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A bstract Boundaries in gauge theory and gravity give rise to symmetries and charges at both finite and asymptotic distance. Due to their structural similarities, it is often held that soft modes are some kind of asymptotic limit of edge modes. Here, we show in Maxwell theory that there is an arguably more interesting relationship between the asymptotic symmetries and their charges, on one hand, and their finite-distance counterparts, on the other, without the need of a limit. Key to this observation is to embed the finite region in the global spacetime and identify edge modes as dynamical U(1)-reference frames for dressing subregion variables. Distinguishing intrinsic and extrinsic frames, according to whether they are built from field content in- or outside the region, we find that non-trivial corner symmetries arise only for extrinsic frames. Further, the asymptotic-to-finite relation requires asymptotically charged ones (like Wilson lines). Such frames, called soft edges , extend to asymptotia and, in fact, realize the corner charge algebra in multiple ways, for example, by “pulling in” the asymptotic one from infinity, or physically through the addition of asymptotic soft and hard radiation. Realizing an infinite-dimensional algebra requires a new set of soft boundary conditions , relying on the distinction between extrinsic and intrinsic data. We identify the subregion Goldstone mode as the relational observable between extrinsic and intrinsic frames and clarify the meaning of vacuum degeneracy. We also connect the asymptotic memory effect with a more operational quasi-local one. A main conclusion is that the relationship between asymptotia and finite distance is frame-dependent ; each choice of soft edge mode probes distinct cross-boundary data of the global theory.

A bstract It is believed that in SU( N ) Yang-Mills theory observables are N -branched functions of the topological θ angle. This is supposed to be due to the existence of a set of locally-stable candidate vacua, which compete for global stability as a function of θ . We study the number of θ vacua, their interpretation, and their stability properties using systematic semiclassical analysis in the context of adiabatic circle compactification on ℝ 3 × S 1 . We find that while observables are indeed N-branched functions of θ, there are only ≈ N/ 2 locally-stable candidate vacua for any given θ . We point out that the different θ vacua are distinguished by the expectation values of certain magnetic line operators that carry non-zero GNO charge but zero ’t Hooft charge. Finally, we show that in the regime of validity of our analysis YM theory has spinodal points as a function of θ , and gather evidence for the conjecture that these spinodal points are present even in the ℝ 4 limit.

A bstract We study SU( N ) Quantum Chromodynamics (QCD) in 3+1 dimensions with N f degenerate fundamental quarks with mass m and a θ -parameter. For generic m and θ the theory has a single gapped vacuum. However, as θ is varied through θ = π for large m there is a first order transition. For N f = 1 the first order transition line ends at a point with a massless η ′ particle (for all N ) and for N f > 1 the first order transition ends at m = 0, where, depending on the value of N f , the IR theory has free Nambu-Goldstone bosons, an interacting conformal field theory, or a free gauge theory. Even when the 4 d bulk is smooth, domain walls and interfaces can have interesting phase transitions separating different 3 d phases. These turn out to be the phases of the recently studied 3 d Chern-Simons matter theories, thus relating the dynamics of QCD 4 and QCD 3 , and, in particular, making contact with the recently discussed dualities in 2+1 dimensions. For example, when the massless 4 d theory has an SU( N f ) sigma model, the domain wall theory at low (nonzero) mass supports a 3 d massless ℂ ℙ N f − 1 nonlinear σ -model with a Wess-Zumino term, in agreement with the conjectured dynamics in 2+1 dimensions.

A bstract Fermion masses can be generated through four-fermion condensates when symmetries prevent fermion bilinear condensates from forming. This less explored mechanism of fermion mass generation is responsible for making four reduced staggered lattice fermions massive at strong couplings in a lattice model with a local four-fermion coupling. The model has a massless fermion phase at weak couplings and a massive fermion phase at strong couplings. In particular there is no spontaneous symmetry breaking of any lattice symmetries in both these phases. Recently it was discovered that in three space-time dimensions there is a direct second order phase transition between the two phases. Here we study the same model in four space-time dimensions and find results consistent with the existence of a narrow intermediate phase with fermion bilinear condensates, that separates the two asymptotic phases by continuous phase transitions.

A variety of models of inflation in the early Universe have been proposed and applied to describe successfully the origin of all possible structures in the Universe. On the other hand, inflation theory is still phenomenological and needs systematic physical foundations, including the relation to dark matter and dark energy. The essence of cosmic inflation would be a dynamical phase transition and the spontaneous symmetry breaking process, which are common in ordinary physics in the laboratory. At the beginning of the phase transition, the system is often in an adiabatic ground state and produces a squeezed state. This is widely interpreted as the generation of classical structures; however, it is not. The common notion of decoherence is not sufficient to describe the inflationary phase transition: a particular trajectory must be singled out in the dynamics. When an interaction turns on, dissipation or the energy flow/cascade is possible, and the c-number random field appears. The separation of these classical statistical fluctuations from the deterministic time evolution is indicated by the secular divergence or the infrared divergence of the system. We describe this phase transition based on the closed-time-path method and derive a quantum Langevin equation with classical noise, which sources the development of a coherent state. Introducing the effective action method to describe the evolution of the coherent state, we describe the order parameter that characterizes the phase transition and the associated spontaneous symmetry breaking. Since this phase transition process is common in physics, we discuss further applications of this formalism in other physical systems.

Abstract Multi-component dark matter scenarios are studied in the model with U(1) X dark gauge symmetry that is broken into its product subgroup Z 2 × Z 3 á la Krauss-Wilczek mechanism. In this setup, there exist two types of dark matter fields, X and Y, distinguished by different Z 2 × Z 3 charges. The real and imaginary parts of the Z 2-charged field, X R and X I , get different masses from the U(1) X symmetry breaking. The field Y, which is another dark matter candidate due to the unbroken Z 3 symmetry, belongs to the Strongly Interacting Massive Particle (SIMP)-type dark matter. Both X I and X R may contribute to Y’s 3 → 2 annihilation processes, opening a new class of SIMP models with a local dark gauge symmetry. Depending on the mass difference between X I and X R , we have either two-component or three-component dark matter scenarios. In particular two- or three-component SIMP scenarios can be realised not only for small mass difference between X and Y, but also for large mass hierarchy between them, which is a new and unique feature of the present model. We consider both theoretical and experimental constraints, and present four case studies of the multi-component dark matter scenarios.

A bstract We examine the structure of global conformal multiplets in 2D celestial CFT. For a 4D bulk theory containing massless particles of spin s = 0 1 2 1 3 2 2 we classify and construct all SL(2, ℂ ) primary descendants which are organized into ‘celestial diamonds’. This explicit construction is achieved using a wavefunction-based approach that allows us to map 4D scattering amplitudes to celestial CFT correlators of operators with SL(2, ℂ ) conformal dimension ∆ and spin J . Radiative conformal primary wavefunctions have J = ± s and give rise to conformally soft theorems for special values of ∆ ∈ 1 2 ℤ . They are located either at the top of celestial diamonds, where they descend to trivial null primaries, or at the left and right corners, where they descend both to and from generalized conformal primary wavefunctions which have | J | ≤ s . Celestial diamonds naturally incorporate degeneracies of opposite helicity particles via the 2D shadow transform relating radiative primaries and account for the global and asymptotic symmetries in gauge theory and gravity.

A bstract SU( N ) gauge theory is time reversal invariant at θ = 0 and θ = π . We show that at θ = π there is a discrete ’t Hooft anomaly involving time reversal and the center symmetry. This anomaly leads to constraints on the vacua of the theory. It follows that at θ = π the vacuum cannot be a trivial non-degenerate gapped state. (By contrast, the vacuum at θ = 0 is gapped, non-degenerate, and trivial.) Due to the anomaly, the theory admits nontrivial domain walls supporting lower-dimensional theories. Depending on the nature of the vacuum at θ = π , several phase diagrams are possible. Assuming area law for space-like loops, one arrives at an inequality involving the temperatures at which CP and the center symmetry are restored. We also analyze alternative scenarios for SU(2) gauge theory. The underlying symmetry at θ = π is the dihedral group of 8 elements. If deconfined loops are allowed, one can have two O (2)-symmetric fixed points. It may also be that the four-dimensional theory around θ = π is gapless, e.g. a Coulomb phase could match the underlying anomalies.

A bstract Poincaré invariance is a well-tested symmetry of nature and sits at the core of our description of relativistic particles and gravity. At the same time, in most systems Poincaré invariance is not a symmetry of the ground state and is hence broken spontaneously. This phenomenon is ubiquitous in cosmology where Lorentz boosts are spontaneously broken by the existence of a preferred reference frame in which the universe is homogeneous and isotropic. This motivates us to study scattering amplitudes without requiring invariance of the interactions under Lorentz boosts. In particular, using on-shell methods and assuming massless, relativistic and luminal particles of any spin, we show that the allowed interactions around Minkowski spacetime are severely constrained by unitarity and locality in the form of consistent factorization. The existence of an interacting massless spin-2 particle enforces (analytically continued) three-particle amplitudes to be Lorentz invariant, even those that do not involve a graviton, such as cubic scalar couplings. We conjecture this to be true for all n -particle amplitudes. Also, particles of spin S > 2 cannot self-interact nor can be minimally coupled to gravity, while particles of spin S > 1 cannot have electric charge. Given the growing evidence that free gravitons are well described by massless, luminal relativistic particles, our results imply that cubic graviton interactions in Minkowski must be those of general relativity up to a unique Lorentz-invariant higher-derivative correction of mass dimension 9. Finally, we point out that consistent factorization for massless particles is highly IR sensitive and therefore our powerful flat-space results do not straightforwardly apply to curved spacetime.

A bstract Some quantum field theories show, in a fundamental or an effective manner, an alternative between a loss of duality for algebras of operators corresponding to complementary regions, or a loss of additivity. In this latter case, the algebra contains some operator that is not generated locally, in the former, the entropies of complementary regions do not coincide. Typically, these features are related to the incompleteness of the operator content of the theory, or, in other words, to the existence of superselection sectors. We review some aspects of the mathematical literature on superselection sectors aiming attention to the physical picture and focusing on the consequences for entanglement entropy (EE). For purposes of clarity, the whole discussion is divided into two parts according to the superselection sectors classification: the present part I is devoted to superselection sectors arising from global symmetries, and the forthcoming part II will consider those arising from local symmetries. Under this perspective, here restricted to global symmetries, we study in detail different cases such as models with finite and Lie group symmetry as well as with spontaneous symmetry breaking or excited states. We illustrate the general results with simple examples. As an important application, we argue the features of holographic entanglement entropy correspond to a picture of an sub-theory with a large number of superselection sectors and suggest some ways in which this identification could be made more precise.