A bstract We analyze topological mass terms of BF type arising in supersymmetric M-theory compactifications to AdS 5 . These describe spontaneously broken higher-form gauge symmetries in the bulk. Different choices of boundary conditions for the BF terms yield dual field theories with distinct global discrete symmetries. We discuss in detail these symmetries and their ât Hooft anomalies for 4d $$ \mathcal{N} $$ N = 1 SCFTs arising from M5-branes wrapped on a Riemann surface without punctures, including theories from M5-branes at a †2 orbifold singularity. The anomaly polynomial is computed via inflow and contains background fields for discrete global 0-, 1-, and 2-form symmetries and continuous 0-form symmetries, as well as axionic background fields. The latter are properly interpreted in the context of anomalies in the space of coupling constants.
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Theory of oblique topological insulators
A long-standing problem in the study of topological phases of matter has been to understand the types of fractional topological insulator (FTI) phases possible in 3+1 dimensions. Unlike ordinary topological insulators of free fermions, FTI phases are characterized by fractional đ-angles,long-range entanglement, and fractionalization. Starting from a simple family of â€_N lattice gauge theories due to Cardy and Rabinovici, we develop a class of FTI phases based on the physical mechanism of oblique confinement and the modern language of generalized global symmetries. We dub these phases oblique topological insulators. Oblique TIs arise when dyonsâbound states of electric charges and monopolesâcondense, leading to FTI phases characterized by topological order, emergent one-forms symmetries, and gapped boundary states not realizable in 2+1-D alone.Based on the lattice gauge theory, we present continuum topological quantum field theories (TQFTs) for oblique TI phases involving fluctuating one-form and two-form gauge fields. We show explicitly that these TQFTs capture both the generalized global symmetries and topological orders seen in the lattice gauge theory. We also demonstrate that these theories exhibit a universal âgeneralized magneto-electric effectâ in the presence of two-form background gauge fields. Moreover,we characterize the possible boundary topological orders of oblique TIs,finding a new set of boundary states not studied previously for these kinds of TQFTs.
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- Award ID(s):
- 2225920
- PAR ID:
- 10496685
- Publisher / Repository:
- SciPost
- Date Published:
- Journal Name:
- SciPost Physics
- Volume:
- 14
- Issue:
- 2
- ISSN:
- 2542-4653
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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We consider a SU(2) lattice gauge theory on the square lattice, with a single fundamental complex fermion and a single fundamental complex boson on each lattice site. Projective symmetries of the gauge-charged fermions are chosen so that they match with those of the spinons of the-flux spin liquid. Global symmetries of all gauge-invariant observables are chosen to match with those of the particle-hole symmetric electronic Hubbard model at half-filling. Consequently, both the fundamental fermion and fundamental boson move in an average background-flux, their gauge-invariant composite is the physical electron, and eliminating gauge fields in a strong gauge-coupling expansion yields an effective extended Hubbard model for the electrons. The SU(2) gauge theory displays several confining/Higgs phases: a nodal-wave superconductor, and states with Néel, valence-bond solid, charge, or staggered current orders. There are also a number of quantum phase transitions between these phases that are very likely described by-dimensional deconfined conformal gauge theories, and we present large flavor expansions for such theories. These include the phenomenologically attractive case of a transition between a conventional insulator with a charge gap and Néel order, and a conventional-wave superconductor with gapless Bogoliubov quasiparticles at four nodal points in the Brillouin zone. We also apply our approach to the honeycomb lattice, where we find a bicritical point at the junction of Néel, valence bond solid (Kekulé), and Dirac semimetal phases.
Published by the American Physical Society 2024 -
Originating with the discovery of the quantum Hall effect (QHE) in condensed matter physics, topological order has been receiving increased attention also for classical wave phenomena. Topological protection enables efficient and robust signal transport; mechanical topological insulators (TIs), in particular, are easy to fabricate and exhibit interfacial wave transport with minimal dissipation, even in the presence of sharp edges, defects, or disorder. Here, we report the experimental demonstration of a phononic crystal Floquet TI (FTI). Hexagonal arrays of circular piezoelectric disks bonded to a PLA substrate, shunted through negative electrical capacitance, and manipulated by external integrated circuits, provide the required spatiotemporal modulation scheme to break time-reversal symmetry and impart a synthetic angular momentum bias that can induce strong topological protection on the lattice edges. Our proposed reconfigurable FTI may find applications for robust acoustic emitters and mechanical logic circuits, with distinct advantages over electronic equivalents in harsh operating conditions.more » « less
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Abstract Symmetry-protected topological phases of matter have challenged our understanding of condensed matter systems and harbour exotic phenomena promising to address major technological challenges. Considerable understanding of these phases of matter has been gained recently by considering additional protecting symmetries, different types of quasiparticles, and systems out of equilibrium. Here, we show that symmetries could be enforced not just on full Hamiltonians, but also on their components. We construct a large class of previously unidentified multiplicative topological phases of matter characterized by tensor product Hilbert spaces similar to the Fock space of multiple particles. To demonstrate our methods, we introduce multiplicative topological phases of matter based on the foundational Hopf and Chern insulator phases, the multiplicative Hopf and Chern insulators (MHI and MCI), respectively. The MHI shows the distinctive properties of the parent phases as well as non-trivial topology of a child phase. We also comment on a similar structure in topological superconductors as these multiplicative phases are protected in part by particle-hole symmetry. The MCI phase realizes topologically protected gapless states that do not extend from the valence bands to the conduction bands for open boundary conditions, which respects to the symmetries protecting topological phase. The band connectivity discovered in MCI could serve as a blueprint for potential multiplicative topology with exotic properties.
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A bstract We study generalized symmetries in a simplified arena in which the usual quantum field theories of physics are replaced with topological field theories and the smooth structure with which the symmetry groups of physics are usually endowed is forgotten. Doing so allows many questions of physical interest to be answered using the tools of homotopy theory. We study both global and gauge symmetries, as well as ât Hooft anomalies, which we show fall into one of two classes. Our approach also allows some insight into earlier work on symmetries (generalized or not) of topological field theories.more » « less
- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.21468/SciPostPhys.14.2.023
