For any quantum system invariant under gauging a higher-form global symmetry, we construct non-invertible topological defect by in only half of spacetime. This generalizes the Kramers-Wannier duality line 1+1 dimensions to higher spacetime dimensions. We focus on case one-form symmetry 3+1 dimensions, and determine fusion rule. From direct analysis protected phases, show that existence certain kinds defects is intrinsically incompatible with trivially gapped phase. give an explicit...

We extend our earlier work on anomalies in the space of coupling constants to four-dimensional gauge theories. Pure Yang-Mills theory (without matter) with a simple and simply connected group has mixed anomaly between its one-form global symmetry (associated center) periodicity $\theta$-parameter. This is at root many recently discovered properties these theories, including their phase transitions interfaces. These new can be used this understanding systems without discrete symmetries (such...

It is customary to couple a quantum system external classical fields. One application the global symmetries of (including Poincaré symmetry) background gauge fields (and metric for symmetry). Failure invariance partition function under transformations these reflects ’t Hooft anomalies. also common view ordinary (scalar) coupling constants as fields, i.e. study theory when they are spacetime dependent. We will show that notion anomalies can be extended naturally include scalar Just allow us...

We identify infinitely many noninvertible generalized global symmetries in QED and QCD for the real world massless limit. In QED, while there is no conserved Noether current U(1)A axial symmetry because of Adler-Bell-Jackiw anomaly, every rational angle 2πp/N, we construct a gauge-invariant topological operator. Intuitively, it composition rotation fractional quantum Hall state coupled to electromagnetic U(1) gauge field. These operators do not obey group multiplication law, but fusion...

We study field theories with global dipole symmetries and gauge symmetries. The famous Lifshitz theory is an example of a symmetry. in detail its $1+1\mathrm{D}$ version compact field. When this symmetry promoted to $U(1)$ symmetry, the corresponding tensor This known lead fractons. To resolve various subtleties precise meaning these or symmetries, we place on lattice then take continuum limit. Interestingly, limit not unique. Different limits different theories, whose operators, defects,...

In gauge theory, it is commonly stated that time-reversal symmetry only exists at $\theta=0$ or $\pi$ for a $2\pi$-periodic $\theta$-angle. this paper, we point out in both the free Maxwell theory and massive QED, there non-invertible every rational $\theta$-angle, i.e., $\theta= \pi p/N$. The implemented by conserved, anti-linear operator without an inverse. It composition of naive transformation fractional quantum Hall state. We also find similar symmetries non-Abelian theories, including...

A bstract In axion-Maxwell theory at the minimal axion-photon coupling, we find non-invertible 0- and 1-form global symmetries arising from naive shift center symmetries. Since Gauss law is anomalous, there no conserved, gauge-invariant, quantized electric charge. Rather, using half higher gauging, a associated with symmetry, which related to Page These act invertibly on axion field Wilson line, but non-invertibly monopoles strings, leading selection rules Witten effect. We also derive...

Our understanding of quantum symmetry systems has considerably broadened over the last decade. The idea become intrinsically linked with topology described and algebraically characterized by higher categories. Studying three-dimensional noninvertible symmetries, authors show here that these symmetries are in general incompatible a unique gapped ground state. Their results extend ideas behind Lieb-Shultz-Mattis theorem to arena higher-dimensional field theories invariant under novel class symmetries.

We derive model-independent quantization conditions on the axion couplings (sometimes known as anomaly coefficients) to standard model gauge group <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:mo stretchy="false">[</a:mo><a:mrow><a:mi>SU</a:mi></a:mrow><a:mo stretchy="false">(</a:mo><a:mn>3</a:mn><a:mo stretchy="false">)</a:mo><a:mo>×</a:mo><a:mrow><a:mi>SU</a:mi></a:mrow><a:mo stretchy="false">(</a:mo><a:mn>2</a:mn><a:mo...

Modulated symmetries are internal that act in a non-uniform, spatially modulated way and generalizations of, for example, dipole symmetries. In this paper, we systematically study the gauging of finite Abelian {1+1} <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mn>1</mml:mn><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:math> dimensions. Working with local Hamiltonians spin chains, explore dual after their potential new spatial modulations. We...

Projective symmetries are ubiquitous in quantum lattice models and can be leveraged to constrain their phase diagram entanglement structure. In this paper, we investigate the consequences of projective algebras formed by non-invertible translations a generalized 1+1 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mn>1</mml:mn><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:math> D XY model based on group-valued qudits. This is specified finite...

A bstract Schwarzian quantum mechanics describes the collective IR mode of SYK model and captures key features 2D black hole dynamics. Exact results for its correlation functions were obtained in [1]. We compare these with bulk gravity expectations. find that semi-classical limit OTO four-point function exactly matches scattering amplitude from Dray-’t Hooft shockwave $$ \mathcal{S} <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>S</mml:mi> </mml:math> -matrix. show two...

Gauge theories in various dimensions often admit discrete theta angles, that arise from gauging a global symmetry with an additional protected topological (SPT) phase. We discuss how the and 't Hooft anomaly depends on angles by coupling gauge theory to quantum field (TQFT). observe Abelian subgroup symmetry, participates extension, SPT phase leads new emergent also extension. The extension of is controlled angle which comes find can lead two-group 4d QCD $SU(N),SU(N)/\mathbb{Z}_k$ or...

We introduce a family of partially entangled thermal states in the SYK model that interpolates between thermo-field double state and pure (product) state. The are prepared by euclidean path integral describing evolution over two time segments separated local scaling operator $\mathcal{O}$. argue holographic dual this class consists black holes with their interior regions connected via domain wall, described worldline massive particle. compute size region entanglement entropy as function...

We reformulate known exotic theories (including of fractons) on a Euclidean spacetime lattice. write them using the Villain approach and then we modify to convenient range parameters. The new lattice models are closer continuum limit than original versions. In particular, they exhibit many recently found properties including emergent global symmetries surprising dualities. Also, these provide clear rigorous formulation their singularities. appendices, use this review well-studied limits....

We continue the exploration of nonstandard continuum field theories related to fractons in 3+1 dimensions. Our exhibit exotic global and gauge symmetries, defects with restricted mobility, interesting dualities. Depending on model, are probe limits either fractonic particles, strings, or strips. One our models is limit plaquette Ising lattice which features an important role construction X-cube model.

We continue our exploration of exotic, gapless lattice and continuum field theories with subsystem global symmetries. In an earlier paper, we presented free models enjoying all the symmetries (except continuous translations), dualities, anomalies theories. Here, study in detail relation between corresponding do that by analyzing spectrum several correlation functions. These lead us to uncover interesting subtleties way limit can be taken. particular, some cases, infinite volume not commute....

We study 't Hooft anomalies and the related anomaly inflow for subsystem global symmetries. These symmetries arise in a number of exotic systems, including models with fracton order such as X-cube model. As is case ordinary symmetries, can be canceled by from bulk theory one higher dimension; corresponding therefore non-trivial symmetry protected topological (SSPT) phase. demonstrate these phenomena several examples continuous discrete well time-reversal symmetry. For each example we...

We investigate the physics of one-dimensional symmetry-protected topological (SPT) phases protected by symmetries whose symmetry generators exhibit spatial modulation. focus in particular on with linear (i.e., dipolar), quadratic, and exponential modulations. present a simple recipe for constructing modulated SPT models generalizing concept decorated domain walls to spatially defects, develop several tools characterizing classifying phases. A salient feature is that they are generically only...

We classify one-dimensional symmetry-protected topological (SPT) phases protected by dipole symmetries. A symmetry comprises two sets of generators: charge and operators, which together form a nontrivial algebra with translations. Using matrix product states (MPS), we show that for $G$ finite Abelian group, the dipolar SPTs are classified group ${H}^{2}[G\ifmmode\times\else\texttimes\fi{}G,U(1)]/{H}^{2}{[G,U(1)]}^{2}$. Because algebra, MPS tensors exhibit an unusual property, prohibiting...

We study general properties of the conformal basis, space wavefunctions in $(d+2)$-dimensional Minkowski that are primaries Lorentz group $SO(1,d+1)$. Scattering amplitudes written this basis have same symmetry as $d$-dimensional correlators. translate optical theorem, which is a direct consequence unitarity, into basis. In particular case tree-level exchange diagram, theorem takes form block decomposition on principal continuous series, with OPE coefficients being three-point coupling...

We study 3d and 4d systems with a one-form global symmetry, explore their consequences, analyze gauging. For simplicity, we focus on $\mathbb{Z}_N$ symmetries. A topological quantum field theory (TQFT) $\mathcal{T}$ such symmetry has $N$ special lines that generate it. The braiding of these spins are characterized by single integer $p$ modulo $2N$. Surprisingly, if $\gcd(N,p)=1$ the TQFT factorizes $\mathcal{T}=\mathcal{T}'\otimes \mathcal{A}^{N,p}$. Here $\mathcal{T}'$ is decoupled TQFT,...

The 2+1d continuum Lifshitz theory of a free compact scalar field plays prominent role in variety quantum systems condensed matter physics and high energy physics. It is known that space, it has an infinite ground state degeneracy. In order to understand this better, we consider two candidate lattice regularizations using the modified Villain formalism. We show these theories have significantly different global symmetries (including dipole symmetry), anomalies, degeneracies, dualities....

We analyze the internal symmetries and their anomalies in Kitaev spin- S <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>S</mml:mi></mml:math> models. Importantly, these models have a lattice version of \mathbb{Z}_2 display="inline"><mml:msub><mml:mi>ℤ</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:math> 1-form symmetry, denoted by \mathbb{Z}_2^{[1]} display="inline"><mml:msubsup><mml:mi>ℤ</mml:mi><mml:mn>2</mml:mn><mml:mrow><mml:mo stretchy="true"...