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Generalized symmetry enriched criticality in (3+1)d
by Benjamin Moy
Submission summary
| Authors (as registered SciPost users): | Benjamin Moy |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202507_00088v2 (pdf) |
| Date accepted: | Nov. 11, 2025 |
| Date submitted: | Oct. 20, 2025, 12:56 a.m. |
| Submitted by: | Benjamin Moy |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
We construct two classes of continuous phase transitions in 3+1 dimensions between gapped phases that break distinct generalized global symmetries. Our analysis focuses on $SU(N)/\mathbb{Z}_N$ gauge theory coupled to $N_f$ flavors of Majorana fermions in the adjoint representation. For $N$ even and sufficiently large odd $N_f$, upon imposing time-reversal symmetry and an $SO(N_f)$ flavor symmetry, the massless theory realizes a quantum critical point between a gapped phase in which a $\mathbb{Z}_N$ one-form symmetry is completely broken and a phase where it is broken to $\mathbb{Z}_2$, leading to $\mathbb{Z}_{N/2}$ topological order. We provide an explicit lattice model that exhibits this transition. The critical point has an enhanced symmetry, which includes non-invertible analogues of time-reversal symmetry. Enforcing a non-invertible time-reversal symmetry and the $SO(N_f)$ flavor symmetry, for $N$ and $N_f$ both odd, we demonstrate that this critical point can appear between a topologically ordered phase and a phase that spontaneously breaks the non-invertible time-reversal symmetry, furnishing an analogue of deconfined quantum criticality for generalized symmetries.
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List of changes
p. 5: “we emphasize that these quasiparticles need not be magnetic monopoles of the electromagnetic field” -> “we emphasize that these quasiparticles should not be confused with magnetic monopoles of the $U(1)$ electromagnetic field”
Just below Eq. 2.3: Added an explicit definition of the ’t Hooft loop
Just below Eq. 2.10 and just below Eq. 2.13: Added a comment that the constants associated with the perimeter law are scheme-dependent
p. 17: Moved a comment about Pin$^+$ structure from a footnote to the main text since it is relevant for the revised discussion of symmetry fractionalization
pp. 23-24: Added more details on symmetry fractionalization to Section 4.2
pp. 27-28: Added two paragraphs on how the SPT response for the SET phase studied in Section 4.3 is correlated with the symmetry fractionalization of SET studied in Section 4.2. (Figure 2 caption and Section 4.3 summary paragraph also updated accordingly.)
p. 30: Added a sentence after Eq. 4.19 about its regime of validity
p. 32: Instead of referring to T as the “standard invertible time-reversal operator”, call it an interface that reverses orientation
Moved lattice model subsection (previously Subsection 4.4) to a new appendix (Appendix D)
Published as SciPost Phys. 19, 145 (2025)
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