arXiv subjects

Nicola Maggiore

Publications and source records attributed to Nicola Maggiore.

At least 19 recordsLinked to original sources

arXiv2026

Edge physics and the Casimir interaction in Maxwell-Chern-Simons theory on a strip

We study how boundaries affect Maxwell-Chern-Simons theory, a three-dimensional gauge theory that combines ordinary electromagnetic propagation with a topological Chern-Simons term. On a strip, the two boundaries can support edge excitations while the single massive bulk mode mediates a Casimir interaction between them. We use Symanzik's local boundary-field-theory framework, deriving the boundary conditions from the most general quadratic local boundary action considered here rather than imposing them by hand. Requiring these conditions to act consistently on the unique physical bulk mode selects a continuous family of admissible boundaries, characterized by an impedance and an edge velocity. The associated conserved currents form two boundary current algebras with opposite levels, and for a symmetric strip the edge modes propagate in opposite directions. The bulk and residual edge sectors factorize, leaving a single physical scattering channel for the Casimir problem. We derive its reflection amplitude, identify a stable pole-free domain, and show that the force is attractive there. In the Maxwell limit the usual long-range one-channel Casimir interaction is recovered, whereas the topological mass produces exponential screening at large separation. Outside the pole-free domain, localized surface modes can appear and must be included separately. The analysis provides a unified description of edge dynamics, boundary conditions and vacuum forces in a topologically massive gauge theory.

hep-th↗

arXiv2026

Covariant Fracton Electrodynamics in Six Dimensions

We formulate a covariant version of Maxwell-like fracton electrodynamics in six dimensions using a symmetric tensor gauge field with scalar gauge symmetry $δA_{μν}=\partial_μ\partial_νΛ$. This provides a relativistic setting in which the characteristic fractonic restriction on mobility follows directly from gauge invariance and the allowed coupling to matter. We construct the stress--energy tensor and show that its trace has a universal dimension-dependent structure that becomes a total derivative in $d=6$. In the presence of sources, the theory enforces conservation of charge and dipole moment, capturing the immobility of isolated charges and the mobility of dipolar bound states. This structure can also be viewed as a higher-moment form of generalized global symmetry.

hep-th↗

arXiv2026

Edge modes in Chern-Simons theory on a strip

We investigate abelian Chern-Simons gauge theory on a strip geometry with two spatial boundaries. In the presence of boundaries, gauge invariance is broken by boundary conditions, leading to physical edge excitations. By deriving the most general local boundary conditions consistent with power counting in the sense of Symanzik, we show that the bulk equations of motion determine the boundary degrees of freedom through a broken gauge Ward identity, yielding boundary Kac-Moody current algebras with opposite central charges on the two edges. The corresponding two-dimensional boundary actions are of Tomonaga-Luttinger type and describe chiral bosons propagating in opposite directions along the two boundaries. A consistency condition, interpreted as a holographic-like bulk-boundary matching, relates the Chern-Simons coupling constant and the boundary parameters to the physical edge velocities. Within this framework, the equality and opposite sign of the two velocities in a symmetric setup follow directly from the boundary structure rather than from model-dependent assumptions about confining potentials, and the velocities are independent of the strip width. Our analysis provides a fully field-theoretic realization of bulk-boundary correspondence in Chern-Simons theory with two boundaries, with direct applications to edge physics in quantum Hall systems and related topological/hydrodynamic settings.

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arXiv2025

Covariant field theory of 3D massive fractons

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.

hep-th↗

arXiv2025

Quasi-topological mass generation for 3D linearized gravity

We 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 DoF, 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.

hep-th↗

arXiv2025

Fractons from covariant higher-rank 3D BF theory

In this paper we study the 3D gauge theory of two tensor gauge fields: $a_{μν}(x)$, which we take symmetric, and $B_{μν}(x)$, with no symmetry on its indices. The corresponding invariant action is a higher-rank BF-like model, which is first considered from a purely field theoretical point of view, and the propagators with their poles and the degrees of freedom are studied. Once matter is introduced, a fracton behaviour naturally emerges. We show that our theory can be mapped to the low-energy effective field theory describing the Rank-2 Toric Code (R2TC). This relation between our covariant BF-like theory and the R2TC is a higher-rank generalization of the equivalence between the ordinary 3D BF theory and the Kitaev's Toric Code. In the last part of the paper we analyze the case in which the field $B_{μν}(x)$ is a symmetric tensor. It turns out that the obtained BF-like action can be cast into the sum of two rank-2 Chern-Simons actions, thus generalizing the ordinary abelian case. Therefore, this represents a higher-rank generalization of the ordinary 3D BF theory, which well describes the low-energy physics of quantum spin Hall insulators in two spatial dimensions.

cond-mat.str-el↗

arXiv2025

Quasi-topological fractons: a 3D dipolar gauge theory

We consider the theory of a generic rank-2 tensor field in three spacetime dimensions, which involves a symmetric tensor field transforming under infinitesimal diffeomorphisms, and a vector field, whose gauge transformation depends on a local vector parameter. The gauge fixing shows a non-trivial structure, and some non-intuitive possibilities are listed. Despite the fact that the theory is not topological, the energy-momentum tensor vanishes on-shell, which justifies the quasi-topological appellation we give to this theory. We show that the theory has three degrees of freedom. Moreover we find an interesting physical interpretation, which consists in a generalized planar electromagnetism and in the emergence of two vector charges with restricted mobility. These are typical fractonic behaviours which can be related to the so called traceless scalar and vector charge theories.

hep-th↗

arXiv2024

Hall-like behaviour of higher rank Chern-Simons theory of fractons

Fracton phases of matter constitute an interesting point of contact between condensed matter and high-energy physics. The limited mobility property of fracton quasiparticles 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.

hep-th↗

arXiv2023

The theory of symmetric tensor field with boundary: Kac-Moody algebras in linearized gravity

In this paper we consider four dimensional (4D) linearized gravity (LG) with a planar boundary, where the most general boundary conditions are derived following Symanzik's approach. The boundary breaks diffeomorphism invariance and this results in a breaking of the corresponding Ward identity. From this, on the boundary we find two conserved currents which form an algebraic structure of the Kac-Moody type, with a central charge proportional to the action ``coupling''. Moreover, we identify the boundary degrees of freedom, which are two symmetric rank-2 tensor fields, and derive the symmetry transformations, which are diffeomorphisms. The corresponding most general 3D action is obtained and a contact with the higher dimensional theory is established by requiring that the 3D equations of motion coincide with the 4D boundary conditions. Through this kind of holographic procedure, we find two solutions~: LG for a single tensor field and LG for two tensor fields with a mixing term. Curiously, we find that the Symanzik's 4D boundary term which governs the whole procedure contains a mass term of the Fierz-Pauli type for the bulk graviton.

hep-th↗

arXiv2023

Covariant fracton gauge theory with boundary

In 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) Kaç-Moody algebra and the induced 3D theory is characterized by the conservation of the dipole moment.

hep-th↗

arXiv2023

Gauging fractons and linearized gravity

We consider the covariant gauge field theory of fractons, which describe a new type of quasiparticles exhibiting novel and nontrivial properties. In particular, we focus on the field theoretical peculiarities which characterize this theory, starting from the fact that, if we accept the paradigm that quantum field theories are defined by their symmetries, fractons unavoidably come together with linearized gravity. The standard Faddeev-Popov procedure to gauge fix the theory leads to a scalar gauge condition, which has two important drawbacks: it is frozen in the Landau gauge and linearized gravity cannot be obtained as a limit. In this paper we adopt a tensorially alternative gauge fixing, which avoids both problems. In particular, this allows to show that important physical features, like the counting of the degrees of freedom, do not depend on a particular gauge choice, as expected. Moreover, the resulting gauge fixed theory contains both fractons and linearized gravity as a limit, differently from the standard scalar choice.

hep-th↗

arXiv2022

Maxwell theory of fractons

We 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 $A_{μν}(x)$, we build a partially symmetric rank-3 tensor field strength $F_{μνρ}(x)$ which obeys a kind of Bianchi identity. The most general action invariant under the covariant ``fracton'' transformation $δ_{fract}A_{μν}(x)=\partial_μ\partial_νΛ(x)$ 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 $F_{μνρ}(x)$, and the fracton part of the invariant Lagrangian writes as $F^2(x)$, in analogy with 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 ($\partial^μF_{αβμ}(x)=0$), can be written in terms of the generalized electric and magnetic fields and yield two of the four Maxwell equations (generalized electric Gauss and Ampère laws), while the other two (generalized magnetic Gauss and Faraday laws) are consequences of the ``Bianchi identity'' for the tensor $F_{μνρ}(x)$, 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.

hep-th↗

arXiv2022

The theory of symmetric tensor field: from fractons to gravitons and back

We consider the theory of a symmetric tensor field in 4D, invariant under a subclass of infinitesimal diffeomorphism transformations, where the vector diff parameter is the 4-divergence of a scalar parameter. The resulting gauge symmetry characterizes the "fracton" quasiparticles and identifies a theory which depends on a dimensionless parameter, which cannot be reabsorbed by a redefinition of the tensor field, despite the fact that the theory is free of interactions. This kind of "electromagnetic gauge symmetry" is weaker that the original diffeomorphism invariance, in the sense that the most general action contains, but is not limited to, linearized gravity, and we show how it is possible to switch continuously from linearized gravity to a mixed phase where both gravitons and fractons are present, without changing the degrees of freedom of the theory. The gauge fixing procedure is particularly rich and rather peculiar, and leads to the computation of propagators which in the massive case we ask to be tachyonic-free, thus constraining the domain of the parameter of the theory. Finally, a closer contact to fractons is made by the introduction of a parameter related to the "rate of propagation". For a particular value of this parameter the theory does not propagate at all, and we guess that, for this reason, the resulting theory should be tightly related to the fracton excitations.

hep-th↗

arXiv2022

Topological BF description of 2D accelerated chiral edge modes

We consider the topological abelian BF theory with radial boundary on a generic 3D manifold. Our aim is to study if, where and how the boundary keeps memory of the details of the background metric. We find that some features are topologically protected and do not depend on the bulk metric. The 2D action holographically induced on the boundary depends on two scalar fields, and can be decoupled in two Luttinger actions describing two chiral bosons moving on the edge of the 3D bulk. The outcome is that these edge excitations are accelerated, as a direct consequence of the non-flat nature of the bulk spacetime. The chiral velocities of the edge modes, indeed, acquire a local dependence through the determinant of the induced metric on the boundary. We find three possibilities for the motion of the edge quasiparticles: same directions, opposite directions and a single-moving mode. But, requiring that the Hamiltonian of the 2D theory is bounded by below, the case of edge modes moving in the same direction is ruled out: systems involving parallel Hall currents (for instance Fractional Quantum Hall Effect with $ν=2/5$) cannot be described by a BF theory with boundary, independently from the geometry of the bulk spacetime, because of positive energy considerations. We are therefore left with physical situations characterized by edge excitations moving with opposite velocities (examples are FQHE with $ν=1-1/n$, with $n$ positive integer, and Helical Luttinger Liquids phenomena) or a single-moving mode (Quantum Anomalous Hall). A strong restriction is obtained by requiring Time Reversal symmetry, which uniquely identifies modes with equal and opposite velocities, and we know that this is the case of Topological Insulators. The novelty, with respect to the flat bulk background, is that the modes have local velocities, which corresponds to Topological Insulators with accelerated edge modes.

hep-th↗

arXiv2021

Notes from the bulk: metric dependence of the edge states of Chern-Simons theory

The abelian Chern-Simons theory is considered on a cylindrical spacetime $\mathbb{R} \times D$, 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.

hep-th↗

arXiv2021

Fierz-Pauli theory reloaded: from a theory of a symmetric tensor field to linearized massive gravity

Modifying gravity at large distances by means of a massive graviton may explain the observed acceleration of the Universe without Dark Energy. The standard paradigm for Massive Gravity is the Fierz-Pauli theory, which, nonetheless, displays well known flaws in its massless limit. The most serious one is represented by the vDVZ discontinuity, which consists in a disagreement between the massless limit of the Fierz-Pauli theory and General Relativity. Our approach is based on a field theoretical treatment of Massive Gravity: General Relativity, in the weak field approximation, is treated as a gauge theory of a symmetric rank-2 tensor field. This leads us to propose an alternative theory of linearized Massive Gravity, describing five degrees of freedom of the graviton, with a good massless limit, without vDVZ discontinuity, and depending on one mass parameter only, in agreement with the Fierz-Pauli theory.

gr-qc↗

arXiv2020

Holographic Projection of Electromagnetic Maxwell Theory

The 4D Maxwell theory with single-sided planar boundary is considered. As a consequence of the presence of the boundary, two broken Ward identities are recovered, which, on-shell, give rise to two conserved currents living on the edge. A Kaç-Moody algebra formed by a subset of the bulk fields is obtained with central charge proportional to the inverse of the Maxwell coupling constant, and the degrees of freedom of the boundary theory are identified as two vector fields, also suggesting that the 3D theory should be a gauge theory. Finally the holographic contact between bulk and boundary theory is reached in two inequivalent ways, both leading to a unique 3D action describing a new gauge theory of two coupled vector fields with a topological Chern-Simons term with massive coefficient. In order to check that the 3D projection of 4D Maxwell theory is well defined, we computed the energy-momentum tensor and the propagators. The role of discrete symmetries is briefly discussed.

hep-th↗

arXiv2020

A note on Harmonic Gauge(s) in Massive Gravity

We consider the harmonic gauge condition in linearized gravity, seen as a gauge theory for a symmetric tensor field. Once the harmonic gauge condition is implemented, as customary, according to the Faddeev-Popov procedure, the gauge fixed action still depends on one gauge parameter. Consequently, the harmonic gauge appears to be a class of conditions, rather than a particular one. This allows to give a physical motivation for the covariant harmonic gauge(s), which emerges when the gravitational perturbation is given a mass term. In fact, for a particular choice of harmonic gauge, we find a theory of linearized massive gravity displaying five degrees of freedom, as it should, and which is not affected by the vDVZ discontinuity, differently from what happens in the standard Fierz-Pauli theory.

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