Revisiting Wess-Zumino-Witten terms

Lee, Yasunori; Ohmori, Kantaro

doi:10.21468/scipostphys.10.3.061

Cited by 27 publications

(23 citation statements)

References 65 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…homomorphisms going horizontally from right to left, these splitting maps do not give rise to commutative squares. We remark that the same pullback diagram (2.10) was recently used in [28] to study gauged Wess-Zumino-Witten terms from a bordism perspective.…”

Section: Anomaly Interplay As Non-canonical Splittingmentioning

confidence: 83%

“…A particularly interesting special case of the Spin-/2 n anomaly interplay occurs when n = 2. This case is most straightforward to analyse because there is only one independent global anomaly corresponding to 28 Ω…”

Section: Example: Standard Model and The Topological Superconductormentioning

confidence: 99%

“…[23,37] due to a connection with the Standard Model (SM) of particle physics. The key observation was that there is a linear combination of SM global U(1) symmetries under which every SM fermion has a charge 28 This bordism group can also be given a lower-dimensional interpretation thanks to a Smith isomorphism Ω Spin-/4 5 ∼ = Ω Pin + 4 [37]. From the physics perspective, one can relate each 4d Weyl fermion with Spin-/4 charge to a 3d Pin + Majorana fermion on a domain wall, offering an alternative way to understand this 4d global anomaly in terms of a 3d 'topological superconductor'.…”

Section: Example: Standard Model and The Topological Superconductormentioning

confidence: 99%

See 2 more Smart Citations

The algebra of anomaly interplay

Davighi

Lohitsiri

2021

SciPost Phys.

View full text Add to dashboard Cite

We give a general description of the interplay that can occur between local and global anomalies, in terms of (co)bordism. Mathematically, such an interplay is encoded in the non-canonical splitting of short exact sequences known to classify invertible field theories. We study various examples of the phenomenon in 2, 4, and 6 dimensions. We also describe how this understanding of anomaly interplay provides a rigorous bordism-based version of an old method for calculating global anomalies (starting from local anomalies in a related theory) due to Elitzur and Nair.

show abstract

Section: Anomaly Interplay As Non-canonical Splittingmentioning

confidence: 83%

Section: Example: Standard Model and The Topological Superconductormentioning

confidence: 99%

Section: Example: Standard Model and The Topological Superconductormentioning

confidence: 99%

See 1 more Smart Citation

The algebra of anomaly interplay

Davighi

Lohitsiri

2021

SciPost Phys.

View full text Add to dashboard Cite

show abstract

“…For odd k, in order for the gauge anomaly (5.98) to vanish, the manifold must be equipped with additional structures. Instead of defining the 5d Chern-Simons term using the bulk, we can study how it transforms under large gauge transformations, which produces a Wess-Zumino term in 4d of the form Tr(g −1 dg) 5 for transformation by SU(N ) valued field g. As discussed in [91], for N ≥ 3 the unit Wess-Zumino-Witten term is not an integer on general 5-manifold but requires a spin c structure. The background spin c connection A satisfies dA/2π = 1 2 w 2 (on a spin manifold we can set A = 0); then, the following combination of Wess-Zumino-Witten terms is an integer on spin c 5-manifold…”

Section: Jhep04(2021)232mentioning

confidence: 99%

Generalized global symmetries of T[M] theories. Part I

Gukov

Hsin

Pei

2021

J. High Energ. Phys.

103

View full text Add to dashboard Cite

We study reductions of 6d theories on a d-dimensional manifold Md, focusing on the interplay between symmetries, anomalies, and dynamics of the resulting (6 −d)-dimensional theory T[Md]. We refine and generalize the notion of “polarization” to polarization on Md, which serves to fix the spectrum of local and extended operators in T[Md]. Another important feature of theories T[Md] is that they often possess higher-group symmetries, such as 2-group and 3-group symmetries. We study the origin of such symmetries as well as physical implications including symmetry breaking and symmetry enhancement in the renormalization group flow. To better probe the IR physics, we also investigate the ’t Hooft anomaly of 5d Chern-Simons matter theories. The present paper focuses on developing the general framework as well as the special case of d = 0 and 1, while an upcoming paper will discuss the case of d = 2, 3 and 4.

show abstract

“…A geometric construction of gauged WZ terms in a scope and form relevant for strong nuclear interactions was advanced nearly four decades ago [63][64][65][66], soon after Witten elucidated their geometric nature [67]. Quite recently, the intricate topological properties of WZ and other topological terms have become subject to a renewed scrutiny [68][69][70][71]. It has however been known already since the 1990s that in systems where a continuous global compact (0-form) symmetry group G is spontaneously broken to its subgroup H, possible WZ terms in the low-energy EFT for the ensuing NG bosons are determined by de Rham cohomology of the coset space G/H, modulo some assumptions on the topology of the coset space and of the spacetime manifold [53,54].…”

Section: Jhep04(2021)045mentioning

confidence: 99%

Field theories with higher-group symmetry from composite currents

Brauner

2021

J. High Energ. Phys.

View full text Add to dashboard Cite

Higher-form symmetries are associated with transformations that only act on extended objects, not on point particles. Typically, higher-form symmetries live alongside ordinary, point-particle (0-form), symmetries and they can be jointly described in terms of a direct product symmetry group. However, when the actions of 0-form and higher-form symmetries become entangled, a more general mathematical structure is required, related to higher categorical groups. Systems with continuous higher-group symmetry were previously constructed in a top-down manner, descending from quantum field theories with a specific mixed ’t Hooft anomaly. I show that higher-group symmetry also naturally emerges from a bottom-up, low-energy perspective, when the physical system at hand contains at least two different given, spontaneously broken symmetries. This leads generically to a hierarchy of emergent higher-form symmetries, corresponding to the Grassmann algebra of topological currents of the theory, with an underlying higher-group structure. Examples of physical systems featuring such higher-group symmetry include superfluid mixtures and variants of axion electrodynamics.

show abstract

Revisiting Wess-Zumino-Witten terms

Cited by 27 publications

References 65 publications

The algebra of anomaly interplay

The algebra of anomaly interplay

Generalized global symmetries of T[M] theories. Part I

Field theories with higher-group symmetry from composite currents

Contact Info

Product

Resources

About