$ is lacking. Our approach to determine these models is based on 6d conformal matter: we determine these theories as generalized 6d quivers. All these LSTs have a higher-one form symmetry which forms a 2-group with the zero-form Poincar\'e symmetry, the R-symmetry and the other global symmetries: the matching of the R-symmetry two-group structure constant is a stringent constraint for T-dualities, which we use in combination with the matching of 5d Coulomb branches and flavor symmetries upon circle reduction, as a consistency check for the realization of the 6d LSTs we propose.Comment: are welcome