We explore the necessary conditions for 1-form symmetries to emerge in the long-distance limit when they are explicitly broken at short distances. A minimal requirement is that there exist operators which become topological at long distances and that these operators have non-trivial correlation functions. These criteria are obeyed when the would-be emergent symmetry is spontaneously broken, or is involved in 't Hooft anomalies. On the other hand, confinement, i.e. a phase with unbroken 1-form symmetry, is nearly incompatible with the emergence of 1-form symmetries. We comment on some implications of our results for QCD as well as the idea of Higgs-confinement continuity.
In this paper we study dualities for $\mathcal{N}=2$ gauge theories in three dimensions with matter in the fundamental and adjoint representation. The duality we propose, analogous to mirror symmetry, is obtained starting from $\mathcal{N}=4$ mirror theories and turning on a certain superpotential deformation involving monopole operators. We study the role of emergent symmetries in the dual theory, focusing on the case of models with gauge symmetry $U(2)$ or $SU(2)$. We find that $SU(2)$ adjoint SQCD with one flavor and zero superpotential is dual to SQED with two flavors and three singlets. A…
Gauge symmetries indicate redundancies in the description of the relevant degrees of freedom of a given field theory and restrict the nature of observable quantities. One of the problems faced by emergent theories of relativistic fields is to understand how gauge symmetries can show up in systems that contain no trace of these symmetries at a more fundamental level. In this paper we start a systematic study aimed to establish a satisfactory mathematical and physical picture of this issue, dealing first with abelian field theories. We discuss how the trivialization, due to the decoupling and la…
Gauge symmetries play an essential role in determining the interactions of particle physics. Where do they come from? Might the gauge symmetries of the Standard Model unify in the ultraviolet or might they be emergent in the infrared, below some large scale close to the Planck scale? Emergent gauge symmetries are important in quantum many-body systems in quantum phases associated with long range entanglement and topological order, e.g., they arise in high temperature superconductors, with string-net condensation and in the A-phase of superfluid He-3. String-nets and superfluid He-3 exhibit eme…
Hidden theories coupled to the SM may provide emergent (dark) vectors, that are composites/bound-states of the hidden fields. This is motivated by paradigms emerging from the AdS/CFT correspondence but it is a more general phenomenon. We explore the general setup and find that UV interactions among currents or charged fields give rise to emergent vectors in the IR. We study the general properties of such vectors and argue that they can be generically different from fundamental dark photons that have been studied so far.
The usual condensed matter lattice theories do not include dynamical electromagnetic (EM) field and do not have higher symmetries naturally (unless we engineer fine-tuned toy models to realize higher symmetries). However, for gapped systems, (anomalous) higher symmetries can emerge from the usual condensed matter theories at low energies (usually in a spontaneously broken form). We pointed out that spontaneously broken emergent higher symmetries are nothing but a kind of topological orders. The emergent (anomalous) higher symmetries can be used to constrain possible phase transitions and possi…
These are intended to be review notes on emergent symmetries, i.e., symmetries which manifest themselves in specific sectors of energy in many systems. The emphasis is on the physical aspects rather than computation methods. We include some background material and go through more recent problems in field theory, statistical mechanics and condensed matter. These problems illustrate how some important symmetries, such as Lorentz invariance and supersymmetry, usually believed to be fundamental, can arise naturally in low-energy regimes of systems involving a large number of degrees of freedom. Th…
Type-IV 't Hooft Anomalies on the Lattice: Emergent Higher-Categorical Symmetries and Applications to LSM Systems
Yukawa Institute for Theoretical Physics, Kyoto University（京都大学汤川理论物理研究所）；Interdisciplinary Theoretical and Mathematical Sciences Program (iTHEMS) RIKEN（理化学研究所交叉理论与数学科学项目）
Entanglement suppression in the strong interaction $S$-matrix is shown to be correlated with approximate spin-flavor symmetries that are observed in low-energy baryon interactions, the Wigner $SU(4)$ symmetry for two flavors and an $SU(16)$ symmetry for three flavors. We conjecture that dynamical entanglement suppression is a property of the strong interactions in the infrared, giving rise to these emergent symmetries and providing powerful constraints on the nature of nuclear and hypernuclear forces in dense matter.
Gauge symmetries remove unphysical states and guarantee that field theories are free from the pathologies associated with these states. In this work we find a set of general conditions that guarantee the removal of unphysical states in field theories describing interacting vector fields. These conditions are obtained through the extension of a mechanism for the emergence of gauge symmetries proposed in a previous article [C. Barceló et al. JHEP 10 (2016) 084] in order to account for non-Abelian gauge symmetries, and are the following: low-energy Lorentz invariance, emergence of massless vector…
We focus on the question of how relativistic fluid dynamics should be thought of as a Wilsonian effective field theory emerging from Schwinger-Keldysh path integrals. Taking the basic principles of Schwinger-Keldysh formalism seriously, we are led to a series of remarkable statements and conjectures, which we phrase in terms of a broad programme relating relativistic fluid dynamics and topological sigma models. Apart from the intrinsic interest for these ideas from the non-equilibrium field theory viewpoint, we also emphasize its relevance to various fundamental questions in black hole physics…
We consider and derive the gravitational soft theorem up to the sub-subleading power from the perspective of effective Lagrangians. The emergent soft gauge symmetries of the effective Lagrangian provide a transparent explanation of why soft graviton emission is universal to sub-subleading power, but gauge boson emission is not. They also suggest a physical interpretation of the form of the soft factors in terms of the charges related to the soft transformations and the kinematics of the multipole expansion. The derivation is done directly at Lagrangian level, resulting in an operatorial form o…
Axions, periodic scalar fields coupled to gauge fields through the instanton density, have a rich variety of higher-form global symmetries. These include a two-form global symmetry, which measures the charge of axion strings. As we review, these symmetries typically combine into a higher-group, a kind of non-abelian structure where symmetries that act on operators of different dimensions, such as points, lines, and strings, are mixed. We use this structure to derive model independent constraints on renormalization group flows that realize theories of axions at long distances. These give univer…
Entanglement suppression and emergent symmetries in hadron scatterings
University of Chinese Academy of Sciences（中国科学院大学）；Tokyo Metropolitan University（东京都立大学）；Chinese Academy of Sciences（中国科学院）；Argonne National Laboratory（阿贡国家实验室）；Northwestern University（西北大学）
There are many examples where geometry and gravity are concepts that emerge from a theory of quantum mechanics without gravity. This suggests thinking of gravity as an exotic phase of matter. Quantifying this phase in the Landau paradigm requires some sort of symmetry principle or order parameter that captures its appearance. In this essay we propose higher-form symmetries as a symmetry principle underlying emergent spacetime. We explore higher-form symmetries in gauge-gravity duality and explain how their breaking describes features of a gravitational theory. Such symmetries imply the existen…
Rydberg atoms in optical tweezer arrays provide a playground for nonequilibrium quantum many-body physics. The PXP model describes the dynamics of such systems in the strongly interacting Rydberg blockade regime and notably exhibits weakly nonergodic dynamics due to quantum many-body scars. Here, we study the PXP model in a strong staggered external field, which has been proposed to manifest quasiparticle confinement in light of a mapping to a lattice gauge theory. We characterize this confining regime using both numerical exact diagonalization and perturbation theory around the strong-field l…
There are strong reasons to believe that global symmetries of quantum theories cannot be exact in the presence of gravity. While this has been argued at the qualitative level, establishing a quantitative statement is more challenging. In this work we take new steps towards quantifying symmetry violation in EFTs with gravity. First, we evaluate global charge violation by microscopic black holes present in a thermal system, which represents an irreducible, universal effect at finite temperature. Second, based on general QFT considerations, we propose that local symmetry-violating processes shoul…
It might be expected that only global symmetries are fundamental symmetries of Nature, whereas local symmetries and associated massless gauge fields could solely emerge due to spontaneous breaking of underlying spacetime symmetries involved, such as relativistic invariance and supersymmetry. This breaking, taken in the form of the nonlinear sigma-model type pattern for vector fields or superfields, puts essential restrictions on geometrical degrees of freedom of a physical field system that makes it to adjust itself in such a way that its global internal symmetry G turns into the local symmetr…
The canonical tensor model (CTM) is a tensor model proposing a classically and quantum mechanically consistent model of gravity, formulated as a first-class constraint system with structural similarities to the ADM formalism of general relativity. A recent study on the formal continuum limit of the classical CTM has shown that it produces a general relativistic system. This formal continuum limit assumes the emergence of a continuous space, but ultimately continuous spaces should be obtained as preferred configurations of the quantum CTM. In this paper we study the symmetry properties of a wav…
We argue that extra dimensions with a properly chosen compactification scheme could be a natural source for emergent gauge symmetries. Actually, some proposed vector field potential terms or polynomial vector field constraints introduced in five-dimensional Abelian and non-Abelian gauge theory is shown to smoothly lead to spontaneous violation of an underlying 5D spacetime symmetry and generate pseudo-Goldstone vector modes as conventional 4D gauge boson candidates. As a special signature, there appear, apart from conventional gauge couplings, some properly suppressed direct multi-photon (mult…
University of Tokyo（东京大学）；Kavli Institute for Physics and Mathematics of the Universe (Kavli IPMU), UTIAS, University of Tokyo（东京大学宇宙线研究所（Kavli IPMU））；Trans-Scale Quantum Science Institute, University of Tokyo（东京大学跨尺度量子科学研究所）；Center for Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS), RIKEN（理化学研究所交叉理论数学科学中心（iTHEMS））
The quantum phase diagram and critical behavior of two-dimensional Dirac fermions coupled to two compatible order-parameter fields with $O(N_1)\oplus O(N_2)$ symmetry is investigated. Recent numerical studies of such systems have reported evidence for non-Landau-Ginzburg-Wilson transitions and emergent $O(N_1+N_2)$ symmetry between the two ordered states, which has been interpreted within a scenario of deconfined quantum criticality in (2+1)-dimensional Dirac materials. Here, we provide two theoretical approaches to refine the phase diagrams of such systems. In the immediate vicinity of the mu…
University of British Columbia（不列颠哥伦比亚大学）；Institut des Hautes Études Scientifiques（高等科学研究所）；Walter Burke Institute for Theoretical Physics, Caltech（加州理工学院沃尔特·伯克理论物理研究所）
We investigate the stationary-state fluctuations of a growing one-dimensional interface described by the KPZ dynamics with a noise featuring smooth spatial correlations of characteristic range $ξ$. We employ Non-perturbative Functional Renormalization Group methods in order to resolve the properties of the system at all scales. We show that the physics of the standard (uncorrelated) KPZ equation emerges on large scales independently of $ξ$. Moreover, the Renormalization Group flow is followed from the initial condition to the fixed point, that is from the microscopic dynamics to the large-dist…
The structure of half-BPS representations of psu$(2,2|4)$ leads to the definition of a super-polynomial ring $\mathcal{R}(8|8)$ which admits a realisation of psu$(2,2|4)$ in terms of differential operators on the super-ring. The character of the half-BPS fundamental field representation encodes the resolution of the representation in terms of an exact sequence of modules of $\mathcal{R}(8|8)$. The half-BPS representation is realized by quotienting the super-ring by a quadratic ideal, equivalently by setting to zero certain quadratic polynomials in the generators of the super-ring. This descrip…
We consider operator growth for generic large-N gauge theories at finite temperature. Our analysis is performed in terms of Fourier modes, which do not mix with other operators as time evolves, and whose correlation functions are determined by their two-point functions alone, at leading order in the large-N limit. The algebra of these modes allows for a simple analysis of the operators with whom the initial operator mixes over time, and guarantees the existence of boundary CFT operators closing the bulk Poincaré algebra, describing the experience of infalling observers. We discuss several exis…
The deconfined quantum critical point (QCP), separating the Néel and valence bond solid phases in a 2D antiferromagnet, was proposed as an example of $2+1$D criticality fundamentally different from standard Landau-Ginzburg-Wilson-Fisher {criticality}. In this work we present multiple equivalent descriptions of deconfined QCPs, and use these to address the possibility of enlarged emergent symmetries in the low energy limit. The easy-plane deconfined QCP, besides its previously discussed self-duality, is dual to $N_f = 2$ fermionic quantum electrodynamics (QED), which has its own self-duality an…
The algebraic approach to quantum physics emphasizes the role played by the structure of the algebra of observables and its relation to the space of states. An important feature of this point of view is that subsystems can be described by subalgebras, with partial trace being replaced by the more general notion of restriction to a subalgebra. This, in turn, has recently led to applications to the study of entanglement in systems of identical particles. In the course of those investigations on entanglement and particle identity, an emergent gauge symmetry has been found by Balachandran, de Quei…
I discuss gauge and global symmetries in particle physics, condensed matter physics, and quantum gravity. In a modern understanding, global symmetries are approximate and gauge symmetries may be emergent. (Based on a lecture at the April, 2016 meeting of the American Physical Society in Salt Lake City, Utah.)
We address emergent higher-form symmetry in Higgs phases with superfluidity. The emergent symmetry appears if a matter field is invariant under a transformation of a common subgroup of gauge and global $\mathrm{U}(1)$ symmetries. We explicitly construct the symmetry generator that is topological and gauge invariant in a low-energy effective theory. Such emergent symmetry is helpful to distinguish the Higgs and other phases with superfluidity, such as phases of QCD at finite density. We also discuss the possibility of phase transition between these phases.
We classify and characterize three dimensional $U(1)$ quantum spin liquids (deconfined $U(1)$ gauge theories) with global symmetries. These spin liquids have an emergent gapless photon and emergent electric/magnetic excitations (which we assume are gapped). We first discuss in great detail the case with time reversal and $SO(3)$ spin rotational symmetries. We find there are 15 distinct such quantum spin liquids based on the properties of bulk excitations. We show how to interpret them as gauged symmetry-protected topological states (SPTs). Some of these states possess fractional response to an…
We consider a model of Dirac fermions in $2+1$ dimensions with dynamically generated, anticommuting SO(3) Néel and Z$_2$ Kekulé mass terms that permits sign-free quantum Monte Carlo simulations. The phase diagram is obtained from finite-size scaling and includes a direct and continuous transition between the Néel and Kekulé phases. The fermions remain gapped across the transition, and our data support an emergent SO(4) symmetry unifying the two order parameters. While the bare symmetries of our model do not allow for spinon-carrying Z$_3$ vortices in the Kekulé mass, the emergent SO(4) invaria…
We investigate a class of relativistic fermion theories in 2<d<4 space-time dimensions with continuous chiral U(Nf)xU(Nf) symmetry. This includes a number of well-studied models, e.g., of Gross-Neveu and Thirring type, in a unified framework. Within the limit of pointlike interactions, the RG flow of couplings reveals a network of interacting fixed points, each of which defines a universality class. A subset of fixed points are "critical fixed points" with one RG relevant direction being candidates for critical points of second-order phase transitions. Identifying invariant hyperplanes of the …
Outer automorphisms of symmetries ("symmetries of symmetries") in relativistic quantum field theories are studied, including charge conjugation (C), space-reflection (P) , and time-reversal (T) transformations. The group theory of outer automorphisms is pedagogically introduced and it is shown that CP transformations are special outer automorphisms of the global, local, and space-time symmetries of a theory. It is shown that certain discrete groups allow for a group theoretical prediction of parameter independent CP violating complex phases with fixed geometrical values. The remainder of this …
Recently, the steady states of non-unitary free fermion dynamics are found to exhibit novel critical phases with power-law squared correlations and a logarithmic subsystem entanglement. In this work, we theoretically understand the underlying physics by constructing solvable static/Brownian quadratic Sachdev-Ye-Kitaev chains with non-Hermitian dynamics. We find the action of the replicated system generally shows (one or infinite copies of) ${O(2)\times O(2)}$ symmetries, which is broken to ${O(2)}$ by the saddle-point solution. This leads to an emergent conformal field theory of the Goldstone …
One path to high-temperature cuprate superconductors is doping a Mott insulator. In this paper, we study this system from the view point of higher-form symmetries. On the introduction of slave bosons, the $t-J$ model at a finite hole doping can be written in the form of $U(1)$ gauge theories. After a duality transformation, they can be written as a generalized $BF$ theory, in which the higher-form symmetries are more manifest. We identify the emergent continuous and discrete higher-form symmetries in both $s-wave$ and $d-wave$ superconducting phases, expected to be realized from a doped Mott i…
