Snowmass White Paper: Generalized Symmetries in Quantum Field Theory and Beyond

Córdova, Clay; Dumitrescu, Thomas T.; Intriligator, Kenneth; Shao, Shu-Heng

doi:10.48550/arxiv.2205.09545

Cited by 45 publications

(49 citation statements)

References 234 publications

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“…For our purpose, we choose this term to be iN k 4π b ∧ b, where k is the multiplicative inverse of p modulo N , i.e., pk = 1 mod N . 7 Putting everything together, gauging the Z…”

Section: Gauging the Magnetic One-form Symmetrymentioning

confidence: 99%

“…This question echoes with the recent developments of a novel kind of generalized global symmetries. (See [6,7] for reviews.) While every ordinary global symmetry is associated with a topological symmetry operator (such as (1.1)), the converse is not true.…”

Section: Introductionmentioning

confidence: 99%

“…In[1], the Noether current of a q-form symmetry is defined as a (d−q −1)-form current, where d is the spacetime dimensions. The Noether currents in this paper are the Hodge duals of those in[1] 7. Such an integer k always exist since gcd(p, N ) = 1.…”

mentioning

confidence: 97%

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Non-invertible Global Symmetries in the Standard Model

Choi¹,

Lam²,

Shao³

2022

Preprint

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We identify infinitely many non-invertible generalized global symmetries in QED and QCD for the real world in the massless limit. In QED, while there is no conserved Noether current for the U (1) A axial symmetry because of the ABJ anomaly, for every rational angle 2πp/N , we construct a conserved and gauge-invariant topological symmetry operator. Intuitively, it is a composition of the axial rotation and a fractional quantum Hall state coupled to the electromagnetic U (1) gauge field. These conserved symmetry operators do not obey a group multiplication law, but a non-invertible fusion algebra over TQFT coefficients. They act invertibly on all local operators as axial rotations, but non-invertibly on the 't Hooft lines. These non-invertible symmetries lead to selection rules, which are consistent with the scattering amplitudes in QED. We further generalize our construction to QCD, and show that the coupling π 0 F ∧ F in the effective pion Lagrangian is necessary to match these non-invertible symmetries in the UV. Therefore, the conventional argument for the neutral pion decay using the ABJ anomaly is now rephrased as a matching condition of a generalized global symmetry.

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“…For our purpose, we choose this term to be iN k 4π b ∧ b, where k is the multiplicative inverse of p modulo N , i.e., pk = 1 mod N . 7 Putting everything together, gauging the Z…”

Section: Gauging the Magnetic One-form Symmetrymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Non-invertible Global Symmetries in the Standard Model

Choi¹,

Lam²,

Shao³

2022

Preprint

Self Cite

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“…The above result is established when G is an ordinary 0-symmetry that acts on the 0D point operator. The symmetry extension construction can also be generalized to higher global symmetries [173] such as the 1-symmetry that acts on the 1D line operator (see a recent review [174,175]). Here are some examples (Table 8 for a summary) including ordinary and higher symmetries: (59).…”

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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“…Exotic global symmetries such as (planar or fractal) subsystem global symmetries [7,3], multipole global symmetries [8][9][10][11], etc. (See [12,13] for recent reviews on generalized global symmetries [14]. )…”

Section: Introductionmentioning

confidence: 99%

Fractons on Graphs and Complexity

Gorantla,

Lam,

Shao

2022

Preprint

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We introduce two exotic lattice models on a general spatial graph. The first one is a matter theory of a compact Lifshitz scalar field, while the second one is a certain rank-2 U (1) gauge theory of fractons. Both lattice models are defined via the discrete Laplacian operator on a general graph. We unveil an intriguing correspondence between the physical observables of these lattice models and graph theory quantities. For instance, the ground state degeneracy of the matter theory equals the number of spanning trees of the spatial graph, which is a common measure of complexity in graph theory ("GSD = complexity"). The discrete global symmetry is identified as the Jacobian group of the graph. In the gauge theory, superselection sectors of fractons are in one-to-one correspondence with the divisor classes in graph theory. In particular, under mild assumptions on the spatial graph, the fracton immobility is proven using a graph-theoretic Abel-Jacobi map.

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Snowmass White Paper: Generalized Symmetries in Quantum Field Theory and Beyond

Cited by 45 publications

References 234 publications

Non-invertible Global Symmetries in the Standard Model

Non-invertible Global Symmetries in the Standard Model

Symmetric Mass Generation

Fractons on Graphs and Complexity

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