Noninvertible anomalies and mapping-class-group transformation of anomalous partition functions

Ji, Wenjie; Wen, Xiao-Gang

doi:10.1103/physrevresearch.1.033054

Cited by 61 publications

(69 citation statements)

References 62 publications

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“…This forbids a symmetric gapped ground state within the low-energy sector. In this section, we will show that the anomaly property of the Z 2 ∨ Z 2 categorical symmetry is actually an effect of a noninvertible gravitational anomaly [31]. More precisely, the theory with the categorical symmetry can be a boundary theory of a Z 2 topological order in one higher dimension.…”

Section: Symmetric Sector Of the 1 + 1d Ising Model As The Boundarmentioning

confidence: 91%

“…Thus the symmetric sector of the Ising model can be viewed as having a noninvertible gravitational anomaly [31]. Indeed, the symmetric sector of the Ising model can be viewed as a boundary of 2 + 1D Z 2 topological order (the topological order characterized by Z 2 gauge theory), and thus has a 1 + 1D noninvertible gravitational anomaly characterized by 2 + 1D Z 2 topological order [31].…”

Section: Symmetric Sector Of the 1 + 1d Ising Model As The Boundarmentioning

confidence: 99%

“…Its partition function has four components. For such a m-condensed boundary (with |J| < B), the fourcomponent partition function is given by (after shifting the ground-state energy density to zero) [31] ⎛…”

Section: E How Categorical Symmetry Determines the Gapless Statementioning

confidence: 99%

“…When J = B, the boundary effective theory is gapless. From H Is P and H Is A , we can obtain the gapless partition functions [31,[50][51][52]:…”

Section: E How Categorical Symmetry Determines the Gapless Statementioning

confidence: 99%

“…There is a holographic way to see the appearance of categorical symmetry in any G-symmetric system. We note that when restricted to the symmetric sub-Hilbert space a nD G-symmetric system can be viewed as a system that has a noninvertible gravitational anomaly, i.e., can be viewed as the boundary of the G-gauge theory in one higher dimension [30,31]. The bulk gauge charges, when brought to the boundary, are the excitations of the G 0-symmetry, and the gauge fluxes, brought to the boundary, are excitations of the algebraic (n − 1)-symmetry.…”

Section: Introductionmentioning

confidence: 99%

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Categorical symmetry and noninvertible anomaly in symmetry-breaking and topological phase transitions

Wen

2020

Phys. Rev. Research

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117

130

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For a zero-temperature Landau symmetry-breaking transition in n-dimensional space that completely breaks a finite symmetry G, the critical point at the transition has the symmetry G. In this paper, we show that the critical point also has a dual symmetry-a (n − 1)-symmetry described by a higher group when G is Abelian or an algebraic (n − 1)-symmetry beyond a higher group when G is non-Abelian. In fact, any G-symmetric system can be viewed as a boundary of G-gauge theory in one higher dimension. The conservation of gauge charge and gauge flux in the bulk G-gauge theory gives rise to the symmetry and the dual symmetry, respectively. So any G-symmetric system actually has a larger symmetry called categorical symmetry, which is a combination of the symmetry and the dual symmetry. However, part (and only part) of the categorical symmetry must be spontaneously broken in any gapped phase of the system, but there exists a gapless state where the categorical symmetry is not spontaneously broken. Such a gapless state corresponds to the usual critical point of Landau symmetry-breaking transition. The above results remain valid even if we expand the notion of symmetry to include higher symmetries and algebraic higher symmetries. Thus our result also applies to critical points for transitions between topological phases of matter. In particular, we show that there can be several critical points for the transition from the 3 + 1-dimensional Z 2 gauge theory to a trivial phase. The critical point from Higgs condensation has a categorical symmetry formed by a Z 2 0-symmetry and its dual, a Z 2 2-symmetry, while the critical point of the confinement transition has a categorical symmetry formed by a Z 2 1-symmetry and its dual, another Z 2 1-symmetry.

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Section: Symmetric Sector Of the 1 + 1d Ising Model As The Boundarmentioning

confidence: 91%

Section: Symmetric Sector Of the 1 + 1d Ising Model As The Boundarmentioning

confidence: 99%

Section: E How Categorical Symmetry Determines the Gapless Statementioning

confidence: 99%

“…When J = B, the boundary effective theory is gapless. From H Is P and H Is A , we can obtain the gapless partition functions [31,[50][51][52]:…”

Section: E How Categorical Symmetry Determines the Gapless Statementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Categorical symmetry and noninvertible anomaly in symmetry-breaking and topological phase transitions

Wen

2020

Phys. Rev. Research

Self Cite

117

130

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The anomaly that was not meant IIB

Debray

Dierigl²,

Heckman

et al. 2021

Fortschritte der Physik

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Type IIB supergravity enjoys a discrete non-Abelian duality group, which has potential quantum anomalies. In this paper we explicitly compute these, and present the bordism group that controls them, modulo some physically motivated assumptions. Quite surprisingly, we find that they do not vanish, which naively would signal an inconsistency of F-theory. Remarkably, a subtle modification of the standard 10d Chern-Simons term cancels these anomalies, a fact which relies on the specific field content of type IIB supergravity. We also discover other ways to cancel this anomaly, via a topological analog of the Green-Schwarz mechanism. These alternative type IIB theories have the same low energy supergravity limit as ordinary type IIB, but a different spectrum of extended objects. They could either be part of the Swampland, or connect to the standard theory via domain walls.

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Orbifold groupoids

Gaiotto

Kulp

2021

J. High Energ. Phys.

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We review the properties of orbifold operations on two-dimensional quantum field theories, either bosonic or fermionic, and describe the “Orbifold groupoids” which control the composition of orbifold operations. Three-dimensional TQFT’s of Dijkgraaf-Witten type will play an important role in the analysis. We briefly discuss the extension to generalized symmetries and applications to constrain RG flows.

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Noninvertible anomalies and mapping-class-group transformation of anomalous partition functions

Cited by 61 publications

References 62 publications

Categorical symmetry and noninvertible anomaly in symmetry-breaking and topological phase transitions

Categorical symmetry and noninvertible anomaly in symmetry-breaking and topological phase transitions

The anomaly that was not meant IIB

Orbifold groupoids

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