Non-topological Defects Research Articles

Anomaly of subsystem symmetries in exotic and foliated BF theories

We study the mixed ’t Hooft anomaly of the subsystem symmetries in the exotic BF theory and the foliated BF theory in 2+1 dimensions, both of which are fractonic quantum field theories describing the equivalent physics. In the anomaly inflow mechanism, the ’t Hooft anomaly of the subsystem symmetries can be canceled by combining a subsystem symmetry-protected topological (SSPT) phase in one dimension higher. In this work, we construct the exotic and foliated BF theories with background gauge fields, and the exotic and foliated forms of the SSPT phases using the foliated-exotic duality. In the foliated form, we see that the non-topological defect that describes a fracton can be viewed as a symmetry-like operator. We also newly construct the foliated and exotic SSPT phases with different foliation structures via the foliated-exotic duality. We can show that the SSPT phases with different foliation structures cancel the same anomaly. This may provide a clue to the characterization of the ’t Hooft anomaly of subsystem symmetries.

Entanglement asymmetry in CFT and its relation to non-topological defects

The entanglement asymmetry is an information based observable that quantifies the degree of symmetry breaking in a region of an extended quantum system. We investigate this measure in the ground state of one dimensional critical systems described by a CFT. Employing the correspondence between global symmetries and defects, the analysis of the entanglement asymmetry can be formulated in terms of partition functions on Riemann surfaces with multiple non-topological defect lines inserted at their branch cuts. For large subsystems, these partition functions are determined by the scaling dimension of the defects. This leads to our first main observation: at criticality, the entanglement asymmetry acquires a subleading contribution scaling as log ℓ/ℓ for large subsystem length ℓ. Then, as an illustrative example, we consider the XY spin chain, which has a critical line described by the massless Majorana fermion theory and explicitly breaks the U(1) symmetry associated with rotations about the z-axis. In this situation the corresponding defect is marginal. Leveraging conformal invariance, we relate the scaling dimension of these defects to the ground state energy of the massless Majorana fermion on a circle with equally-spaced point defects. We exploit this mapping to derive our second main result: the exact expression for the scaling dimension associated with n defects of arbitrary strengths. Our result generalizes a known formula for the n = 1 case derived in several previous works. We then use this exact scaling dimension to derive our third main result: the exact prefactor of the log ℓ/ℓ term in the asymmetry of the critical XY chain.

Anomalies of generalized symmetries from solitonic defects

We propose the general idea that ’t Hooft anomalies of generalized global symmetries can be understood in terms of the properties of solitonic defects, which generically are non-topological defects. The defining property of such defects is that they act as sources for background fields of generalized symmetries. ’t Hooft anomalies arise when solitonic defects are charged under these generalized symmetries. We illustrate this idea for several kinds of anomalies in various spacetime dimensions. A systematic exploration is performed in 3d for 0-form, 1-form, and 2-group symmetries, whose ’t Hooft anomalies are related to two special types of solitonic defects, namely vortex line defects and monopole operators. This analysis is supplemented with detailed computations of such anomalies in a large class of 3d gauge theories. Central to this computation is the determination of the gauge and 0-form charges of a variety of monopole operators: these involve standard gauge monopole operators, but also fractional gauge monopole operators, as well as monopole operators for 0-form symmetries. The charges of these monopole operators mainly receive contributions from Chern-Simons terms and fermions in the matter content. Along the way, we interpret the vanishing of the global gauge and ABJ anomalies, which are anomalies not captured by local anomaly polynomials, as the requirement that gauge monopole operators and mixed monopole operators for 0-form and gauge symmetries have non-fractional integer charges.

Exact instantons via worldline deformations

The imaginary part of the one loop effective action in external backgrounds can be efficiently computed using worldline instantons which are closed periodic paths in spacetime. Exact solutions for nonstatic backgrounds are only known in certain cases. In this paper, we propose a novel technique allowing the construction of further exactly solvable models. In order to do so, we introduce a deformation function which maps the worldline instantons for a given model to the closed periodic stationary paths of a new model. Executing this procedure iteratively results in a chain of infinitely many solvable models. Similar ideas were applied to topological and nontopological defects in quantum field theory. We explicitly discuss the tunneling exponential in the Schwinger pair creation rate and illustrate the validity of the proposed technique for well-known cases.

Snaking without subcriticality: grain boundaries as non-topological defects

AbstractNon-topological defects in spatial patterns such as grain boundaries in crystalline materials arise from local variations of the pattern properties such as amplitude, wavelength and orientation. Such non-topological defects may be treated as spatially localized structures, i.e. as fronts connecting distinct periodic states. Using the two-dimensional quadratic-cubic Swift–Hohenberg equation, we obtain fully nonlinear equilibria containing grain boundaries that separate a patch of hexagons with one orientation (the grain) from an identical hexagonal state with a different orientation (the background). These grain boundaries take the form of closed curves with multiple penta-hepta defects that arise from local orientation mismatches between the two competing hexagonal structures. Multiple isolas occurring robustly over a wide range of parameters are obtained even in the absence of a unique Maxwell point, underlining the importance of retaining pinning when analysing patterns with defects, an effect omitted from the commonly used amplitude-phase description. Similar results are obtained for quasiperiodic structures in a two-scale phase-field model.

Inflation inside Non-Topological Defects and Scalar Black Holes

In this paper, we demonstrate that a phenomenon described as topological inflation, during which inflation occurs inside the core of topological defects, has a non–topological counterpart. This appears in a simple set-up containing Einstein gravity coupled minimally to an electromagnetic field as well as a self-interacting, complex valued scalar field. The U(1) symmetry of the model is unbroken and leads to the existence of globally regular solutions, so-called boson stars, that develop a horizon for sufficiently strong gravitational coupling. We also find that the same phenomenon exists for black holes with scalar hair.

Cosmological evolution of semilocal string networks.

Semilocal strings-a particular limit of electroweak strings-are an interesting example of a stable non-topological defect whose properties resemble those of their topological cousins, the Abrikosov-Nielsen-Olesen vortices. There is, however, one important difference: a network of semilocal strings will contain segments. These are 'dumbbells' whose ends behave almost like global monopoles that are strongly attracted to one another. While closed loops of string will eventually shrink and disappear, the segments can either shrink or grow, and a cosmological network of semilocal strings will reach a scaling regime. We discuss attempts to find a 'thermodynamic' description of the cosmological evolution and scaling of a network of semilocal strings, by analogy with well-known descriptions for cosmic strings and for monopoles. We propose a model for the time evolution of an overall length scale and typical velocity for the network as well as for its segments, and some supporting (preliminary) numerical evidence. This article is part of a discussion meeting issue 'Topological avatars of new physics'.

Entanglement entropy in integrable field theories with line defects II. Non-topological defect

This is the second part of two papers where we study the effect of integrable line defects on bipartite entanglement entropy in integrable field theories. In this paper, we consider non-topological line defects in Ising field theory. We derive an infinite series expression for the entanglement entropy and show that both the UV and IR limits of the bulk entanglement entropy are modified by the line defect. In the UV limit, we give an infinite series expression for the coefficient in front of the logarithmic divergence and the exact defect g-function. By tuning the defect to be purely transmissive and reflective, we recover correctly the entanglement entropy of the bulk and with integrable boundary respectively.

Entanglement entropy in integrable field theories with line defects. Part I. Topological defect

In this paper and a companion one [1], we study the effect of integrable line defects on entanglement entropy in massive integrable field theories in 1+1 dimensions. The current paper focuses on topological defects that are purely transmissive. Using the form factor bootstrap method, we show that topological defects do not affect the the entanglement entropy in the UV limit and modify slightly the leading exponential correction in the IR. This conclusion holds for both unitary and non-unitary field theories. In contrast, non-topological defects affect the entanglement entropy more significantly both in UV and IR limit and will be studied in the companion paper.

Monopoles on strings

In cosmological scenarios based on grand unification, string theory or braneworlds, many kinds of topological or non-topological defects, including monopoles and cosmic strings, are predicted to be formed in the early Universe. Here we review specifically the physics of composite objects involving monopoles tied to strings. There is a wide variety of these, including for example ‘dumbbells’ and ‘necklaces’, depending on how many strings attach to each monopole and on the extent to which the various fluxes are confined to the strings. We also briefly survey the prospects for observing such structures, the existing observational limits, and potential evidence for a cosmological role.

Topological origin of quantum mechanical vacuum transitions and tunneling

The quantum transition between shifted zero-mode wave functions is shown to be induced by the systematic deformation of topological and non-topological defects that support the one-dimensional double-well (DW) potential tunneling dynamics. The topological profile of the zero-mode ground state, [Formula: see text], and the first excited state, [Formula: see text], of DW potentials are obtained through the analytical technique of topological defect deformation. Deformed defects create two inequivalent topological scenarios connected by a symmetry breaking that support the quantum conversion of a zero-mode stable vacuum into an unstable tachyonic quantum state. Our theoretical findings reveal the topological origin of two-level models where a nonstationary quantum state of unitary evolution, [Formula: see text], that exhibits a stable tunneling dynamics, is converted into a quantum superposition involving a self-vanishing tachyonic mode, [Formula: see text], that parametrizes a tunneling coherent destruction. The non-classical nature of the symmetry breaking dynamics is recreated in terms of the single particle quantum mechanics of one-dimensional DW potentials.

The local B-polarization of the CMB: A very sensitive probe of cosmic defects

We present a new and especially powerful signature of cosmic strings and other topological or non-topological defects in the polarization of the cosmic microwave background (CMB). We show that even if defects contribute 1% or less in the CMB temperature anisotropy spectrum, their signature in the local B˜-polarization correlation function at angular scales of tens of arc-minutes is much larger than that due to gravitational waves from inflation, even if the latter contribute with a ratio as big as r≃0.1 to the temperature anisotropies. We show that when going from non-local to local B˜-polarization, the ratio of the defect signal-to-noise with respect to the inflationary value increases by about an order of magnitude. Proposed B-polarization experiments, with a good sensitivity on arc-minute scales, may either detect a contribution from topological defects produced after inflation or place stringent limits on them. Already Planck should be able to improve present constraints on defect models by about an order of magnitude, to the level of ϵ=Gv2<10−7. A future full-sky experiment like CMBpol, with polarization sensitivities of the order of 1 μK arcmin, will be able to constrain the defect parameter ϵ to less than a few×10−9, depending on the defect model.

A Simple Model for Non-Topological Defects in Sheared Nematic Polymer Monodomains

Nematic fluids have a propensity for orientational defects. In Leslie-Ericksen theory for small molecule liquid crystals, defects are topological in nature and easily visible in textural snapshots. However, kinetic and mesoscopic theories of nematic polymers possess a richer class of defects, including non-topological defects in which the second moment tensor of the orientational probability distribution fails to uniquely define a major director. These defects include the isotropic phase, where the major director lies anywhere on the unit sphere, and so-called oblate defect phases where the major director lies on a circle in the plane normal to a well-defined minor axis. These isotropic and oblate defect phases are independent of the physical space dimension, and while they have appeared in dynamics of heterogeneous attractors [5, 12, 13], a simple monodomain model of defect phases has not previously been developed. Here we present such a model by restricting to the in-plane monodomain response to an imposed shear flow. The orientational dynamics are described by a three-dimensional dynamical system on a compact domain. We show that the set of isotropic and oblate defect phases separates this compact orientational space into two sets of well-defined orientational distributions, one parallel and another orthogonal to the vorticity axis. We identify orbits that pass through the oblate defect set, and how often they do so. Finally, we observe intriguing behavior at the tumbling-wagging bifurcation where limit cycles pass infinitely often through the oblate defect set. 2000 Mathematics Subject Classification. 76A15, 82D60.

Cosmic microwave anisotropies from BPS semilocal strings

We present the first ever calculation of cosmic microwave background (CMB) anisotropypower spectra from semilocal cosmic strings, obtained via simulations of a classical fieldtheory. Semilocal strings are a type of non-topological defect arising in some models ofinflation motivated by fundamental physics, and are thought to relax the constraints on thesymmetry breaking scale as compared to models with (topological) cosmic strings. Wederive constraints on the model parameters, including the string tension parameterμ,from fits to cosmological data, and find that in this regard Bogomol’nyi–Prasad–Sommerfield (BPS)semilocal strings resemble global textures more than topological strings. The observedmicrowave anisotropy at is reproduced if Gμ = 5.3 × 10−6 (G is Newton’s constant). However as with other defects the spectral shape does not matchobservations, and in models with inflationary perturbations plus semilocal strings the95% confidence levelupper bound is Gμ<2.0 × 10−6 when CMB, Hubble key project and big bang nucleosynthesis data are used(cf Gμ<0.9 × 10−6 for cosmic strings). We additionally carry out a Bayesian model comparison of severalmodels with and without defects, showing that models with defects are neither conclusivelyfavoured nor disfavoured at present.

Kink-antikink, trapping bags and five-dimensional Gauss-Bonnet gravity

Five-dimensional Gauss-Bonnet gravity, with one warped extra-dimension, allows classes of solutions where two scalar fields combine either in a kink-antikink system or in a trapping-bag configuration. While the kink-antikink system can be interpreted as a pair of gravitating domain walls with opposite topological charges, the trapping-bag solution consists of a domain wall supplemented by a nontopological defect. In both classes of solutions, for large absolute values of the bulk coordinate (i.e. far from the core of the defects), the geometry is given by five-dimensional anti--de Sitter space.

Particle Emission from Dark Matter

When some kinds of symmetry breaking occur at the cosmological phase transition, the production of topological and/or non-topological defects can be expected. Here we consider the interaction of the defects within which the condensation of various fields may be realized at the core with dark matter particles, for example, axions or neutralinos. The astrophysical limits on the particle physics model are discussed.

Particle Emission from the Interaction of Defects with Dark Matter

If some kinds of symmetry breaking occur at the cosmological phase transition, the production of topological and/or non-topological defects can be expected. Within the core of such defects, symmetric states, that is, the high energy states where the expectation value of the scalar field equals zero remains even below the critical temperature. Here we consider the interaction of the defects in which the condensation of various fields may be realized with any kind of surrounding dark matter particles.

Deformed defects

We introduce a method to obtain deformed defects starting from a given scalar field theory which possesses defect solutions. The procedure allows the construction of infinitely many new theories that support defect solutions, analytically expressed in terms of the defects of the original theory. The method is general, valid for both topological and non-topological defects, and we show how it extends to quantum mechanics, and how it works when the scalar field couples to fermions. We illustrate the general procedure with several examples, which support kink-like or lump-like defects.

The evolution and persistence of dumbbells

We use large-scale numerical simulations to study the formation and evolution of non-topological defects in a generalized electroweak phase transition described by the Glashow-Salam-Weinberg model without fermions. Such defects include dumbbells, comprising a pair of monopoles joined by a segment of electroweak string. These exhibit complex dynamics, with some shrinking under the string tension and others growing due to the monopole-antimonopole attractions between near neighbours. We estimate the range of parameters where the network of dumbbells persists, and show that this region is narrower than the region within which infinite straight electroweak strings are perturbatively stable.

On the formation of non-topological string networks

We review recent simulations of the formation of a particular class of non-topological defects known as semilocal strings during a phase transition. Semilocal strings have properties that are intermediate between topological cosmic strings and stable electroweak strings, and therefore the observation that they could form in substantial quantities during a cosmological phase transition has implications for structure formation, baryogenesis, etc. At the same time, and from a purely theoretical point of view, they provide a very good testing ground for investigating the role of gauge fields in defect formation.