1,720,963 research outputs found
Maxwell theory of fractons
No full textWe show that the main properties of the fracton quasiparticles can be derived from a generalized covariant Maxwell-like action. Starting from a rank-2 symmetric tensor field, we build a partially symmetric rank-3 tensor field strength which obeys a kind of Bianchi identity. The most general action invariant under the covariant “fracton” transformation consists of two independent terms: one describing linearized gravity (LG) and the other referable to fractons. The whole action can be written in terms of the generlized field strength, and the fracton part of the invariant Lagrangian writes exactly as Maxwell theory. The canonical momentum derived from the fracton Lagrangian coincides with the tensor electric field appearing in the fracton literature, and the field equations of motion, which have the same form as the covariant Maxwell equations, can be written in terms of the generalized electric and magnetic fields and yield two of the four Maxwell equations (generalized electric Gauss and Ampere laws), while the other two (generalized magnetic Gauss and Faraday laws) are consequences of the “Bianchi identity” for the stress tensor , as in Maxwell theory. In the covariant generalization of the fracton theory, the equations describing the fracton limited mobility, i.e., the charge and dipole conservation, are not external constraints, but rather consequences of the field equations of motion, hence of the invariant action and, ultimately, of the fracton covariant symmetry. Finally, we increase the known analogies between LG and fracton theory by noting that both satisfy the generalized Gauss constraint which underlies the limited mobility property, which one would not expect in LG
Notes from the bulk
No full textIn most cases Quantum Field Theories (QFTs) are considered without boundaries and have been successful in providing descriptions of fundamental interactions, including gravity and cosmology. This is because one is generally interested in bulk effects, where the boundary can be neglected. Nevertheless, boundaries do exist, and in some cases, their effects are self-evident and dominant. Important phenomena pertaining to condensed matter physics, like the Fractional Quantum Hall Effect and the behavior of Topological Insulators have been explained in terms of topological QFTs with boundaries. This is rather counterintuitive : topological QFTs, when considered without boundaries, have a vanishing Hamiltonian and no energy-momentum tensor. They might appear as the least physical theories one can imagine. Despite this, when a
boundary is introduced, an extremely rich physics emerges, which can be observed experimentally. The scope of this Ph.D thesis is to study the effects of the presence of a boundary from a Quantum Field Theoretical perspective, searching for new physics and explanations of observed phenomena. In particular, thanks to the formal QFT setting, the issue of the existence of local, accelerated, edge modes in Hall systems is analyzed and understood in terms of the bulk-to-boundary approach as related to a curved background in topological QFTs with boundary. Within this formalism the induced metric on the boundary can be associated to the ad hoc potential introduced in the phenomenological models in order to obtain such non-constant edge velocities. This also leads to the prediction of local modes for Topological Insulators, and Quantum Spin Hall systems in general. The paradigm for which only topological QFTs have a physical content on the boundary is broken, and also non-Topological Quantum Field Theories such as fracton models and Linearized Gravity are shown to have non-trivial boundary dynamics. Indeed due to the breaking of their defining symmetry both models have a current algebra of the Kac-Moody type on the boundary. In the case of fractons this algebra is in a generalized form, which also appears in some kinds of higher order Topological Insulators, a sign of a possible relation between these materials and edge states of fracton quasiparticles. Concerning the theory of Linearized Gravity, instead, the algebra is a standard Kac-Moody one, whose presence was suspected, but never proved before. Physical results on the boundary range between condensed matter, elasticity and (massive) gravity models. A collateral result, which enrich this Thesis, is the building of a new covariant QFT for fractons with a peculiar gauge structure. This new model better highlight the properties of these quasiparticles
Notes from the bulk: Metric dependence of the edge states of Chern-Simons theory
Full text linkThe Abelian Chern-Simons theory is considered on a cylindrical spacetime R×D, in a not necessarily flat Lorentzian background. As in the flat bulk case with planar boundary, we find that also on the radial boundary of a curved background a Kaç-Moody algebra exists, with the same central charge as in the flat case, which henceforth depends neither on the bulk metric nor on the geometry of the boundary. The holographically induced theory on the 2D boundary is topologically protected, in the sense that it describes a Luttinger liquid, no matter which the bulk metric is. The main result of this paper is that a remnant of the 3D bulk theory resides in the chiral velocity of the edge modes, which is not a constant like in the flat bulk case, but it is local, depending on the determinant of the induced metric on the boundary. This result may provide a theoretical framework for the recently observed accelerated chiral bosons on the edge of some Hall systems
Quasitopological mass generation for 3D linearized gravity
No full textWe present a new mass generation mechanism for linearized gravity in three spacetime dimensions, which consists of a lower-dimensional Chern-Simons-like term added to the invariant action. The propagators of the gauge-fixed massive action show a massive pole and a good massless limit. Moreover, we show that, as the topological massive gravity model of Deser, Jackiw, and Templeton, this theory displays one propagating massive degree of freedom, which can be traced back to the transverse part of the spatial Ricci tensor. Finally, the action of this linearized massive gravity is characterized by an algebraic structure formed by a set of Ward operators, which uniquely determine the theory
Covariant fracton gauge theory with boundary
Full text linkIn this paper we study the consequences of the introduction of a flat
boundary on a 4D covariant rank-2 gauge theory described by a linear
combination of linearized gravity and covariant fracton theory. We show that
this theory gives rise to a Maxwell-Chern-Simons-like theory of two rank-2
traceless symmetric tensor fields. This induced 3D theory can be physically
traced back to the traceless scalar charge theory of fractons, where the
Chern-Simons-like term plays the role of a matter contribution. By further
imposing time reversal invariance on the boundary, the Chern-Simons-like term
disappears. Importantly, on the boundary of our 4D gauge theory we find a
generalized U(1) Ka\c{c}-Moody algebra and the induced 3D theory is
characterized by the conservation of the dipole moment.Comment: 37 pages, to appear in Physical Review
Covariant field theory of 3D massive fractons
No full textAbstract We construct a covariant and gauge-invariant theory describing massive fractons in three spacetime dimensions, based on a symmetric rank-2 tensor field. The model includes a Chern–Simons-like term that plays a dual role: it generates a topological mass for the tensor gauge field and simultaneously acts as a source of intrinsic fractonic matter. This dual mechanism is novel and leads to a propagating fractonic degree of freedom described by a massive Klein–Gordon equation. The theory propagates two degrees of freedom – one massive, one massless – whose number is preserved in the massless limit, in analogy with the Maxwell–Chern–Simons mechanism of Deser–Jackiw–Templeton. We analyze the resulting equations of motion and show that the intrinsic fractonic matter satisfies Gauss- and Ampère-like laws, with conserved dipole and trace of the quadrupole moment. Upon coupling to external matter, a second fractonic sector emerges, leading to a coexistence of intrinsic and extrinsic subsystems with different mobility and conservation properties. Our model provides a unified framework for describing massive fractons with internal structure, and offers a covariant setting for exploring their interactions and extensions
Hall-like behaviour of higher rank Chern-Simons theory of fractons
Full text linkAbstract Fracton phases of matter constitute an interesting point of contact between condensed matter and high-energy physics. The limited mobility property of fracton quasi-particles finds applications in many different contexts, including quantum information, spin liquids, elasticity, hydrodynamics, gravity and holography. In this paper we adopt a field theoretical approach to investigate the three dimensional action of a rank-2 symmetric tensor field invariant under the covariant fracton symmetry. The theory appears as a non-topological higher rank generalization of the ordinary Chern-Simons model, depending only on the traceless part of the tensor gauge field. After defining a field strength, a rank-2 traceless “electric” field and a “magnetic” vector field are identified, in analogy with the standard Chern-Simons ones. Once matter is introduced, a Hall-like behaviour with fractonic features emerges. In particular, our model shows a Hall-like dipole current, together with a vectorial “flux-attachment” relation for dipoles. This gives a possible starting point for a fracton-vortex duality. A gauge-fixing term is then introduced, from which propagators are computed and the counting of the degrees of freedom is performed. Finally, the energy-momentum tensor is shown to be conserved and the integrated energy density is proved to be zero, which reminds the topological nature of the standard Chern-Simons model
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
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