Global Symmetries, Counterterms, and Duality in Chern-Simons Matter  Theories with Orthogonal Gauge Groups

Córdova, Clay; Hsin, Po-Shen; Seiberg, Nathan

doi:10.21468/scipostphys.4.4.021

Cited by 108 publications

(227 citation statements)

References 60 publications

(234 reference statements)

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“…Parallel to the orthogonal group case, quantum phase can be determined as follows under the n * steps of duality chain : 5 It is necessary to comment that only for the special case of SO(2) 2 + 2 ψ sym the dual description obtained from a naive application of the duality chain SO(2) 2 + 2 ψ asym doesn't preserve global symmetry, namely Z C 2 × Z M 2 symmetry. The main reason is the lack of gauge invariant monopole operator in the dual side due to the decoupled fermions and non-zero Chern-Simons level.…”

Section: Quantum Phase For G = Sp(n )mentioning

confidence: 99%

“…exhibit the spontaneous breaking of Z M 2 magnetic symmetry has following implication. Since the charge conjugation symmetry C and magnetic symmetry M is interchanged under the each step of duality chain similar to [5], we have following special phases for the SO(N ) gauge theory : We first point out that there is a great simplification when 2 adjoints fermions are charged under U (N ) gauge group, where generalized level/rank duality is no more required. We explain the connection between the case of SU (N ) gauge group through SL(2, Z) transformation in section 5.4.…”

Section: Quantum Phase For G = Sp(n )mentioning

confidence: 99%

“…For the treatment of various discrete gauge fields in the orthogonal gauge groups and its level/rank dualities, see[5].…”

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confidence: 99%

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Phases of two adjoints QCD3 and a duality chain

Choi

2020

J. High Energ. Phys.

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We analyze the 2+1 dimensional gauge theory with two fermions in the real adjoint representation with non-zero Chern-Simons level. We propose a new fermion-fermion dualities between strongly-coupled theories and determine the quantum phase using the structure of a 'Duality Chain'. We argue that when Chern-Simons level is sufficiently small, the theory in general develops a strongly coupled quantum phase described by an emergent topological field theory. For special cases, our proposal predicts an interesting dynamical scenario with spontaneous breaking of partial 1-form or 0-form global symmetry. It turns out that SL(2, Z) transformation and the generalized level/rank duality are crucial for the unitary group case. We further unveil the dynamics of the 2+1 dimensional gauge theory with any pair of adjoint/rank-two fermions or two bifundamental fermions using similar 'Duality Chain'.

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Section: Quantum Phase For G = Sp(n )mentioning

confidence: 99%

Section: Quantum Phase For G = Sp(n )mentioning

confidence: 99%

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Phases of two adjoints QCD3 and a duality chain

Choi

2020

J. High Energ. Phys.

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“…For our application, it is sufficient to know the result for the spin Chern-Simons theory SO(M ) 1 . In SO(M ) 1 , changing the spin structure by a classical Z 2 gauge field can be identified with changing the background for the Z 2 magnetic symmetry generated by exp(iπ w SO(M ) 2 ) [48,38]. Thus summing over the spin structures in SO(M ) 1 produces the non-spin Chern-Simons theory Spin(M ) 1 .…”

Section: Lifting Spin Dualities With the Fractionalization Mapmentioning

confidence: 99%

Lorentz symmetry fractionalization and dualities in (2+1)d

Hsin

Shao

2020

SciPost Phys.

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We discuss symmetry fractionalization of the Lorentz group in (2+1)d non-spin quantum field theory (QFT), and its implications for dualities. We prove that two inequivalent non-spin QFTs are dual as spin QFTs if and only if they are related by a Lorentz symmetry fractionalization with respect to an anomalous Z 2 one-form symmetry. Moreover, if the framing anomalies of two non-spin QFTs differ by a multiple of 8, then they are dual as spin QFTs if and only if they are also dual as non-spin QFTs. Applications to summing over the spin structures, time-reversal symmetry, and level/rank dualities are explored. The Lorentz symmetry fractionalization naturally arises in Chern-Simons matter dualities that obey certain spin/charge relations, and is instrumental for the dualities to hold when viewed as non-spin theories.1 See [9,[11][12][13] for related works in (3+1)d.

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“…Global symmetries and 't Hooft anomalies are key ingredients characterizing topological phases of quantum matters [1][2][3][4][5][6][7][8][9]. For a generic quantum field theory Q d in d spacetime dimensions with global symmetry G, if one modifies Q d to Q ′ d by G-invariant deformations, it has been shown [10] that the 't Hooft anomaly of Q d and Q ′ d are the same.…”

Section: Introductionmentioning

confidence: 99%

Higher anomalies, higher symmetries, and cobordisms III: QCD matter phases anew

Wan

Wang

2020

Nuclear Physics B

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We discuss the topological terms, the global symmetries and their 't Hooft anomalies of pure gauge theories in various dimensions, with dynamical gauge group G, the Lorentz symmetry group G Lorentz , and the internal global symmetry G e,[1] × G m, [d−3] which consists of 1-form electric center symmetry G e,[1] and (d − 3) form magnetic symmetry G m, [d−3] . The topological terms are determined by the cobordism invariants (Ω d ) G ′ where G ′ is the group extension of G Lorentz by G, which also characterize the invertible TQFTs or SPTs with global symmetry G ′ . The 't Hooft anomalies are determined by the cobordism invariants (Ω d+1 ) G ′′ where G ′′ is the symmetry extension of G Lorentz by the higher form symmetry G e,[1] × G m, [d−3] . Different symmetry extensions correspond to different fractionalizations of G Lorentz quantum numbers on the symmetry defects of G e,[1] × G m, [d−3] . We compute the cobordism groups/invariants described above for G = U(1), SU(2) and SO(3) in d ≤ 5, thus systematically classifies all the topological terms and the 't Hooft anomalies of d dimensional quantum gauge theories with the above gauge groups. December 2019W −

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Global Symmetries, Counterterms, and Duality in Chern-Simons Matter Theories with Orthogonal Gauge Groups

Cited by 108 publications

References 60 publications

Phases of two adjoints QCD3 and a duality chain

Phases of two adjoints QCD3 and a duality chain

Lorentz symmetry fractionalization and dualities in (2+1)d

Higher anomalies, higher symmetries, and cobordisms III: QCD matter phases anew

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