Juven Wang

Field theory representation of gauge-gravity symmetry-protected topological invariants, group cohomology and beyond

The challenge of identifying symmetry-protected topological states (SPTs) is due to their lack of symmetry-breaking order parameters and intrinsic topological orders. For this reason, it is impossible to formulate SPTs under Ginzburg-Landau theory or probe SPTs via fractionalized bulk excitations and topology-dependent ground state degeneracy. However, the partition functions from path integrals with various symmetry twists are universal SPT invariants, fully characterizing SPTs. In this work, we use gauge fields to represent those symmetry twists in closed spacetimes of any dimensionality and arbitrary topology. This allows us to express the SPT invariants in terms of continuum field theory. We show that SPT invariants of pure gauge actions describe the SPTs predicted by group cohomology, while the mixed gauge-gravity actions describe the beyond-group-cohomology SPTs. We find new examples of mixed gauge-gravity actions for U(1) SPTs in (4+1)D via the gravitational Chern-Simons term. Field theory representations of SPT invariants not only serve as tools for classifying SPTs, but also guide us in designing physical probes for them. In addition, our field theory representations are independently powerful for studying group cohomology within the mathematical context.

Non-Abelian string and particle braiding in topological order: Modular SL(3,Z) representation and (3 + 1)-dimensional twisted gauge theory

String and particle braiding statistics are examined in a class of topological orders described by discrete gauge theories with a gauge group G and a 4-cocycle twist ω 4 of G s cohomology group H 4 ( G , R / Z ) in three-dimensional space and one-dimensional time ( 3 + 1 D ) . We establish the topological spin and the spin-statistics relation for the closed strings and their multistring braiding statistics. The 3 + 1 D twisted gauge theory can be characterized by a representation of a modular transformation group, SL ( 3 , Z ) . We express the SL ( 3 , Z ) generators S x y z and T x y in terms of the gauge group G and the 4-cocycle ω 4 . As we compactify one of the spatial directions z into a compact circle with a gauge flux b inserted, we can use the generators S x y and T x y of an SL ( 2 , Z ) subgroup to study the dimensional reduction of the 3D topological order C 3 D to a direct sum of degenerate states of 2D topological orders C b 2 D in different flux b sectors: C 3 D = ⊕ b C b 2 D . The 2D topological orders C b 2 D are described by 2D gauge theories of the group G twisted by the 3-cocycle ω 3 ( b ) , dimensionally reduced from the 4-cocycle ω 4 . We show that the SL ( 2 , Z ) generators, S x y and T x y , fully encode a particular type of three-string braiding statistics with a pattern that is the connected sum of two Hopf links. With certain 4-cocycle twists, we discover that, by threading a third string through two-string unlink into a three-string Hopf-link configuration, Abelian two-string braiding statistics is promoted to non-Abelian three-string braiding statistics.

Gapped Domain Walls, Gapped Boundaries, and Topological Degeneracy

Gapped domain walls, as topological line defects between (2+1)D topologically ordered states, are examined. We provide simple criteria to determine the existence of gapped domain walls, which apply to both Abelian and non-Abelian topological orders. Our criteria also determine which (2+1)D topological orders must have gapless edge modes, namely, which (1+1)D global gravitational anomalies ensure gaplessness. Furthermore, we introduce a new mathematical object, the tunneling matrix W, whose entries are the fusion-space dimensions W(ia), to label different types of gapped domain walls. By studying many examples, we find evidence that the tunneling matrices are powerful quantities to classify different types of gapped domain walls. Since a gapped boundary is a gapped domain wall between a bulk topological order and the vacuum, regarded as the trivial topological order, our theory of gapped domain walls inclusively contains the theory of gapped boundaries. In addition, we derive a topological ground state degeneracy formula, applied to arbitrary orientable spatial 2-manifolds with gapped domain walls, including closed 2-manifolds and open 2-manifolds with gapped boundaries.

Bulk viscosity of a gas of massless pions

In the hadronic phase, the dominant configuration of quantum chromodynamics (QCD) with two flavors of massless quarks is a gas of massless pions. We calculate the bulk viscosity (

Twisted gauge theory model of topological phases in three dimensions

\ensuremath{\zeta}

Boundary degeneracy of topological order

) using the Boltzmann equation with the kinetic theory generalized to incorporate the trace anomaly. We find that the dimensionless ratio

Multikink topological terms and charge-binding domain-wall condensation induced symmetry-protected topological states: Beyond Chern-Simons/BF field theories

\ensuremath{\zeta}/s

Schrödinger Fermi liquids

,

Possible competing order-induced Fermi arcs in cuprate superconductors

s

Symmetry-protected many-body Aharonov-Bohm effect

being the entropy density, is monotonic increasing below