12,971 research outputs found
Emergent gauge dynamics of highly frustrated magnets
Condensed matter exhibits a wide variety of exotic emergent phenomena such as
the fractional quantum Hall effect and the low temperature cooperative behavior
of highly frustrated magnets. I consider the classical Hamiltonian dynamics of
spins of the latter phenomena using a method introduced by Dirac in the 1950s
by assuming they are constrained to their lowest energy configurations as a
simplifying measure. Focusing on the kagome antiferromagnet as an example, I
find it is a gauge system with topological dynamics and non-locally connected
edge states for certain open boundary conditions similar to doubled
Chern-Simons electrodynamics expected of a spin liquid. These dynamics
are also similar to electrons in the fractional quantum Hall effect. The
classical theory presented here is a first step towards a controlled
semi-classical description of the spin liquid phases of many pyrochlore and
kagome antiferromagnets and towards a description of the low energy classical
dynamics of the corresponding unconstrained Heisenberg models.Comment: Updated with some appendices moved to the main body of the paper and
some additional improvements. 21 pages, 5 figure
Condensing Nielsen-Olesen strings and the vortex-boson duality in 3+1 and higher dimensions
The vortex-boson (or Abelian-Higgs, XY) duality in 2+1 dimensions
demonstrates that the quantum disordered superfluid is equivalent to an ordered
superconductor and the other way around. Such a duality structure should be
ubiquitous but in 3+1 (and higher) dimensions a precise formulation of the
duality is lacking. The problem is that the topological defects become extended
objects, strings in 3+1D. We argue how the condensate of such vortex strings
must behave from the known physics of the disordered superfluid, namely the
Bose-Mott insulator. A flaw in earlier proposals is repaired, and a more direct
viewpoint, avoiding gauge fields, in terms of the physical supercurrent is laid
out, that also easily generalizes to higher-dimensional and more complicated
systems. Furthermore topological defects are readily identified; we demonstrate
that the Bose-Mott insulator supports line defects, which may be seen in cold
atom experiments.Comment: LaTeX, 25 pages, 5 figures; several revisions and addition
Topological Entanglement Entropy of Fracton Stabilizer Codes
Entanglement entropy provides a powerful characterization of two-dimensional
gapped topological phases of quantum matter, intimately tied to their
description by topological quantum field theories (TQFTs). Fracton topological
orders are three-dimensional gapped topologically ordered states of matter, but
the existence of a TQFT description for these phases remains an open question.
We show that three-dimensional fracton phases are nevertheless characterized,
at least partially, by universal structure in the entanglement entropy of their
ground state wave functions. We explicitly compute the entanglement entropy for
two archetypal fracton models --- the `X-cube model' and `Haah's code' --- and
demonstrate the existence of a topological contribution that scales linearly in
subsystem size. We show via Schrieffer-Wolff transformations that the
topological entanglement of fracton models is robust against arbitrary local
perturbations of the Hamiltonian. Finally, we argue that these results may be
extended to characterize localization-protected fracton topological order in
excited states of disordered fracton models.Comment: published versio
BPS Microstates and the Open Topological String Wave Function
It has recently been conjectured that the closed topological string wave
function computes a grand canonical partition function of BPS black hole states
in 4 dimensions: Z_BH=|psi_top|^2. We conjecture that the open topological
string wave function also computes a grand canonical partition function, which
sums over black holes bound to BPS excitations on D-branes wrapping cycles of
the internal Calabi-Yau: Z^open_BPS=|psi^open_top|^2. This conjecture is
verified in the case of Type IIA on a local Calabi-Yau threefold involving a
Riemann surface, where the degeneracies of BPS states can be computed in
q-deformed 2-dimensional Yang-Mills theory.Comment: 50 pages, LaTe
Comments on the Chern-Simons photon term in the QED description of graphene
We revisit the Coleman-Hill theorem in the context of reduced planar QED.
Using the global U(1) Ward identity for this non-local but still gauge
invariant theory, we can confirm that the topological piece of the photon
self-energy at zero momentum does not receive further quantum corrections apart
from the potential one-loop contribution, even when considering the Lorentz
non-invariant case due to the Fermi velocity . This is of relevance to
probe possible time parity odd dynamics in a planar sheet of graphene which has
an effective description in terms of -dimensional planar reduced QED.Comment: New section added, published versio
Wilson Loops in Non-Compact U(1) Gauge Theories at Criticality
We study the properties of Wilson loops in three dimensional non-compact U(1)
gauge theories with global abelian symmetries. We use duality in the continuum
and on the lattice, to argue that close to the critical point between the Higgs
and Coulomb phases, all correlators of the Wilson loops are periodic functions
of the Wilson loop charge, Q. The period depends on the global symmetry of the
theory, which determines the magnetic flux carried by the dual particles. For
single flavour scalar electrodynamics, the emergent period is Q = 1. In the
general case of N complex scalars with a U(1)^{N-1} global symmetry, the period
is Q = N. We also give some arguments why this phenomenon does not generalize
to theories with a full non-abelian SU(N) symmetry, where no periodicity in Q
is expected. Implications for lattice simulations, as well as for physical
systems, such as easy plane antiferromagnets and disordered superfluids, are
noted.Comment: 25 pages, 1 figur
Pure-spinor superstrings in d=2,4,6
We continue the study of the d=2,4,6 pure-spinor superstring models
introduced in [1]. By explicitly solving the pure-spinor constraint we show
that these theories have vanishing central charge and work out the (covariant)
current algebra for the Lorentz currents. We argue that these super-Poincare
covariant models may be thought of as compactifications of the superstring on
CY_{4,3,2}, and take some steps toward making this precise by constructing a
map to the RNS superstring variables. We also discuss the relation to the so
called hybrid superstrings, which describe the same type of compactifications.Comment: 27 page
Black Holes in Type IIA String on Calabi-Yau Threefolds with Affine ADE Geometries and q-Deformed 2d Quiver Gauge Theories
Motivated by studies on 4d black holes and q-deformed 2d Yang Mills theory,
and borrowing ideas from compact geometry of the blowing up of affine ADE
singularities, we build a class of local Calabi-Yau threefolds (CY^{3})
extending the local 2-torus model \mathcal{O}(m)\oplus \mathcal{O}(-m)\to
T^{2\text{}} considered in hep-th/0406058 to test OSV conjecture. We first
study toric realizations of T^{2} and then build a toric representation of
X_{3} using intersections of local Calabi-Yau threefolds \mathcal{O}(m)\oplus
\mathcal{O}(-m-2)\to \mathbb{P}^{1}. We develop the 2d \mathcal{N}=2 linear
\sigma-model for this class of toric CY^{3}s. Then we use these local
backgrounds to study partition function of 4d black holes in type IIA string
theory and the underlying q-deformed 2d quiver gauge theories. We also make
comments on 4d black holes obtained from D-branes wrapping cycles in
\mathcal{O}(\mathbf{m}) \oplus \mathcal{O}(\mathbf{-m-2}%) \to \mathcal{B}_{k}
with \mathbf{m=}(m_{1},...,m_{k}) a k-dim integer vector and \mathcal{B}_{k} a
compact complex one dimension base consisting of the intersection of k
2-spheres S_{i}^{2} with generic intersection matrix I_{ij}. We give as well
the explicit expression of the q-deformed path integral measure of the
partition function of the 2d quiver gauge theory in terms of I_{ij}.Comment: 36 pages, latex, 9 figures. References adde
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