Exploring 2-group global symmetries

Córdova, Clay; Dumitrescu, Thomas T.; Intriligator, Kenneth

doi:10.1007/jhep02(2019)184

Cited by 258 publications

(429 citation statements)

References 68 publications

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“…From a broader perspective, it would be useful to develop systematic geometric tools for the computation of 't Hooft anomalies of theories engineered in type IIA, type IIB string theories and F-theory. Moreover, the methods of this work can be straightforwardly generalized to include anomalies for continuous higher-form symmetries [43,44]. grant PHY-1820784.…”

Section: Discussionmentioning

confidence: 99%

Anomalies of QFTs from M-theory and holography

Bah

Bonetti

Minasian

et al. 2020

J. High Energ. Phys.

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We describe a systematic way of computing the 't Hooft anomalies for continuous symmetries of Quantum Field Theories in even dimensions that can be geometrically engineered from M5-branes. Our approach is based on anomaly inflow, and characterizes the anomaly polynomial of the QFT in terms of the geometric definition of the field theory. In particular, when the QFT admits a holographic dual, the topological data of the solution is sufficient to compute the anomalies of the dual field theory, including finite terms in N . We study several classes of examples in four and six dimensions, with or without known M5-brane probe configurations.

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Section: Discussionmentioning

confidence: 99%

Anomalies of QFTs from M-theory and holography

Bah

Bonetti

Minasian

et al. 2020

J. High Energ. Phys.

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“…where the factor |G||H| 1 2 ensures that the isomorphism preserves the normalisation of states. 3 Since isomorphisms of this form play a crucial role in the following, let us explain it in more detail: The 1-holonomies associated with the edges (04) and (15) are provided by the oriented product of the 1-holonomies along the 1-paths (02) ∪ (24) and (13) ∪ (35), respectively, namely g 02 g 24 and g 13 g 35 . Similarly, the 2-holonomy that labels the plaquette (0145) is obtained as the composition (from right to left) of the 2-holonomies associated with the initial plaquettes (0123) and (2345) such that bp(0123) = (0), s(0123) = (02) ∪ (23), t(0123) = (01) ∪ (13) and bp(2345) = (2), s(2345) = (24) ∪ (45), t(2345) = (23) ∪ (35).…”

Section: Ground State Subspacementioning

confidence: 99%

“…These generalized symmetries have been a very active topic of research within the physics community over the past few years. For instance, q-form global symmetries together with their higher anomalies have been thoroughly investigated in the quantum field theory context [1][2][3][4][5], where a (higher) q-form global symmetry is a global symmetry whose symmetry operators are all q-dimensional. A theory displaying a non-anomalous q-form global symmetry can be gauged by coupling it to a (q+1)-form background connection, then resulting in a (q+1)-form gauge theory.…”

Section: Introductionmentioning

confidence: 99%

Excitations in strict 2-group higher gauge models of topological phases

Bullivant

Delcamp

2020

J. High Energ. Phys.

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We consider an exactly solvable model for topological phases in (3+1)d whose input data is a strict 2-group. This model, which has a higher gauge theory interpretation, provides a lattice Hamiltonian realisation of the Yetter homotopy 2-type topological quantum field theory. The Hamiltonian yields bulk flux and charge composite excitations that are either point-like or loop-like. Applying a generalised tube algebra approach, we reveal the algebraic structure underlying these excitations and derive the irreducible modules of this algebra, which in turn classify the elementary excitations of the model. As a further application of the tube algebra approach, we demonstrate that the ground state subspace of the three-torus is described by the central subalgebra of the tube algebra for torus boundary, demonstrating the ground state degeneracy is given by the number of elementary loop-like excitations.arXiv:1909.07937v1 [cond-mat.str-el]

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“…Terms of the form F 3 gauge F global represent an ABJ anomaly, which leads to a divergence in the global anomaly current and thus violates the putative global symmetry. Terms of the form F 2 gauge F 2 global and F gauge F 3 global are also forbidden in 6D SCFTs but for a different reason: there is no multiplet in the 6D superconformal algebra that would give rise to such terms [68,108]. Finally, F 4 global terms represent 't Hooft anomalies, which are benign and do not need to be canceled.…”

Section: Discussionmentioning

confidence: 99%

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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Exploring 2-group global symmetries

Cited by 258 publications

References 68 publications

Anomalies of QFTs from M-theory and holography

Anomalies of QFTs from M-theory and holography

Excitations in strict 2-group higher gauge models of topological phases

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

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