Orbifold groupoids

Gaiotto, Davide; Kulp, Justin

doi:10.1007/jhep02(2021)132

Cited by 114 publications

(101 citation statements)

References 68 publications

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“…Note added. When this work was being completed, we learned of [80] which has overlap with section 7.2.…”

Section: Organization Of the Papermentioning

confidence: 99%

“…For the sake of completeness in this appendix we discuss the symmetries and vacua of the fermionic theory. In order to return to the fermionic theory from the bosonic one, we can "gauge back" the (−1) F symmetry in (1.1) by gauging a Z 2 symmetry with the twist defined by the Arf invariant [80,88,89,93,96,100]. Applying this operation to the bosonization (1.1), we get the duality Having analyzed the vacua of the Spin(N 2 − 1) 1 / SU(N ) N theory, we can now gauge the Z v 2 center of Spin(N 2 − 1) with an Arf twist to analyze the vacua of adjoint QCD.…”

Section: Jhep03(2021)103mentioning

confidence: 99%

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Symmetries and strings of adjoint QCD2

Komargodski

Ohmori

Roumpedakis

et al. 2021

J. High Energ. Phys.

198

149

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We revisit the symmetries of massless two-dimensional adjoint QCD with gauge group SU(N). The dynamics is not sufficiently constrained by the ordinary symmetries and anomalies. Here we show that the theory in fact admits ∼ 22N non-invertible symmetries which severely constrain the possible infrared phases and massive excitations. We prove that for all N these new symmetries enforce deconfinement of the fundamental quark. When the adjoint quark has a small mass, m ≪ gYM, the theory confines and the non-invertible symmetries are softly broken. We use them to compute analytically the k-string tension for N ≤ 5. Our results suggest that the k-string tension, Tk, is Tk ∼ |m| sin(πk/N) for all N. We also consider the dynamics of adjoint QCD deformed by symmetric quartic fermion interactions. These operators are not generated by the RG flow due to the non-invertible symmetries, thus violating the ordinary notion of naturalness. We conjecture partial confinement for the deformed theory by these four-fermion interactions, and prove it for SU(N ≤ 5) gauge theory. Comparing the topological phases at zero and large mass, we find that a massless particle ought to appear on the string for some intermediate nonzero mass, consistent with an emergent supersymmetry at nonzero mass. We also study the possible infrared phases of adjoint QCD allowed by the non-invertible symmetries, which we are able to do exhaustively for small values of N. The paper contains detailed reviews of ideas from fusion category theory that are essential for the results we prove.

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“…Note added. When this work was being completed, we learned of [80] which has overlap with section 7.2.…”

Section: Organization Of the Papermentioning

confidence: 99%

Section: Jhep03(2021)103mentioning

confidence: 99%

Symmetries and strings of adjoint QCD2

Komargodski

Ohmori

Roumpedakis

et al. 2021

J. High Energ. Phys.

198

149

View full text Add to dashboard Cite

show abstract

“…Therefore, the critical theories of fermions (e.g., the critical theory of Majorana chains) are called "fermionic conformal field theories" to be distinguished from the critical bosonic theories, i.e., the so-called conformal field theories (CFTs). The classification [29] and the minimal and rational models of fermionic CFTs [27,[30][31][32] are of intense interest recently.…”

Section: Jhep04(2021)285mentioning

confidence: 99%

“…The bosonic minimal models have been exactly solved and classified into an ADE classification [35,36]. The fermionic (i.e., Z k=2parafermionic) minimal models are also exhausted by fermionizations of the bosonic minimal models with a global Z 2 symmetry [27,30,31].…”

Section: Minimal Parafermionic Models and Fractional Statisticsmentioning

confidence: 99%

“…Moreover, this bosonic theory has a global Z k>2 symmetry "inherited" from the parafermionic model. However, it has been shown that the only bosonic minimal models with a global Z k>2 symmetry are the critical and the tricritical three-state Potts models [30,31,42], where k = 3. The central charges are c = 4/5 for the critical Potts model and c = 6/7 for the tricritical Potts model.…”

Section: Minimal Z K>2 -Parafermionic Modelsmentioning

confidence: 99%

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Parafermionization, bosonization, and critical parafermionic theories

Yao

Furusaki

2021

J. High Energ. Phys.

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We formulate a ℤk-parafermionization/bosonization scheme for one-dimensional lattice models and field theories on a torus, starting from a generalized Jordan-Wigner transformation on a lattice, which extends the Majorana-Ising duality at k = 2. The ℤk-parafermionization enables us to investigate the critical theories of parafermionic chains whose fundamental degrees of freedom are parafermionic, and we find that their criticality cannot be described by any existing conformal field theory. The modular transformations of these parafermionic low-energy critical theories as general consistency conditions are found to be unconventional in that their partition functions on a torus transform differently from any conformal field theory when k > 2. Explicit forms of partition functions are obtained by the developed parafermionization for a large class of critical ℤk-parafermionic chains, whose operator contents are intrinsically distinct from any bosonic or fermionic model in terms of conformal spins and statistics. We also use the parafermionization to exhaust all the ℤk-parafermionic minimal models, complementing earlier works on fermionic cases.

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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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Orbifold groupoids

Cited by 114 publications

References 68 publications

Symmetries and strings of adjoint QCD2

Symmetries and strings of adjoint QCD2

Parafermionization, bosonization, and critical parafermionic theories

The Branes Behind Generalized Symmetry Operators

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