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-branes, string junctions, and 6D SCFTs

Haßler, Falk; Heckman, Jonathan J.; Rochais, Thomas B.; Rudelius, Tom; Zhang, Hao Y.

doi:10.1103/physrevd.101.086018

Cited by 33 publications

(21 citation statements)

References 74 publications

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“…It should also be mentioned that notions of Hasse diagrams have appeared in recent physics literature. For instance, the relation between Hasse diagrams of nilpotent orbits and 6d SCFTs has been studied in [22][23][24]. In addition, brane systems have been used in [25,26] to obtain Hasse diagrams corresponding to circular 3d N = 4 quiver gauge theories.…”

Section: Contentsmentioning

confidence: 99%

The Higgs mechanism — Hasse diagrams for symplectic singularities

Bourget¹,

Cabrera²,

Grimminger³

et al. 2020

J. High Energ. Phys.

107

221

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We explore the geometrical structure of Higgs branches of quantum field theories with 8 supercharges in 3, 4, 5 and 6 dimensions. They are symplectic singularities, and as such admit a decomposition (or foliation) into so-called symplectic leaves, which are related to each other by transverse slices. We identify this foliation with the pattern of partial Higgs mechanism of the theory and, using brane systems and recently introduced notions of magnetic quivers and quiver subtraction, we formalise the rules to obtain the Hasse diagram which encodes the structure of the foliation. While the unbroken gauge symmetry and the number of flat directions are obtainable by classical field theory analysis for Lagrangian theories, our approach allows us to characterise the geometry of the Higgs branch by a Hasse diagram with symplectic leaves and transverse slices, thus refining the analysis and extending it to non-Lagrangian theories. Most of the Hasse diagrams we obtain extend beyond the cases of nilpotent orbit closures known in the mathematics literature. The geometric analysis developed in this paper is applied to Higgs branches of several Lagrangian gauge theories, Argyres-Douglas theories, five dimensional SQCD theories at the conformal fixed point, and six dimensional SCFTs.

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Section: Contentsmentioning

confidence: 99%

The Higgs mechanism — Hasse diagrams for symplectic singularities

Bourget¹,

Cabrera²,

Grimminger³

et al. 2020

J. High Energ. Phys.

107

221

View full text Add to dashboard Cite

show abstract

“…Beside the techniques employed in [39,41,42], an alternative approach to classify the deformations associated to T-brane data is via (p, q) string junctions, see e.g. [82], which can also be utilized in geometries with restricted monodromies, i.e. Mordell-Weil torsion.…”

Section: Jhep10(2020)173mentioning

confidence: 99%

Non-simply-connected symmetries in 6D SCFTs

Dierigl

Oehlmann

Ruehle

2020

J. High Energ. Phys.

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Six-dimensional $$ \mathcal{N} $$ N = (1, 0) superconformal field theories can be engineered geometrically via F-theory on elliptically-fibered Calabi-Yau 3-folds. We include torsional sections in the geometry, which lead to a finite Mordell-Weil group. This allows us to identify the full non-Abelian group structure rather than just the algebra. The presence of torsion also modifies the center of the symmetry groups and the matter representations that can appear. This in turn affects the tensor branch of these theories. We analyze this change for a large class of superconformal theories with torsion and explicitly construct their tensor branches. Finally, we elaborate on the connection to the dual heterotic and M-theory description, in which our configurations are interpreted as generalizations of discrete holonomy instantons.

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“…See Appendix B for additional details on the interplay between group theory and 6D SCFTs. Let us note that there are additional Higgs branch deformations which come from more general seven-brane recombination moves [44]. For our present purposes of viewing all 6D SCFTs as fission and fusion products this additional class of flows will not play a role.…”

Section: )mentioning

confidence: 98%

“…The second theory with k = 1, however, experiences an accidental flavor symmetry enhancement, SU (5) × U (1) → SU (6), leaving us without an abelian flavor symmetry. Such symmetry enhancement occurs frequently when dealing with "short SCFT quivers," which are characterized by the absence of a plateau of gauge algebras [37,39,44].…”

Section: A-type Progenitor Theoriesmentioning

confidence: 99%

“…In F-theory, these homomorphisms arise as "T-brane" data for two intersecting stacks of seven-branes probing a C 2 /Z N singularity (for a partial list of references to the T-brane literature, see references [37,39,44,91,107,[112][113][114][115][116][117][118][119][120][121][122][123][124][125][126][127][128][129][130][131]). In particular, we can turn on T-brane data for either stack of seven-branes, resulting in a theory labeled by a pair of homomorphisms ρ 1 , ρ 2 ∈ Hom(su(2), g).…”

Section: B U (1)'s From Group 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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T -branes, string junctions, and 6D SCFTs

Cited by 33 publications

References 74 publications

The Higgs mechanism — Hasse diagrams for symplectic singularities

The Higgs mechanism — Hasse diagrams for symplectic singularities

Non-simply-connected symmetries in 6D SCFTs

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

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