54 research outputs found
On the Emergent Dynamics of Fermions in Curved Spacetime
Relativistic spin-1/2 particles in curved spacetime are naturally described
by Dirac theory, which is a dynamical and Lorentz-invariant field theory. In
this work, we propose a non-dynamical fermion theory in 3+1 dimensions dubbed
spinor topological field theory, built in terms of a spinor field and a Cartan
connection related to de Sitter group. We show that our model gives rise to the
Dirac theory in curved spacetime when the local de Sitter gauge invariance of
the model breaks down to the Lorentz gauge invariance, providing also a
geometric origin to the fermion mass. Finally, we show that other gauge fields
and suitable four-fermion interactions can be included in a straightforward
way.Comment: 3 pages, published versio
From topological to topologically massive gravity through the gauge principle
It is well known that three-dimensional Einstein's gravity without matter is
topological, i.e. it does not have local propagating degrees of freedom. The
main result of this work is to show that dynamics in the gravitational sector
can be induced by employing the gauge principle on the matter sector. This is
described by a non-dynamical fermion model that supports a global gauge
symmetry. By gauging this symmetry, a vector-spinor field is added to the
original action to preserve the local gauge invariance. By integrating out this
spin-3/2 field, we obtain a gravitational Chern-Simons term that gives rise to
local propagating degrees of freedom in the gravitational sector. This is
defined, after the gauging, by topologically massive gravity.Comment: 5 pages, this essay has received an Honorable Mention from the
Gravity Research Foundation - 2019 Awards for Essays on Gravitatio
Tensor Berry connections and their topological invariants
The Berry connection plays a central role in our description of the geometric
phase and topological phenomena. In condensed matter, it describes the parallel
transport of Bloch states and acts as an effective "electromagnetic" vector
potential defined in momentum space. Inspired by developments in mathematical
physics, where higher-form (Kalb-Ramond) gauge fields were introduced, we
hereby explore the existence of "tensor Berry connections" in quantum matter.
Our approach consists in a general construction of effective gauge fields,
which we ultimately relate to the components of Bloch states. We apply this
formalism to various models of topological matter, and we investigate the
topological invariants that result from generalized Berry connections. For
instance, we introduce the 2D Zak phase of a tensor Berry connection, which we
then relate to the more conventional first Chern number; we also reinterpret
the winding number characterizing 3D topological insulators to a Dixmier-Douady
invariant, which is associated with the curvature of a tensor connection.
Besides, our approach identifies the Berry connection of tensor monopoles,
which are found in 4D Weyl-type systems [Palumbo and Goldman, Phys. Rev. Lett.
121, 170401 (2018)]. Our work sheds light on the emergence of gauge fields in
condensed-matter physics, with direct consequences on the search for novel
topological states in solid-state and quantum-engineered systems.Comment: 10 pages, 1 table. Published versio
Fermion-fermion duality in 3+1 dimensions
Dualities play a central role in both quantum field theories and condensed
matter systems. Recently, a web of dualities has been discovered in 2+1
dimensions. Here, we propose in particular a generalization of the Son's
fermion-fermion duality to 3+1 dimensions. We show that the action of charged
Dirac fermions coupled to an external electromagnetic field is dual to an
action of neutral fermions minimally coupled to an emergent vector gauge field.
This dual action contains also a further tensor (Kalb-Ramond) gauge field
coupled to the emergent and electromagnetic vector potentials. We firstly
demonstrate the duality in the massive case. We then show the duality in the
case of massless fermions starting from a lattice model and employing the
slave-rotor approach already used in the 2+1-dimensional duality [Burkov, Phys.
Rev. B 99, 035124 (2019)]. We finally apply this result to 3D Dirac semimetals
in the low-energy regime. Besides the implications in topological phases of
matter, our results shed light on the possible existence of a novel web of
dualities in 3+1-dimensional (non-supersymmetric) quantum field theories.Comment: 4 pages, accepted version on Annals of Physic
Noncommutative Geometry and Deformation Quantization in the Quantum Hall Fluids with Inhomogeneous Magnetic Fields
It is well known that noncommutative geometry naturally emerges in the
quantum Hall states due to the presence of strong and constant magnetic fields.
Here, we discuss the underlying noncommutative geometry of quantum Hall fluids
in which the magnetic fields are spatially inhomogenoeus. We analyze these
cases by employing symplectic geometry and Fedosov's deformation quantization,
which rely on symplectic connections and Fedosov star-product. Through this
formalism, we unveil some new features concerning the static limit of the
Haldane's unimodular metric and the Girvin-MacDonald-Platzman algebra of the
density operators, which plays a central role in the fractional quantum Hall
effect.Comment: 6 page
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