Fractional topological insulators (FTIs) are electronic systems that carry fractionally charged excitations, conserve charge, and are symmetric to reversal of time. In this review, we introduce the ...basic essential concepts of the field and then survey theoretical understanding of FTIs in two and three dimensions. In between, we discuss the case of "two and a half dimensions," the FTIs that may form on the two-dimensional surface of an unfractionalized three-dimensional topological insulator. We focus on electronic systems and emphasize properties of edges and surfaces, most notably the stability of gapless edge modes to perturbations.
A
bstract
We classify and characterize fully all invertible anomalies and all allowed topo- logical terms related to various Standard Models (SM), Grand Unified Theories (GUT), and Beyond Standard ...Model (BSM) physics. By all anomalies, we mean the inclusion of (1) perturbative local anomalies captured by perturbative Feynman diagram loop calculations, classified by ℤ free classes, and (2) nonperturbative global anomalies, classified by finite group ℤ
N
torsion classes. Our work built from 31 fuses the math tools of Adams spectral sequence, Thom-Madsen-Tillmann spectra, and Freed-Hopkins theorem. For example, we compute bordism groups
Ω
d
G
and their invertible topological field theory invariants, which characterize
d
d topological terms and (
d −
1)d anomalies, protected by the following symmetry group
G
:
Spin
×
SU
3
×
SU
2
×
U
1
ℤ
q
for SM with
q
= 1
,
2
,
3
,
6;
Spin
×
Spin
n
ℤ
2
F
or Spin × Spin(
n
) for SO(10) or SO(18) GUT as
n
= 10
,
18; Spin × SU(
n
) for Georgi-Glashow SU(5) GUT as
n
=
5
;
Spin
×
SU
4
×
SU
2
×
SU
2
ℤ
q
′
ℤ
2
F
for Pati-Salam GUT as
q
′ = 1
,
2; and others. For SM with an extra discrete symmetry, we obtain
new
anomaly matching conditions of ℤ
16
, ℤ
4
and ℤ
2
classes
beyond
the familiar Witten anomaly. Our approach offers an alternative view of all anomaly matching conditions built from the lower-energy (B)SM or GUT, in contrast to high-energy Quantum Gravity or String Theory Landscape v.s. Swampland program, as bottom-up/top-down complements. Symmetries and anomalies provide constraints of kinematics, we further suggest constraints of quantum gauge dynamics, and new predictions of possible extended defects/excitations plus hidden BSM non-perturbative topological sectors.
A
bstract
A number of recent works have argued that quantum complexity, a well-known concept in computer science that has re-emerged recently in the context of the physics of black holes, may be used ...as an efficient probe of novel phenomena such as quantum chaos and even quantum phase transitions. In this article, we provide further support for the latter, using a 1-dimensional p-wave superconductor — the Kitaev chain — as a prototype of a system displaying a topological phase transition. The Hamiltonian of the Kitaev chain manifests two gapped phases of matter with fermion parity symmetry; a trivial strongly-coupled phase and a topologically non-trivial, weakly-coupled phase with Majorana zero-modes. We show that Krylov-complexity (or, more precisely, the associated spread-complexity) is able to distinguish between the two and provides a diagnostic of the quantum critical point that separates them. We also comment on some possible ambiguity in the existing literature on the sensitivity of different measures of complexity to topological phase transitions.
A
bstract
This is the first part of a two-part work on a unified mathematical theory of gapped and gapless edges of 2d topological orders. We analyze all the possible observables on the 1+1D world ...sheet of a chiral gapless edge of a 2d topological order, and show that these observables form an enriched unitary fusion category, the Drinfeld center of which is precisely the unitary modular tensor category associated to the bulk. This mathematical description of a chiral gapless edge automatically includes that of a gapped edge (i.e. a unitary fusion category) as a special case. Therefore, we obtain a unified mathematical description and a classification of both gapped and chiral gapless edges of a given 2d topological order. In the process of our analysis, we encounter an interesting and reoccurring phenomenon: spatial fusion anomaly, which leads us to propose the Principle of Universality at RG fixed points for all quantum field theories. Our theory also implies that all chiral gapless edges can be obtained from a so-called topological Wick rotations. This fact leads us to propose, at the end of this work, a surprising correspondence between gapped and gapless phases in all dimensions.
A
bstract
We study the anomaly induced effects of dense baryonic matter under rotation. We derive the anomalous terms that account for the chiral vortical effect in the low-energy effective theory ...for light Nambu-Goldstone modes. The anomalous terms lead to new physical consequences, such as the anomalous Hall energy current and spontaneous generation of angular momentum in a magnetic field (or spontaneous magnetization by rotation). In particular, we show that, due to the presence of such anomalous terms, the ground state of the quantum chromodynamics (QCD) under sufficiently fast rotation becomes the “chiral soliton lattice” of neutral pions that has lower energy than the QCD vacuum and nuclear matter. We briefly discuss the possible realization of the chiral soliton lattice induced by a fast rotation in noncentral heavy ion collisions.
A
bstract
We consider 3
d
N
= 2 gauge theories with fundamental matter plus a single field in a rank-2 representation. Using iteratively a process of “deconfinement” of the rank-2 field, we produce a ...sequence of Seiberg-dual quiver theories. We detail this process in two examples with zero superpotential: Usp(2
N
) gauge theory with an antisymmetric field and U(
N
) gauge theory with an adjoint field. The fully deconfined dual quiver has
N
nodes, and can be interpreted as an Aharony dual of theories with rank-2 matter. All chiral ring generators of the original theory are mapped into gauge singlet fields of the fully deconfined quiver dual.
A
bstract
The QCD axion or axion-like particles are candidates of dark matter of the universe. On the other hand, axion-like excitations exist in certain condensed matter systems, which implies that ...there can be interactions of dark matter particles with condensed matter axions. We discuss the relationship between the condensed matter axion and a collective spin-wave excitation in an anti-ferromagnetic insulator at the quantum level. The conversion rate of the light dark matter, such as the elementary particle axion or hidden photon, into the condensed matter axion is estimated for the discovery of the dark matter signals.
6D fractional quantum Hall effect Heckman, Jonathan J.; Tizzano, Luigi
The journal of high energy physics,
05/2018, Letnik:
2018, Številka:
5
Journal Article
Recenzirano
Odprti dostop
A
bstract
We present a 6D generalization of the fractional quantum Hall effect involving membranes coupled to a three-form potential in the presence of a large background four-form flux. The low ...energy physics is governed by a bulk 7D topological field theory of abelian three-form potentials with a single derivative Chern-Simons-like action coupled to a 6D anti-chiral theory of Euclidean effective strings. We derive the fractional conductivity, and explain how continued fractions which figure prominently in the classification of 6D superconformal field theories correspond to a hierarchy of excited states. Using methods from conformal field theory we also compute the analog of the Laughlin wavefunction. Compactification of the 7D theory provides a uniform perspective on various lower-dimensional gapped systems coupled to boundary degrees of freedom. We also show that a supersymmetric version of the 7D theory embeds in M-theory, and can be decoupled from gravity. Encouraged by this, we present a conjecture in which IIB string theory is an edge mode of a 10 + 2-dimensional bulk topological theory, thus placing all twelve dimensions of F-theory on a physical footing.
A
bstract
We discuss a strategy to construct gapped boundaries for a large class of symmetry-protected topological phases (SPT phases) beyond group cohomology. This is done by a generalization of the ...symmetry extension method previously used for cohomo- logical SPT phases. We find that this method allows us to construct gapped boundaries for time-reversal-invariant bosonic SPT phases and for fermionic Gu-Wen SPT phases for arbitrary finite internal symmetry groups.
A
bstract
We study generalized discrete symmetries of quantum field theories in 1+1D generated by topological defect lines with no inverse. In particular, we describe ’t Hooft anomalies and classify ...gapped phases stabilized by these symmetries, including new 1+1D topological phases. The algebra of these operators is not a group but rather is described by their fusion ring and crossing relations, captured algebraically as a fusion category. Such data defines a Turaev-Viro/Levin-Wen model in 2+1D, while a 1+1D system with this fusion category acting as a global symmetry defines a boundary condition. This is akin to gauging a discrete global symmetry at the boundary of Dijkgraaf-Witten theory. We describe how to “ungauge” the fusion category symmetry in these boundary conditions and separate the symmetry-preserving phases from the symmetry-breaking ones. For Tambara-Yamagami categories and their generalizations, which are associated with Kramers-Wannier-like self-dualities under orbifolding, we develop gauge theoretic techniques which simplify the analysis. We include some examples of CFTs with fusion category symmetry derived from Kramers-Wannier-like dualities as an appetizer for the Part II companion paper.
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