2,908 research outputs found
Universal Non-Invertible Symmetries
It is well-known that gauging a finite 0-form symmetry in a quantum field
theory leads to a dual symmetry generated by topological Wilson line defects.
These are described by the representations of the 0-form symmetry group which
form a 1-category. We argue that for a d-dimensional quantum field theory the
full set of dual symmetries one obtains is in fact much larger and is described
by a (d-1)-category, which is formed out of lower-dimensional topological
quantum field theories with the same 0-form symmetry. We study in detail a
2-categorical piece of this (d-1)-category described by 2d topological quantum
field theories with 0-form symmetry. We further show that the objects of this
2-category are the recently discussed 2d condensation defects constructed from
higher-gauging of Wilson lines. Similarly, dual symmetries obtained by gauging
any higher-form or higher-group symmetry also form a (d-1)-category formed out
of lower-dimensional topological quantum field theories with that higher-form
or higher-group symmetry. A particularly interesting case is that of the
2-category of dual symmetries associated to gauging of finite 2-group
symmetries, as it describes non-invertible symmetries arising from gauging
0-form symmetries that act on (d-3)-form symmetries. Such non-invertible
symmetries were studied recently in the literature via other methods, and our
results not only agree with previous results, but our approach also provides a
much simpler way of computing various properties of these non-invertible
symmetries. We describe how our results can be applied to compute
non-invertible symmetries of various classes of gauge theories with continuous
disconnected gauge groups in various spacetime dimensions. We also discuss the
2-category formed by 2d condensation defects in any arbitrary quantum field
theory.Comment: 75 pages. v2: Minor improvement
Generalized Global Symmetries
A -form global symmetry is a global symmetry for which the charged
operators are of space-time dimension ; e.g. Wilson lines, surface defects,
etc., and the charged excitations have spatial dimensions; e.g. strings,
membranes, etc. Many of the properties of ordinary global symmetries (=0)
apply here. They lead to Ward identities and hence to selection rules on
amplitudes. Such global symmetries can be coupled to classical background
fields and they can be gauged by summing over these classical fields. These
generalized global symmetries can be spontaneously broken (either completely or
to a subgroup). They can also have 't Hooft anomalies, which prevent us from
gauging them, but lead to 't Hooft anomaly matching conditions. Such anomalies
can also lead to anomaly inflow on various defects and exotic Symmetry
Protected Topological phases. Our analysis of these symmetries gives a new
unified perspective of many known phenomena and uncovers new results.Comment: 49 pages plus appendices. v2: references adde
Non-Liquid Cellular States
The existence of quantum non-liquid states and fracton orders, both gapped
and gapless states, challenges our understanding of phases of entangled matter.
We generalize Wen's cellular topological states to liquid or non-liquid
cellular states. We propose a mechanism to construct more general non-abelian
states by gluing gauge-symmetry-breaking vs gauge-symmetry-extension interfaces
as extended defects in a cellular network, including defects of
higher-symmetries. Our approach also includes the anyonic particle/string
condensation and composite string (p-string)/membrane condensations. This also
shows gluing the familiar extended topological quantum field theory or
conformal field theory data via topology, geometry, and renormalization
consistency criteria (via certain modified group cohomology or cobordism theory
data) in a tensor network can still guide us to analyze the non-liquid states.
(Part of the abelian construction can be understood from the K-matrix
Chern-Simons theory approach and coupled-layer-by-junction constructions.) This
may also lead us toward a unifying framework for quantum systems of both
higher-symmetries and sub-system/sub-dimensional symmetries.Comment: 42 pages. Subtitle: Gluing Gauge-(Higher)-Symmetry-Breaking vs
-Extension Interfacial Defect
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