Physics of F-theory compactifications without section

140

570

We consider F-theory compactifications on genus-one fibered Calabi-Yau manifolds with their fibers realized as hypersurfaces in the toric varieties associated to the 16 reflexive 2D polyhedra. We present a base-independent analysis of the codimension one, two and three singularities of these fibrations. We use these geometric results to determine the gauge groups, matter representations, 6D matter multiplicities and 4D Yukawa couplings of the corresponding effective theories. All these theories have a non-trivial gauge group and matter content. We explore the network of Higgsings relating these theories. Such Higgsings geometrically correspond to extremal transitions induced by blow-ups in the 2D toric varieties. We recover the 6D effective theories of all 16 toric hypersurface fibrations by repeatedly Higgsing the theories that exhibit Mordell-Weil torsion. We find that the three Calabi-Yau manifolds without section, whose fibers are given by the toric hypersurfaces in P 2 , P 1 × P 1 and the recently studied P 2 (1, 1, 2), yield F-theory realizations of SUGRA theories with discrete gauge groups Z 3 , Z 2 and Z 4 . This opens up a whole new arena for model building with discrete global symmetries in F-theory. In these three manifolds, we also find codimension two I 2 -fibers supporting matter charged only under these discrete gauge groups. Their 6D matter multiplicities are computed employing ideal techniques and the associated Jacobian fibrations. We also show that the Jacobian of the biquadric fibration has one rational section, yielding one U(1)-gauge field in F-theory. Furthermore, the elliptically fibered Calabi-Yau manifold based on dP 1 has a U(1)-gauge field JHEP01 (2015)142 induced by a non-toric rational section. In this model, we find the first F-theory realization of matter with U(1)-charge q = 3.

Section: Summary Of Resultsmentioning

confidence: 99%

Section: Jhep01(2015)142mentioning

confidence: 99%

See 1 more Smart Citation

F-theory on all toric hypersurface fibrations and its Higgs branches

Klevers

Pena²,

Oehlmann³

et al. 2015

140

570

“…Generically, by the Green-Schwarz mechanism, this enhanced U(1) couples to the Kähler axions of the base CY geometry (which transforms via shift symmetries) and becomes massive (see [47][48][49][50]52]). Since the presence of Green-Schwarz massive U(1)s in F-theory has been the topic of much recent interest (see for example [71][72][73][74][75][76][77][78]), we turn now to the appearance of this enhanced U(1) in heterotic/F-theory pair described above.…”

Section: Jhep04(2016)080mentioning

confidence: 98%

Matter in transition

Anderson

Gray

Raghuram

et al. 2016

Self Cite

We explore a novel type of transition in certain 6D and 4D quantum field theories, in which the matter content of the theory changes while the gauge group and other parts of the spectrum remain invariant. Such transitions can occur, for example, for SU(6) and SU(7) gauge groups, where matter fields in a three-index antisymmetric representation and the fundamental representation are exchanged in the transition for matter in the two-index antisymmetric representation. These matter transitions are realized by passing through superconformal theories at the transition point. We explore these transitions in dual F-theory and heterotic descriptions, where a number of novel features arise. For example, in the heterotic description the relevant 6D SU(7) theories are described by bundles on K3 surfaces where the geometry of the K3 is constrained in addition to the bundle structure. On the F-theory side, non-standard representations such as the threeindex antisymmetric representation of SU(N ) require Weierstrass models that cannot be realized from the standard SU(N ) Tate form. We also briefly describe some other situations, with groups such as Sp (3), SO(12), and SU(3), where analogous matter transitions can occur between different representations. For SU(3), in particular, we find a matter transition between adjoint matter and matter in the symmetric representation, giving an explicit Weierstrass model for the F-theory description of the symmetric representation that complements another recent analogous construction.

“…When the elliptic fibration has a (holomorphic zero-) section, as we shall assume, the off-diagonal terms in the metric vanish, which is equivalent to requiring that ρ = η = 0 [22,29]. Furthermore, we set the volume V to be constant.…”

Section: Jhep12(2016)058mentioning

confidence: 99%

Six-dimensional origin of N $$ \mathcal{N} $$ = 4 SYM with duality defects

Assel

Schäfer‐Nameki

2016

We study the topologically twisted compactification of the 6d (2, 0) M5-brane theory on an elliptically fibered Kähler three-fold preserving two supercharges. We show that upon reducing on the elliptic fiber, the 4d theory is N = 4 Super-Yang Mills, with varying complexified coupling τ , in the presence of defects. For abelian gauge group this agrees with the so-called duality twisted theory, and we determine a non-abelian generalization to U(N ). When the elliptic fibration is singular, the 4d theory contains 3d walls (along the branch-cuts of τ ) and 2d surface defects, around which the 4d theory undergoes SL(2, Z) duality transformations. Such duality defects carry chiral fields, which from the 6d point of view arise as modes of the two-form B in the tensor multiplet. Each duality defect has a flavor symmetry associated to it, which is encoded in the structure of the singular elliptic fiber above the defect. Generically 2d surface defects will intersect in points in 4d, where there is an enhanced flavor symmetry. The 6d point of view provides a complete characterization of this 4d-3d-2d-0d 'Matroshka'-defect configuration.