Topologically Protected Duality on The Boundary of Maxwell-BF Theory

Blasi, Alberto; Maggiore, Nicola

doi:10.3390/sym11070921

Cited by 8 publications

(4 citation statements)

References 38 publications

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“…In the flat limit, the parameters α ij , β ij and ζ ij in S bd are constant [40]. Finally, the total action, containing BF bulk, gauge fixing, external sources, and boundary terms, is…”

Section: The Actionmentioning

confidence: 99%

Topological BF Description of 2D Accelerated Chiral Edge Modes

2022

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In this paper, we consider the topological abelian BF theory with radial boundary on a generic 3D manifold, as we were motivated by the recently discovered accelerated edge modes on certain Hall systems. Our aim was to research if, where, and how the boundary keeps the memory of the details of the background metrics. We discovered that some features were topologically protected and did not depend on the bulk metric. The outcome was that these edge excitations were accelerated, as a direct consequence of the non-flat nature of the bulk spacetime. We found three possibilities for the motion of the edge quasiparticles: same directions, opposite directions, and a single-moving mode. However, requiring that the Hamiltonian of the 2D theory is bounded by below, the case of the edge modes moving in the same direction was ruled out. Systems involving parallel Hall currents (for instance, a fractional quantum Hall effect with ν=2/5) cannot be described by a BF theory with the boundary, independently from the geometry of the bulk spacetime, because of positive energy considerations. Thus, we were left with physical situations characterized by edge excitations moving with opposite velocities (for example, the fractional quantum Hall effect with ν=1−1/n, with the n positive integer, and the helical Luttinger liquids phenomena) or a single-moving mode (quantum anomalous Hall). A strong restriction was 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 correspond to topological insulators with accelerated edge modes.

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“…In the flat limit, the parameters α ij , β ij and ζ ij in S bd are constant [40]. Finally, the total action, containing BF bulk, gauge fixing, external sources, and boundary terms, is…”

Section: The Actionmentioning

confidence: 99%

Topological BF Description of 2D Accelerated Chiral Edge Modes

2022

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“…In particular, the CS coupling constant has been found to be tightly related to the filling factor of FQHE [15] and to the central charge of the Kaç-Moody (KM) algebras [16,17] formed by conserved currents on the edge of CS theory [18,19,20]. Similarly, another class of TFT, the BF models [21,22,23,24,25], which can be defined on any spacetime dimensions, have been found to describe the bulk theory of the Topological Insulators [26,27]. Hence, the introduction of a boundary in TFT is the only way to give local, physical and measurable observables to theories which otherwise show "only" formal interest [28,29,30], and major results have been achieved in condensed matter theory, mainly.…”

Section: Introductionmentioning

confidence: 99%

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

Bertolini,

Gambuti,

Maggiore

2021

Preprint

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The 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.

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“…This is the case, for instance, of 3D Maxwell-Chern-Simons theory, where the Maxwell term is completely transparent in case of double-sided boundary [35] and algebraically active in the single-sided case [36,37]. It is precisely the different role of the non-topological Maxwell term that motivated the study of non-TFT, or theories with non-topological terms, defined in half-spaces [38,39]. In fact, all the mentioned results obtained for quantum field theories with boundary concern TFT: 3D Chern-Simons and BF theories, the latter being defined on any spacetime dimensions [6,[40][41][42][43].…”

Section: Introductionmentioning

confidence: 99%

Holographic Projection of Electromagnetic Maxwell Theory

Bertolini

Maggiore

2020

Symmetry

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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.

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Topologically Protected Duality on The Boundary of Maxwell-BF Theory

Cited by 8 publications

References 38 publications

Topological BF Description of 2D Accelerated Chiral Edge Modes

Topological BF Description of 2D Accelerated Chiral Edge Modes

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

Holographic Projection of Electromagnetic Maxwell Theory

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