17,929 research outputs found
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
Tensor models and embedded Riemann surfaces
Tensor models and, more generally, group field theories are candidates for
higher-dimensional quantum gravity, just as matrix models are in the 2d
setting. With the recent advent of a 1/N-expansion for coloured tensor models,
more focus has been given to the study of the topological aspects of their
Feynman graphs. Crucial to the aforementioned analysis were certain subgraphs
known as bubbles and jackets. We demonstrate in the 3d case that these graphs
are generated by matrix models embedded inside the tensor theory. Moreover, we
show that the jacket graphs represent (Heegaard) splitting surfaces for the
triangulation dual to the Feynman graph. With this in hand, we are able to
re-express the Boulatov model as a quantum field theory on these Riemann
surfaces.Comment: 9 pages, 7 fi
Nematic Structure of Space-Time and its Topological Defects in 5D Kaluza-Klein Theory
We show, that classical Kaluza-Klein theory possesses hidden nematic
dynamics. It appears as a consequence of 1+4-decomposition procedure, involving
4D observers 1-form \lambda. After extracting of boundary terms the, so called,
"effective matter" part of 5D geometrical action becomes proportional to square
of anholonomicity 3-form \lambda\wedge d\lambda. It can be interpreted as twist
nematic elastic energy, responsible for elastic reaction of 5D space-time on
presence of anholonomic 4D submanifold, defined by \lambda. We derive both 5D
covariant and 1+4 forms of 5D nematic equilibrium equations, consider simple
examples and discuss some 4D physical aspects of generic 5D nematic topological
defects.Comment: Latex-2e, 14 pages, 1 Fig., submitted to GR
M5-branes on S^2 x M_4: Nahm's Equations and 4d Topological Sigma-models
We study the 6d N=(0,2) superconformal field theory, which describes multiple
M5-branes, on the product space S^2 x M_4, and suggest a correspondence between
a 2d N=(0,2) half-twisted gauge theory on S^2 and a topological sigma-model on
the four-manifold M_4. To set up this correspondence, we determine in this
paper the dimensional reduction of the 6d N=(0,2) theory on a two-sphere and
derive that the four-dimensional theory is a sigma-model into the moduli space
of solutions to Nahm's equations, or equivalently the moduli space of
k-centered SU(2) monopoles, where k is the number of M5-branes. We proceed in
three steps: we reduce the 6d abelian theory to a 5d Super-Yang-Mills theory on
I x M_4, with I an interval, then non-abelianize the 5d theory and finally
reduce this to 4d. In the special case, when M_4 is a Hyper-Kahler manifold, we
show that the dimensional reduction gives rise to a topological sigma-model
based on tri-holomorphic maps. Deriving the theory on a general M_4 requires
knowledge of the metric of the target space. For k=2 the target space is the
Atiyah-Hitchin manifold and we twist the theory to obtain a topological
sigma-model, which has both scalar fields and self-dual two-forms.Comment: 78 pages, 2 figure
Multi-scale statistics of turbulence motorized by active matter
A number of micro-scale biological flows are characterized by spatio-temporal
chaos. These include dense suspensions of swimming bacteria, microtubule
bundles driven by motor proteins, and dividing and migrating confluent layers
of cells. A characteristic common to all of these systems is that they are
laden with active matter, which transforms free energy in the fluid into
kinetic energy. Because of collective effects, the active matter induces
multi-scale flow motions that bear strong visual resemblance to turbulence. In
this study, multi-scale statistical tools are employed to analyze direct
numerical simulations (DNS) of periodic two- (2D) and three-dimensional (3D)
active flows and compare them to classic turbulent flows. Statistical
descriptions of the flows and their variations with activity levels are
provided in physical and spectral spaces. A scale-dependent intermittency
analysis is performed using wavelets. The results demonstrate fundamental
differences between active and high-Reynolds number turbulence; for instance,
the intermittency is smaller and less energetic in active flows, and the work
of the active stress is spectrally exerted near the integral scales and
dissipated mostly locally by viscosity, with convection playing a minor role in
momentum transport across scales.Comment: Accepted in Journal of Fluid Mechanics (2017
The microscopic dynamics of quantum space as a group field theory
We provide a rather extended introduction to the group field theory approach
to quantum gravity, and the main ideas behind it. We present in some detail the
GFT quantization of 3d Riemannian gravity, and discuss briefly the current
status of the 4-dimensional extensions of this construction. We also briefly
report on recent results obtained in this approach and related open issues,
concerning both the mathematical definition of GFT models, and possible avenues
towards extracting interesting physics from them.Comment: 60 pages. Extensively revised version of the contribution to
"Foundations of Space and Time: Reflections on Quantum Gravity", edited by G.
Ellis, J. Murugan, A. Weltman, published by Cambridge University Pres
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