Search

We discuss a variety of codimension-one, non-invertible topological defects in general 3+1d QFTs with a discrete one-form global symmetry. These include condensation defects from higher gauging of the one-form symmetries on a codimension-one manifold, each labeled by a discrete torsion class, and duality and triality defects from gauging in half of spacetime. The universal fusion rules between these non-invertible topological defects and the one-form symmetry surface defects are determined. Interestingly, the fusion coefficients are generally not numbers, but 2+1d TQFTs, such as invertible SPT phases, $\mathbb{Z}_N$ gauge theories, and $U(1)_N$ Chern-Simons theories. The associativity of these algebras over TQFT coefficients relies on nontrivial facts about 2+1d TQFTs. We further prove that some of these non-invertible symmetries are intrinsically incompatible with a trivially gapped phase, leading to nontrivial constraints on renormalization group flows. Duality and triality defects are realized in many familiar gauge theories, including free Maxwell theory, non-abelian gauge theories with orthogonal gauge groups, ${\cal N}=1,$ and ${\cal N}=4$ super Yang-Mills theories., 61 pages, 9 figures. v2: minor changes

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. In this paper, we point out that in both the free Maxwell theory and massive QED, there is a non-invertible time-reversal symmetry at every rational $\theta$-angle, i.e., $\theta= \pi p/N$. The non-invertible time-reversal symmetry is implemented by a conserved, anti-linear operator without an inverse. It is a composition of the naive time-reversal transformation and a fractional quantum Hall state. We also find similar non-invertible time-reversal symmetries in non-Abelian gauge theories, including the $\mathcal{N}=4$ $SU(2)$ super Yang-Mills theory along the locus $|\tau|=1$ on the conformal manifold., Comment: 30 pages

Cannabis is the fourth psychoactive substance to be legalized which are of far-reaching significance to the world. We analyzed data from the 2019 Global Burden of Disease Study (GBD) to estimate the incidence and prevalence of cannabis use disorder (CUD) and calculated the disease burden of CUD in 204 countries and territories and 21 regions over the past three decades. We reported disease burden due to CUD in terms of disability-adjusted life years (DALYs), age-standardized rate (ASR), estimated annual percentage change (EAPC), and analyzed associations between the burden of CUD and sociodemographic index (SDI) quintiles. Globally, the number of incidence cases of CUD was estimated to be increasing by 32.3% from 1990 to 2019 and males are nearly double higher than that of female. DALYs increase 38.6% from 1990. Young people aged 20–24 years old with cannabis use disorder have the highest DALYs in 2019, followed by those younger than 20 years old. India, Canada, USA, Qatar, Kenya, and high SDI quintile areas showed a high burden of disease. Nearly 200 million individuals are cannabis users worldwide, and CUD is a notable condition of GBD. The global cultivation of cannabis, rooted in different cultures, diversified access to cannabis, legalization in controversy, the promotion of medical cannabis, and many other factors promote the global cannabis industry is constantly updated and upgraded. It deserves more discussion in the future in terms of pathophysiological mechanisms, socioeconomics, law, and policy improvement.

We introduce a $\mathbb{Z}_N$ stabilizer code that can be defined on any spatial lattice of the form $\Gamma\times C_{L_z}$, where $\Gamma$ is a general graph. We also present the low-energy limit of this stabilizer code as a Euclidean lattice action, which we refer to as the anisotropic $\mathbb{Z}_N$ Laplacian model. It is gapped, robust (i.e., stable under small deformations), and has lineons. Its ground state degeneracy (GSD) is expressed in terms of a "mod $N$-reduction" of the Jacobian group of the graph $\Gamma$. In the special case when space is an $L\times L\times L_z$ cubic lattice, the logarithm of the GSD depends on $L$ in an erratic way and grows no faster than $O(L)$. We also discuss another gapped model, the $\mathbb{Z}_N$ Laplacian model, which can be defined on any graph. It has fractons and a similarly strange GSD., Comment: 51+1 pages, 5 figures, 1 table. v2: minor clarifications

Skeletal muscle insulin resistance (IR) is closely linked to hyperglycemia and metabolic disorders. Regular exercise enhances insulin sensitivity in skeletal muscle, but its underlying mechanisms remain unknown. Sestrin3 (SESN3) is a stress-inducible protein that protects against obesity-induced hepatic steatosis and insulin resistance. Regular exercise training is known to increase SESN3 expression in skeletal muscle. The purpose of this study was to explore whether SESN3 mediates the metabolic effects of exercise in the mouse model of high-fat diet (HFD)-induced IR. SESN3

For any quantum system invariant under gauging a higher-form global symmetry, we construct a non-invertible topological defect by gauging in only half of spacetime. This generalizes the Kramers-Wannier duality line in 1+1 dimensions to higher spacetime dimensions. We focus on the case of a one-form symmetry in 3+1 dimensions, and determine the fusion rule. From a direct analysis of one-form symmetry protected topological phases, we show that the existence of certain kinds of duality defects is intrinsically incompatible with a trivially gapped phase. We give an explicit realization of this duality defect in the free Maxwell theory, both in the continuum and in a modified Villain lattice model. The duality defect is realized by a Chern-Simons coupling between the gauge fields from the two sides. We further construct the duality defect in non-abelian gauge theories and the $\mathbb{Z}_N$ lattice gauge theory., 41 pages, 8 figures, 1 table. v2: clarifications to defect orientations; references added. v3: major changes in section 3

We identify infinitely many noninvertible generalized global symmetries in QED and QCD for the real world in the massless limit. In QED, while there is no conserved Noether current for the U(1)A axial symmetry because of the Adler-Bell-Jackiw anomaly, for every rational angle 2πp/N, we construct a conserved and gauge-invariant topological symmetry operator. Intuitively, it is a composition of the axial rotation and a fractional quantum Hall state coupled to the electromagnetic U(1) gauge field. These conserved symmetry operators do not obey a group multiplication law, but a noninvertible fusion algebra. They act invertibly on all local operators as axial rotations, but noninvertibly on the ’t Hooft lines. We further generalize our construction to QCD, and show that the coupling π0F∧F in the effective pion Lagrangian is necessary to match these noninvertible symmetries in the UV. Therefore, the conventional argument for the neutral pion decay using the ABJ anomaly is now rephrased as a matching condition of a generalized global symmetry.

Soil pollution by microplastics (MPs, 0.1 μm ~ 5 mm) and nanoplastics (NPs, ≤0.1 μm) has drawn much attention in recent years due to its potential ecological and human health risks; however, there are very limited studies and a general lack of consensus regarding the transport and transformation of MPs/NPs in soil environment. This review critically discusses the environmental behaviour of soil MPs/NPs, including the homo‐aggregation or hetero‐aggregation with other particles, sorption of pollutants and the photoaging process. The physicochemical property change of aggregated and aged MPs and its effect on the transport of other pollutants in soil has also been reviewed. Critical factors that affect the fate of MPs/NPs, including the physicochemical properties of MPs/NPs, physicochemical properties of soil and environmental factors, are reviewed to understand the latest progress in the environmental behaviour of soil MPs. Finally, we identify important research gaps, which include standard uniformity of quantification method, transformation mechanism elucidation and long‐term field studies. The review provides an overview of current findings for transport and transformation of MPs/NPs in natural soil environment and gives comments for future work.

This study evaluated the release of bisphenol S (BPS) from polyethersulfone (PES) and polyphenylsulfone microplastics (MPs) derived from baby bottles under UV irradiation. Released BPS fluctuates over time because it undergoes photolysis under UV

We study field theories with global dipole symmetries and gauge dipole symmetries. The famous Lifshitz theory is an example of a theory with a global dipole symmetry. We study in detail its 1+1d version with a compact field. When this global symmetry is promoted to a $U(1)$ dipole gauge symmetry, the corresponding gauge field is a tensor gauge field. This theory is known to lead to fractons. In order to resolve various subtleties in the precise meaning of these global or gauge symmetries, we place these 1+1d theories on a lattice and then take the continuum limit. Interestingly, the continuum limit is not unique. Different limits lead to different continuum theories, whose operators, defects, global symmetries, etc. are different. We also consider a lattice gauge theory with a $\mathbb Z_N$ dipole gauge group. Surprisingly, several physical observables, such as the ground state degeneracy and the mobility of defects depend sensitively on the number of sites in the lattice. Our analysis forces us to think carefully about global symmetries that do not act on the standard Hilbert space of the theory, but only on the Hilbert space in the presence of defects. We refer to them as time-like global symmetries and discuss them in detail. These time-like global symmetries allow us to phrase the mobility restrictions of defects (including those of fractons) as a consequence of a global symmetry., Comment: 88+1 pages, 5 figures, 4 tables

We introduce two exotic lattice models on a general spatial graph. The first one is a matter theory of a compact Lifshitz scalar field, while the second one is a certain rank-2 $U(1)$ gauge theory of fractons. Both lattice models are defined via the discrete Laplacian operator on a general graph. We unveil an intriguing correspondence between the physical observables of these lattice models and graph theory quantities. For instance, the ground state degeneracy of the matter theory equals the number of spanning trees of the spatial graph, which is a common measure of complexity in graph theory ("GSD = complexity"). The discrete global symmetry is identified as the Jacobian group of the graph. In the gauge theory, superselection sectors of fractons are in one-to-one correspondence with the divisor classes in graph theory. In particular, under mild assumptions on the spatial graph, the fracton immobility is proven using a graph-theoretic Abel-Jacobi map., Comment: 28+12+1 pages, 1 table, and 4 figures

Currently, there are many effective pharmacological treatments for generalized anxiety disorder (GAD), formulated herbal granule is also an alternative way. Our research intends to construct a pharmacological network on genetic targets and pathways between Jiu Wei Zhen Xin Formula (JWZXF) and GAD. Through the TCMSP database, we collected the active ingredients of JWZXF and potential targets of the active ingredients. The GAD-related proteins collected from GeneCards database and DisGeNET database were combined. Component-target protein networks were constructed and visualized using Cytoscape 3.8.2 software to comprehensively clarify the relationships between ingredients, components, and targets. The intersection targets were imported into the STRING database, and the protein-protein interaction (PPI) network was constructed. We constructed and analyzed the visualized “drug-target-disease” network. Gene Ontology (GO) enrichment together with Kyoto encyclopedia of genes and genomes (KEGG) enrichment analysis were conducted on the common target through R language. Forty-one effective components and 106 potential targets of JWZXF were found. There were top ten hub genes and multiple important signaling pathways involved in the treatment of GAD with the JWZXF. This study expounded the pharmacological actions and molecular mechanisms of the JWZXF in treating GAD from a holistic perspective. The potential pharmacological effects of the JWZXF are closely related to regulation because not only does it comprehensively analyze the possible mechanism of JWZXF treatment of GAD but it can also facilitate further in-depth research and provide a theoretical basis for the clinical expansion of its application.

We continue our exploration of exotic, gapless lattice and continuum field theories with subsystem global symmetries. In an earlier paper, we presented free lattice models enjoying all the global symmetries (except continuous translations), dualities, and anomalies of the continuum theories. Here, we study in detail the relation between the lattice models and the corresponding continuum theories. We do that by analyzing the spectrum of the theories and several correlation functions. These lead us to uncover interesting subtleties in the way the continuum limit can be taken. In particular, in some cases, the infinite volume limit and the continuum limit do not commute. This signals a surprising UV/IR mixing, i.e., long distance sensitivity to short distance details., 57+1 pages

We explore constraints on (1+1)d unitary conformal field theory with an internal ZN global symmetry, by bounding the lightest symmetry-preserving scalar primary operator using the modular bootstrap. Among the other constraints we have found, we prove the existence of a ZN-symmetric relevant/marginal operator if N−1≤c≤9−N for N≤4, with the end points saturated by various Wess-Zumino-Witten models that can be embedded into (e8)1. Its existence implies that robust gapless fixed points are not possible in this range of c if only a ZN symmetry is imposed microscopically. We also obtain stronger, more refined bounds that depend on the ‘t Hooft anomaly of the ZN symmetry.

We consider XY-spin degrees of freedom on an fcc lattice, such that the system respects some subsystem global symmetry. We then gauge this global symmetry and study the corresponding $U(1)$ gauge theory on the fcc lattice. Surprisingly, this $U(1)$ gauge theory is dual to the original spin system. We also analyze a similar ${\mathbb{Z}}_{N}$ gauge theory on that lattice. All these systems are fractonic. The $U(1)$ theories are gapless and the ${\mathbb{Z}}_{N}$ theories are gapped. We analyze the continuum limits of all these systems and present free continuum Lagrangians for their low-energy physics. Our ${\mathbb{Z}}_{2}$ fcc gauge theory is the continuum limit of the well-known checkerboard model of fractons. Our continuum analysis leads to a straightforward proof of the known fact that this theory is dual to two copies of the ${\mathbb{Z}}_{2}$ X-cube model. We find new models and new relations between known models. The ${\mathbb{Z}}_{N}$ fcc gauge theory can be realized by coupling three copies of an anisotropic model of lineons and planons to a certain exotic ${\mathbb{Z}}_{2}$ gauge theory. Also, although for $N=2$ this model is dual to two copies of the ${\mathbb{Z}}_{2}$ X-cube model, a similar statement is not true for higher $N$.

A 2+1-dimensional topological quantum field theory (TQFT) may or may not admit topological (gapped) boundary conditions. A famous necessary, but not sufficient, condition for the existence of a topological boundary condition is that the chiral central charge $c_-$ has to vanish. In this paper, we consider conditions associated with "higher" central charges, which have been introduced recently in the math literature. In terms of these new obstructions, we identify necessary and sufficient conditions for the existence of a topological boundary in the case of bosonic, Abelian TQFTs, providing an alternative to the identification of a Lagrangian subgroup. Our proof relies on general aspects of gauging generalized global symmetries. For non-Abelian TQFTs, we give a geometric way of studying topological boundary conditions, and explain certain necessary conditions given again in terms of the higher central charges. Along the way, we find a curious duality in the partition functions of Abelian TQFTs, which begs for an explanation via the 3d-3d correspondence., Comment: 51 pages. v2: minor clarifications and references added

We study 't Hooft anomalies and the related anomaly inflow for subsystem global symmetries. These symmetries and anomalies arise in a number of exotic systems, including models with fracton order such as the X-cube model. As is the case for ordinary global symmetries, anomalies for subsystem symmetries can be canceled by anomaly inflow from a bulk theory in one higher dimension; the corresponding bulk is therefore a non-trivial subsystem symmetry protected topological (SSPT) phase. We demonstrate these phenomena in several examples with continuous and discrete subsystem global symmetries, as well as time-reversal symmetry. For each example we describe the boundary anomaly, and present classical continuum actions for the corresponding bulk SSPT phases, which describe the response of background gauge fields associated with the subsystem symmetries. Interestingly, we show that the anomaly does not uniquely specify the bulk SSPT phase. In general, the latter may also depend on how the symmetry and the associated foliation structure on the boundary are extended into the bulk., Comment: 41 pages, 2 figures; the authors were ordered alphabetically

We study several exotic systems, including the X-cube model, on a flat three-torus with a twist in the $xy$-plane. The ground state degeneracy turns out to be a sensitive function of various geometrical parameters. Starting from a lattice, depending on how we take the continuum limit, we find different values of the ground state degeneracy. Yet, there is a natural continuum limit with a well-defined (though infinite) value of that degeneracy. We also uncover a surprising global symmetry in $2+1$ and $3+1$ dimensional systems. It originates from the underlying subsystem symmetry, but the way it is realized depends on the twist. In particular, in a preferred coordinate frame, the modular parameter of the twisted two-torus $\tau = \tau_1 + i \tau_2$ has rational $\tau_1 = k / m$. Then, in systems based on $U(1)\times U(1)$ subsystem symmetries, such as momentum and winding symmetries or electric and magnetic symmetries, the new symmetry is a projectively realized $\mathbb{Z}_m\times \mathbb{Z}_m$, which leads to an $m$-fold ground state degeneracy. In systems based on $\mathbb{Z}_N$ symmetries, like the X-cube model, each of these two $\mathbb{Z}_m$ factors is replaced by $\mathbb{Z}_{\gcd(N,m)}$., Comment: 61 pages, 3 figures

We extend our exploration of nonstandard continuum quantum field theories in 2+1 dimensions to 3+1 dimensions. These theories exhibit exotic global symmetries, a peculiar spectrum of charged states, unusual gauge symmetries, and surprising dualities. Many of the systems we study have a known lattice construction. In particular, one of them is a known gapless fracton model. The novelty here is in their continuum field theory description. In this paper, we focus on models with a global $U(1)$ symmetry and in a followup paper we will study models with a global $\mathbb{Z}_N$ symmetry., 74 pages. v3: significant changes

We discuss an isomorphism between the possible anomalies of $(d+1)$-dimensional quantum field theories with $\mathbb{Z}_{2}$ unitary global symmetry, and those of $d$-dimensional quantum field theories with time-reversal symmetry $\mathsf{T}$. This correspondence is an instance of symmetry defect decoration. The worldvolume of a $\mathbb{Z}_{2}$ symmetry defect is naturally invariant under $\mathsf{T},$ and bulk $\mathbb{Z}_{2}$ anomalies descend to $\mathsf{T}$ anomalies on these defects. We illustrate this correspondence in detail for $(1+1)d$ bosonic systems where the bulk $\mathbb{Z}_{2}$ anomaly leads to a Kramers degeneracy in the symmetry defect Hilbert space, and exhibit examples. We also discuss $(1+1)d$ fermion systems protected by $\mathbb{Z}_{2}$ global symmetry where interactions lead to a $\mathbb{Z}_{8}$ classification of anomalies. Under the correspondence, this is directly related to the $\mathbb{Z}_{8}$ classification of $(0+1)d$ fermions protected by $\mathsf{T}$. Finally, we consider $(3+1)d$ bosonic systems with $\mathbb{Z}_{2}$ symmetry where the possible anomalies are classified by $\mathbb{Z}_{2}\times \mathbb{Z}_{2}$. We construct topological field theories realizing these anomalies and show that their associated symmetry defects support anyons that can be either fermions or Kramers doublets., Comment: 29 pages, 7 figures

Despite great successes in the study of gapped phases, a comprehensive understanding of the gapless phases and their transitions is still under developments. In this paper, we study a general phenomenon in the space of (1+1)$d$ critical phases with fermionic degrees of freedom described by a continuous family of conformal field theories (CFT), a.k.a. the conformal manifold. Along a one-dimensional locus on the conformal manifold, there can be a transition point, across which the fermionic CFTs on the two sides differ by stacking an invertible fermionic topological order (IFTO), point-by-point along the locus. At every point on the conformal manifold, the order and disorder operators have power-law two-point functions, but their critical exponents cross over with each other at the transition point, where stacking the IFTO leaves the fermionic CFT unchanged. We call this continuous transition on the fermionic conformal manifold a topological transition. By gauging the fermion parity, the IFTO stacking becomes a Kramers-Wannier duality between the corresponding bosonic CFTs. Both the IFTO stacking and the Kramers-Wannier duality are induced by the electromagnetic duality of the (2+1)$d$ $\mathbb{Z}_2$ topological order. We provide several examples of topological transitions, including the familiar Luttinger model of spinless fermions (i.e. the $c=1$ massless Dirac fermion with the Thirring interaction), and a new class of $c=2$ examples describing $U(1)\times SU(2)$-protected gapless phases., Comment: 24 pages, 11 figures, 1 table

We continue the exploration of nonstandard continuum field theories related to fractons in 3+1 dimensions. Our theories exhibit exotic global and gauge symmetries, defects with restricted mobility, and interesting dualities. Depending on the model, the defects are the probe limits of either fractonic particles, strings, or strips. One of our models is the continuum limit of the plaquette Ising lattice model, which features an important role in the construction of the X-cube model., 68 pages, 3 figures, 7 tables

How many charged degrees of freedom are necessary to accommodate a certain amount of 't Hooft anomaly? Using the conformal bootstrap for the four-point function of flavor current multiplets, we show that in all $(3+1)\mathrm{D}$ superconformal field theories the 't Hooft anomaly of a continuous flavor symmetry is bounded from above by the $3/2$ power of the current two-point function coefficient, which can be thought of as a measure for the amount of charged degrees of freedom. We check our bounds against free fields and supersymmetric quantum chromodynamics in the conformal window.

We discuss nonstandard continuum quantum field theories in 2+1 dimensions. They exhibit exotic global symmetries, a subtle spectrum of charged excitations, and dualities similar to dualities of systems in 1+1 dimensions. These continuum models represent the low-energy limits of certain known lattice systems. One key aspect of these continuum field theories is the important role played by discontinuous field configurations. In two companion papers, we will present 3+1-dimensional versions of these systems. In particular, we will discuss continuum quantum field theories of some models of fractons., 62 pages. v4: additions about robustness