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4D gauge theories with conformal matter

Abstract One of the hallmarks of 6D superconformal field theories (SCFTs) is that on a partial tensor branch, all known theories resemble quiver gauge theories with links comprised of 6D conformal matter, a generalization of weakly coupled hypermultiplets. In this paper we construct 4D quiverlike gauge theories in which the links are obtained from compactifications of 6D...

Exotic matter on singular divisors in F-theory

We analyze exotic matter representations that arise on singular seven-brane configurations in F-theory. We develop a general framework for analyzing such representations, and work out explicit descriptions for models with matter in the 2-index and 3-index symmetric representations of SU(N) and SU(2) respectively, associated with double and triple point singularities in the seven...

6D SCFTs and phases of 5D theories

Starting from 6D superconformal field theories (SCFTs) realized via F-theory, we show how reduction on a circle leads to a uniform perspective on the phase structure of the resulting 5D theories, and their possible conformal fixed points. Using the correspon-dence between F-theory reduced on a circle and M-theory on the corresponding elliptically fibered Calabi-Yau threefold, we...

F-theory and \( \mathcal{N} \) = 1 SCFTs in four dimensions

Using the F-theory realization, we identify a subclass of 6d (1,0) SCFTs whose compactification on a Riemann surface leads to \( \mathcal{N} \) = 1 4d SCFTs where the moduli space of the Riemann surface is part of the moduli space of the theory. In particular we argue that for a special case of these theories (dual to M5 branes probing ADE singularities), we obtain 4d \( \mathcal...

Tall sections from non-minimal transformations

In previous work, we have shown that elliptic fibrations with two sections, or Mordell-Weil rank one, can always be mapped birationally to a Weierstrass model of a certain form, namely, the Jacobian of a \( {\mathrm{\mathbb{P}}}^{112} \) model. Most constructions of elliptically fibered Calabi-Yau manifolds with two sections have been carried out assuming that the image of this...

On gauge enhancement and singular limits in G 2 compactifications of M-theory

We study the physics of singular limits of G 2 compactifications of M-theory, which are necessary to obtain a compactification with non-abelian gauge symmetry or massless charged particles. This is more difficult than for Calabi-Yau compactifications, due to the absence of calibrated two-cycles that would have allowed for direct control of W-boson masses as a function of moduli...

On the global symmetries of 6D superconformal field theories

We study global symmetry groups of six-dimensional superconformal field theories (SCFTs). In the Coulomb branch we use field theoretical arguments to predict an upper bound for the global symmetry of the SCFT. We then analyze global symmetry groups of F-theory constructions of SCFTs with a one-dimensional Coulomb branch. While in the vast majority of cases, all of the global...

Non-Higgsable clusters for 4D F-theory models

We analyze non-Higgsable clusters of gauge groups and matter that can arise at the level of geometry in 4D F-theory models. Non-Higgsable clusters seem to be generic features of F-theory compactifications, and give rise naturally to structures that include the nonabelian part of the standard model gauge group and certain specific types of potential dark matter candidates. In...

The landscape of M-theory compactifications on seven-manifolds with G 2 holonomy

We study the physics of globally consistent four-dimensional \( \mathcal{N} \) = 1 super-symmetric M-theory compactifications on G 2 manifolds constructed via twisted connected sum; there are now perhaps fifty million examples of these manifolds. We study a rich example that exhibits U(1)3 gauge symmetry and a spectrum of massive charged particles that includes a trifundamental...

F-theory on genus-one fibrations

Volker Braun 0 David R. Morrison 0 0 University of Oxford , Andrew Wiles Building, Radcliffe Observatory Quarter, Woodstock Road, Oxford , OX2 6GG, U.K. Departments of Mathematics and Physics

Geometry of 6D RG flows

We study renormalization group flows between six-dimensional superconformal field theories (SCFTs) using their geometric realizations as singular limits of F-theory compactified on elliptically fibered Calabi-Yau threefolds. There are two general types of flows: one corresponds to giving expectation values to scalars in the tensor multiplets (tensor branch flow) realized as...

Mordell-Weil torsion and the global structure of gauge groups in F-theory

We study the global structure of the gauge group G of F-theory compactified on an elliptic fibration Y. The global properties of G are encoded in the torsion subgroup of the Mordell-Weil group of rational sections of Y. Generalising the Shioda map to torsional sections we construct a specific integer divisor class on Y as a fractional linear combination of the resolution divisors...

6D SCFTs and gravity

We study how to couple a 6D superconformal field theory (SCFT) to gravity. In F-theory, the models in question are obtained working on the supersymmetric background \( \mathbb{R} \) 5,1 × B where B is the base of a compact elliptically fibered Calabi-Yau threefold in which two-cycles have contracted to zero size. When the base has orbifold singularities, we find that the anomaly...

Box graphs and singular fibers

We determine the higher codimension fibers of elliptically fibered Calabi-Yau fourfolds with section by studying the three-dimensional \( \mathcal{N} \) = 2 supersymmetric gauge theory with matter which describes the low energy effective theory of M-theory compactified on the associated Weierstrass model, a singular model of the fourfold. Each phase of the Coulomb branch of this...

On the classification of 6D SCFTs and generalized ADE orbifolds

We study (1, 0) and (2, 0) 6D superconformal field theories (SCFTs) that can be constructed in F-theory. Quite surprisingly, all of them involve an orbifold singularity ℂ2/Γ with Γ a discrete subgroup of U(2). When Γ is a subgroup of SU (2), all discrete subgroups are allowed, and this leads to the familiar ADE classification of (2, 0) SCFTs. For more general U(2) subgroups, the...

Global aspects of the space of 6D \( \mathcal{N} = 1 \) supergravities

We perform a global analysis of the space of consistent 6D quantum gravity theories with \( \mathcal{N} = 1 \) \( \mathcal{N} = 1 \) supersymmetry, including models with multiple tensor multiplets. We prove that for theories with fewer than T = 9 tensor multiplets, a finite number of distinct gauge groups and matter content are possible. We find infinite families of field...

Mapping 6D \( \mathcal{N} = 1 \) supergravities to F-theory

We develop a systematic framework for realizing general anomaly-free chiral 6D supergravity theories in F-theory. We focus on 6D (1, 0) models with one tensor multiplet whose gauge group is a product of simple factors (modulo a finite abelian group) with matter in arbitrary representations. Such theories can be decomposed into blocks associated with the simple factors in the...