The fate of U(1)’s at strong coupling in F-theory

Braun, Andreas P.; Collinucci, Andrès; Valandro, Roberto

doi:10.1007/jhep07(2014)028

Cited by 43 publications

(96 citation statements)

References 37 publications

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“…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%

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Matter in transition

Anderson

Gray

Raghuram

et al. 2016

J. High Energ. Phys.

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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.

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Section: Jhep04(2016)080mentioning

confidence: 98%

“…Thus, it is possible that in F-theory the mass originates (even in 6-dimensions) from a source entirely separate to the holomorphic geometry of Y (i.e. a "Stuckelberg" mechanism [71,[73][74][75]). …”

Section: Comments On Green-schwarz Massive U(1)smentioning

confidence: 99%

Matter in transition

Anderson

Gray

Raghuram

et al. 2016

J. High Energ. Phys.

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“…The conifold form makes it easy to identify the extra generator of the Mordell-Weil group (i.e. a new rational section) [76,92]. Note also that in this new presentation of the singularity, all appearance of "fractional powers" such as M/2 has disappeared, as anticipated.…”

Section: Warmup: Bifundamentals Of Su (M ) × Su (N )mentioning

confidence: 59%

“…However, even in compact models some of these abelian factors may acquire a mass and become non-dynamical via a "geometric Stückelberg mechanism." Those that stay massless (dynamical) are associated to singularities which admit a small Kähler resolution [75,76]. This is clearly the case if the Weierstrass model can be put into conifold form (i.e.…”

Section: Geometry Of Global U (1)'s In F-theorymentioning

confidence: 99%

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General prescription for globalU(1)’s in 6D SCFTs

et al. 2020

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We present a general prescription for determining the global U (1) symmetries of sixdimensional superconformal field theories (6D SCFTs). We use the quiver-like gauge theory description of the tensor branch to identify candidate U (1) symmetries which can act on generalized matter. The condition that these candidate U (1)'s are free of Adler-Bell-Jackiw (ABJ) anomalies provides bottom-up constraints for U (1)'s. This agrees with the answer obtained from symmetry breaking patterns induced by Higgs branch flows. We provide numerous examples illustrating the details of this proposal. In the F-theory realization of these theories, some of these symmetries originate from deformations of non-abelian flavor symmetries localized on a component of the discriminant, while others come from an additional generator of the Mordell-Weil group. We also provide evidence that some of these global U (1)'s do not arise from gauge symmetries, as would happen in taking a decoupling limit of a model coupled to six-dimensional supergravity.There is a striking interplay between stringy extra-dimensional geometric structures and low energy effective field theories. This is particularly manifest in the context of F-theory compactifications, where intersecting seven-branes are geometrized into elliptically fibered Calabi-Yau spaces [1-3]. A prominent example illustrating the power of such methods is the recent classification of six-dimensional superconformal field theories (6D SCFTs) via Ftheory [4,5] (see also [6,7]). This provides a remarkably flexible approach to constructing 6D SCFTs which encompasses essentially all other methods (see [8][9][10][11][12][13][14][15][16][17][18][19][20][21] for a partial list of older references, references [22][23][24][25][26] for recent holographic examples, and [27] for a review).With these results in place, it is natural to ask what detailed features of 6D SCFTs can be extracted from the associated geometries. One piece of information which is readily available from an F-theory model is the tensor branch of the 6D SCFT moduli space, as this is encoded directly in terms of Kähler deformations of the base of an F-theory model. Additionally, some global symmetries correlate with the appearance of non-compact sevenbranes intersecting the localized region inhabited by a 6D SCFT. This, in tandem with field theoretic techniques, has made it possible to tightly constrain the structure of anomalies in 6D SCFTs [28][29][30][31][32][33].Even so, there are a number of outstanding open issues connected with determining the structure of global symmetries in a 6D SCFT. In what follows we exclusively focus on the case of continuous zero-form symmetries. While in many cases there is a close match between the flavor symmetries expected from geometric and field theoretic methods, there are notable examples where either the F-theory model only captures a subset of possible flavor symmetries, and conversely, where a "naïve" field theoretic analysis might at first suggest a bigger flavor symmetry than what can actually be...

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