Global Tensor‐Matter Transitions in F‐Theory

162

278

We propose a graph-based approach to 5d superconformal field theories (SCFTs) based on their realization as M-theory compactifications on singular elliptic Calabi-Yau threefolds. Fieldtheoretically, these 5d SCFTs descend from 6d N = (1, 0) SCFTs by circle compactification and mass deformations. We derive a description of these theories in terms of graphs, so-called Combined Fiber Diagrams, which encode salient features of the partially resolved Calabi-Yau geometry, and provides a combinatorial way of characterizing all 5d SCFTs that descend from a given 6d theory. Remarkably, these graphs manifestly capture strongly coupled data of the 5d SCFTs, such as the superconformal flavor symmetry, BPS states, and mass deformations.The capabilities of this approach are demonstrated by deriving all rank one and rank two 5d SCFTs. The full potential, however, becomes apparent when applied to theories with higher rank. Starting with the higher rank conformal matter theories in 6d, we are led to the discovery of previously unknown flavor symmetry enhancements and new 5d SCFTs.

Section: Part Ii: Box Graphs and Coulomb Branch Phasesmentioning

confidence: 99%

Fibers add flavor. Part I. Classification of 5d SCFTs, flavor symmetries and BPS states

Apruzzi

Lawrie

Lin

et al. 2019

162

278

“…In general we expect that these all represent smooth Calabi-Yau threefolds that can be viewed as non-flat elliptic fibrations over toric bases or flat elliptic fibrations over the non-toric bases resolved at the non-toric (4, 6) points, though we have not checked explicitly that this is true in all cases. Examples of some non-flat elliptic fibrations of this type are analyzed in [31,40,41]. To illustrate this structure, in Appendix B we analyze the non-flat elliptic fibration structure of the toric hypersurfaces associated with (flat) toric fibrations of the reflexive fibered polytopes over the Hirzebruch surfaces F 9 , F 10 , F 11 .…”

Section: Multiplicity In the Ks Databasementioning

confidence: 99%

“…Resolution of non-flat fibers in related cases of tuned Weierstrass models has recently been considered for example in[40,41]; the explicit connection between resolutions giving non-flat fibrations and flat fibrations over a resolved base through sequences of flops are described explicitly in the papers[42,43] that appeared after the initial appearance of this preprint.…”

mentioning

confidence: 99%

Comparing elliptic and toric hypersurface Calabi-Yau threefolds at large Hodge numbers

Huang

Taylor

2019

We compare the sets of Calabi-Yau threefolds with large Hodge numbers that are constructed using toric hypersurface methods with those can be constructed as elliptic fibrations using Weierstrass model techniques motivated by F-theory. There is a close correspondence between the structure of "tops" in the toric polytope construction and Tate form tunings of Weierstrass models for elliptic fibrations. We find that all of the Hodge number pairs (h 1,1 , h 2,1 ) with h 1,1 or h 2,1 ≥ 240 that are associated with threefolds in the Kreuzer-Skarke database can be realized explicitly by generic or tuned Weierstrass/Tate models for elliptic fibrations over complex base surfaces. This includes a relatively small number of somewhat exotic constructions, including elliptic fibrations over non-toric bases, models with new Tate tunings that can give rise to exotic matter in the 6D F-theory picture, tunings of gauge groups over non-toric curves, tunings with very large Hodge number shifts and associated nonabelian gauge groups, and tuned Mordell-Weil sections associated with U(1) factors in the corresponding 6D theory. arXiv:1805.05907v6 [hep-th]

“…Due to the Z 5 quotient in the gauge group, there is no bi-fundamental matter among the two SU (5) groups as one might expect from a simple adjoint breaking of E 8 but instead non-minimal vanishing (V (f, g, ∆) ∼ (4, 6, 12) leads to superconformal matter points with multiplicity n scp = (K −1 b ) 2 (and at best non-flat resolutions over these points in the CY threefold). Since the resolution of each non-flat (4, 6, 12) point contributes exactly one Kähler deformation [59,60] we find for a (weak) Fano base T + n scp = 9 , h (1,1) (X) = 19 .…”

Section: F-theory On a Z 5 Torsion Model And Its Quotientmentioning

confidence: 79%

F-theory on quotients of elliptic Calabi-Yau threefolds

Anderson

Gray

Oehlmann

2019

In this work we consider quotients of elliptically fibered Calabi-Yau threefolds by freely acting discrete groups and the associated physics of F-theory compactifications on such backgrounds. The process of quotienting a Calabi-Yau geometry produces not only new genus one fibered manifolds, but also new effective 6-dimensional physics. These theories can be uniquely characterized by the much simpler covering space geometry and the symmetry action on it. We use this method to construct examples of F-theory models with an array of discrete gauge groups and non-trivial monodromies, including an example with 1. ∆h 1,1 = 0: Gauge symmetry and number of (1, 0) tensors is unchanged.