Boundary Supersymmetry of 
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 Fermionic Symmetry-Protected Topological Phases

Prakash, Abhishodh; Wang, Juven

doi:10.1103/physrevlett.126.236802

Cited by 9 publications

(6 citation statements)

References 52 publications

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“…• Any 0 + 1d theory with an antiunitary Z T 2 symmetry and an odd number of Dirac fermions has exact bose-fermi degeneracy. The supersymmetric spectrum of an odd number of free Dirac fermions was described in [55], and has been studied more recently in [56][57][58]. From our perspective, any theory with a Z T 2 anomaly ν = 2 mod 4 has a supersymmetric spectrum.…”

Section: Jhep11(2021)142mentioning

confidence: 95%

Global anomalies on the Hilbert space

Delmastro

Gaiotto

Gomis

2021

J. High Energ. Phys.

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We show that certain global anomalies can be detected in an elementary fashion by analyzing the way the symmetry algebra is realized on the torus Hilbert space of the anomalous theory. Distinct anomalous behaviours imprinted in the Hilbert space are identified with the distinct cohomology “layers” that appear in the classification of anomalies in terms of cobordism groups. We illustrate the manifestation of the layers in the Hilbert for a variety of anomalous symmetries and spacetime dimensions, including time-reversal symmetry, and both in systems of fermions and in anomalous topological quantum field theories (TQFTs) in 2 + 1d. We argue that anomalies can imply an exact bose-fermi degeneracy in the Hilbert space, thus revealing a supersymmetric spectrum of states; we provide a sharp characterization of when this phenomenon occurs and give nontrivial examples in various dimensions, including in strongly coupled QFTs. Unraveling the anomalies of TQFTs leads us to develop the construction of the Hilbert spaces, the action of operators and the modular data in spin TQFTs, material that can be read on its own.

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Section: Jhep11(2021)142mentioning

confidence: 95%

Global anomalies on the Hilbert space

Delmastro

Gaiotto

Gomis

2021

J. High Energ. Phys.

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“…Can they be more than Z 2 -involutions?" JW also thanks Abhishodh Prakash for the past collaborations on the fractionalization of time-reversal T symmetry in [33,34]. This work is supported by Harvard University CMSA.…”

Section: Contentsmentioning

confidence: 94%

“…Ref. [32][33][34][35][36] suggest that at k = 2 (or k = 2 mod 4 in general) has various supersymmetric quantum mechanical interpretations. Concretely, we follow Ref.…”

Section: Introductionmentioning

confidence: 99%

C-P-T Fractionalization

Wang¹

2021

Preprint

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Discrete spacetime symmetries of parity P or reflection R, and time-reversal T, act naively as a Z2-involution in the passive transformation on the spacetime coordinates; but together with a charge conjugation C, the total C-P-R-T symmetries have enriched active transformations on fields in representations of the spacetime-internal symmetry groups of quantum field theories (QFTs). In this work, we derive that these symmetries can be further fractionalized, especially in the presence of the fermion parity (−1) F . We discover various C-P-R-T-(−1) F group structures, e.g., a nonabelian order-16 finite group, as the central product between an order-8 dihedral or quaternion group and an order-4 group generated by T with T 2 = (−1) F . We elaborate examples including relativistic Lorentz invariant QFTs (e.g., spin-1/2 Dirac or Majorana spinor fermion theories, spin-1 Maxwell electromagnetism, or interacting Yang-Mills gauge theories), and nonrelativistic quantum manybody systems (involving Majorana zero modes). The general theme may be coined as C-P-T or C-R-T fractionalization.

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“…This is called supersymmetry extension that trivializes this (0 + 1)D fermionic anomaly and also trivializes the (1 + 1)D fermionic SPT state [122]. Another related property is that the preserved symmetry demands that the anomalous boundary theory of ±2 mod 8 Majorana zero modes must be N = 2 supersymmetric quantum mechanics with two supercharges [176]. Two Kitaev's chains can also allow G = Z TF 4 symmetry with T 2 = (−1) F [177].…”

Section: Symmetry Extensionmentioning

confidence: 99%

Symmetric Mass Generation

Wang

You

2022

Symmetry

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The most well-known mechanism for fermions to acquire a mass is the Nambu–Goldstone–Anderson–Higgs mechanism, i.e., after a spontaneous symmetry breaking, a bosonic field that couples to the fermion mass term condenses, which grants a mass gap for the fermionic excitation. In the last few years, it was gradually understood that there is a new mechanism of mass generation for fermions without involving any symmetry breaking within an anomaly-free symmetry group, also applicable to chiral fermions with anomaly-free chiral symmetries. This new mechanism is generally referred to as the symmetric mass generation (SMG). It is realized that the SMG has deep connections with interacting topological insulator/superconductors, symmetry-protected topological states, perturbative local and non-perturbative global anomaly cancellations, and deconfined quantum criticality. It has strong implications for the lattice regularization of chiral gauge theories. This article defines the SMG, summarizes the current numerical results, introduces an unifying theoretical framework (including the parton-Higgs and the s-confinement mechanisms, as well as the symmetry-extension construction), and presents an overview of various features and applications of SMG.

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Boundary Supersymmetry of (1+1)D Fermionic Symmetry-Protected Topological Phases

Abstract: We prove that the boundaries of all non-trivial 1+1 dimensional intrinsically fermionic symmetryprotected-topological phases, protected by finite group on-site symmetries (unitary or anti-unitary), are supersymmetric quantum mechanical systems.

Cited by 9 publications

References 52 publications

Global anomalies on the Hilbert space

Global anomalies on the Hilbert space

C-P-T Fractionalization

Symmetric Mass Generation

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