Revisiting the classifications of 6d SCFTs and LSTs

Bhardwaj, Lakshya

doi:10.1007/jhep03(2020)171

Cited by 46 publications

(80 citation statements)

References 117 publications

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“…For su(2) gauge theory paired with a tensor of charge −2, anomaly cancelation considerations imply we have eight half-hypermultiplets in the fundamental representation. Though this might suggest the matter fields transform in the vector representation of Spin(8), the F-theory realization of this model admits only a Spin (7) flavor symmetry at the superconformal fixed point [5], which is in fact confirmed by field theory considerations as well [35,48]. So in this case, the matter fields transform as halfhypermultiplets in the (2, 8) of su(2) × so (7).…”

Section: Candidate U (1)'smentioning

confidence: 65%

“…There is a U (1) R coming from the six fundamentals of su(4), which transform under U (6) ∼ SU (6) × U (1) R . However, this is the only U (1) that shows up: the flavor symmetry SO (7) of the leftmost −2 tensor is gauged by su(4) so (6), but U (1) × SU (4) is not a subgroup of SO (7). As a result, there is no U (1) factor under which bifundamental of su(2) × su(4) transforms.…”

Section: Examples With Su(2) Gauge Symmetrymentioning

confidence: 99%

“…One might have also expected a baryonic U (1) B under which the bifundamental of su(2) and su(3) transforms. However, we recall that eight half-hypermultiplets in the fundamental representation of su(2) transform as a spinor of Spin (7), rather than the naïvely expected vector of SO (8). Since Spin (7) decomposes as Spin (7) ⊃ SU (3) × U (1), it gives only a single U (1), rather than the pair of U (1)'s which would have been expected from the decomposition SO(8) ⊃ SU (3) × U (1) 2 .…”

Section: Examples With Su(2) Gauge Symmetrymentioning

confidence: 99%

“…will have a global symmetry of SU (3) × U (1) 2 , in agreement with our general prescription for U (1) counting. The U (1) charges of the hypermultiplets in the theory may similarly be determined using the branching rules of SO (7) and SU (6).…”

Section: Examples With Su(2) Gauge Symmetrymentioning

confidence: 99%

“…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.…”

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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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Section: Candidate U (1)'smentioning

confidence: 65%

Section: Examples With Su(2) Gauge Symmetrymentioning

confidence: 99%

Section: Examples With Su(2) Gauge Symmetrymentioning

confidence: 99%

Section: Examples With Su(2) Gauge Symmetrymentioning

confidence: 99%

mentioning

confidence: 99%

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

et al. 2020

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The Branes Behind Generalized Symmetry Operators

Heckman

Hübner

Torres

et al. 2022

Fortschritte der Physik

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The modern approach to m-form global symmetries in a d-dimensional quantum field theory (QFT) entails specifying dimension d − m − 1 topological generalized symmetry operators which non-trivially link with m-dimensional defect operators. In QFTs engineered via string constructions on a non-compact geometry X, these defects descend from branes wrapped on non-compact cycles which extend from a localized source / singularity to the boundary 𝝏X. The generalized symmetry operators which link with these defects arise from magnetic dual branes wrapped on cycles in 𝝏X. This provides a systematic way to read off various properties of such topological operators, including their worldvolume topological field theories, and the resulting fusion rules. We illustrate these general features in the context of 6D superconformal field theories, where we use the F-theory realization of these theories to read off the worldvolume theory on the generalized symmetry operators. Defects of dimension 3 which are charged under a suitable 3-form symmetry detect a non-invertible fusion rule for these operators. We also sketch how similar considerations hold for related systems.

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Back to heterotic strings on ALE spaces. Part I. Instantons, 2-groups and T-duality

Zotto

Liu

Oehlmann

2023

J. High Energ. Phys.

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In this paper we begin revisiting the little string theories (LSTs) which govern the dynamics of the instantonic heterotic E8 × E8 five-branes probing ALE singularities, building on and extending previous results on the subject by Aspinwall and Morrison as well as Blum and Intriligator. Our focus are the cases corresponding to choices of non-trivial flat connections at infinity. The latter are in particular interesting for the exceptional ALE singularities, where a brane realization in Type I′ is lacking. Our approach to determine these models is based on 6d conformal matter: we determine these theories as generalized 6d quivers. All these LSTs have a higher-one form symmetry which forms a 2-group with the zero-form Poincaré symmetry, the R-symmetry and the other global symmetries: the matching of the R-symmetry two-group structure constant is a stringent constraint for T-dualities, which we use in combination with the matching of 5d Coulomb branches and flavor symmetries upon circle reduction, as a consistency check for the realization of the 6d LSTs we propose.

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Revisiting the classifications of 6d SCFTs and LSTs

Cited by 46 publications

References 117 publications

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

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

The Branes Behind Generalized Symmetry Operators

Back to heterotic strings on ALE spaces. Part I. Instantons, 2-groups and T-duality

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