760 research outputs found
Giant Nonlinear Optical Activity from Planar Metasurfaces
Second harmonic generation circular dichroism (CD) is more sensitive to the handedness of
chiral materials than its linear optical counterpart. In this work, we show that 3D chiral structures are not
necessary for introducing strong CD for harmonic generations. Specifically, we demonstrate giant CD for
both second harmonic generation and third harmonic generation on suitably designed ultrathin plasmonic
metasurfaces. It is experimentally and theoretically verified that the overwhelming contribution to this
nonlinear CD is of achiral origin. The results shed new light on the origin of the nonlinear CD effect in
achiral planar surfaces
Morse theory of the moment map for representations of quivers
The results of this paper concern the Morse theory of the norm-square of the
moment map on the space of representations of a quiver. We show that the
gradient flow of this function converges, and that the Morse stratification
induced by the gradient flow co-incides with the Harder-Narasimhan
stratification from algebraic geometry. Moreover, the limit of the gradient
flow is isomorphic to the graded object of the
Harder-Narasimhan-Jordan-H\"older filtration associated to the initial
conditions for the flow. With a view towards applications to Nakajima quiver
varieties we construct explicit local co-ordinates around the Morse strata and
(under a technical hypothesis on the stability parameter) describe the negative
normal space to the critical sets. Finally, we observe that the usual Kirwan
surjectivity theorems in rational cohomology and integral K-theory carry over
to this non-compact setting, and that these theorems generalize to certain
equivariant contexts.Comment: 48 pages, small revisions from previous version based on referee's
comments. To appear in Geometriae Dedicat
Wall-Crossing from Boltzmann Black Hole Halos
A key question in the study of N=2 supersymmetric string or field theories is
to understand the decay of BPS bound states across walls of marginal stability
in the space of parameters or vacua. By representing the potentially unstable
bound states as multi-centered black hole solutions in N=2 supergravity, we
provide two fully general and explicit formulae for the change in the (refined)
index across the wall. The first, "Higgs branch" formula relies on Reineke's
results for invariants of quivers without oriented loops, specialized to the
Abelian case. The second, "Coulomb branch" formula results from evaluating the
symplectic volume of the classical phase space of multi-centered solutions by
localization. We provide extensive evidence that these new formulae agree with
each other and with the mathematical results of Kontsevich and Soibelman (KS)
and Joyce and Song (JS). The main physical insight behind our results is that
the Bose-Fermi statistics of individual black holes participating in the bound
state can be traded for Maxwell-Boltzmann statistics, provided the (integer)
index \Omega(\gamma) of the internal degrees of freedom carried by each black
hole is replaced by an effective (rational) index \bar\Omega(\gamma)=
\sum_{m|\gamma} \Omega(\gamma/m)/m^2. A similar map also exists for the refined
index. This observation provides a physical rationale for the appearance of the
rational Donaldson-Thomas invariant \bar\Omega(\gamma) in the works of KS and
JS. The simplicity of the wall crossing formula for rational invariants allows
us to generalize the "semi-primitive wall-crossing formula" to arbitrary decays
of the type \gamma\to M\gamma_1+N\gamma_2 with M=2,3.Comment: 71 pages, 1 figure; v3: changed normalisation of symplectic form
3.22, corrected 3.35, other cosmetic change
Heterologous expression screens in Nicotiana benthamiana identify a candidate effector of the wheat Yellow Rust Pathogen that associates with processing bodies
Rust fungal pathogens of wheat (Triticum spp.) affect crop yields worldwide. The molecular mechanisms underlying the virulence of these pathogens remain elusive, due to the limited availability of suitable molecular genetic research tools. Notably, the inability to perform high-throughput analyses of candidate virulence proteins (also known as effectors) impairs progress. We previously established a pipeline for the fast-forward screens of rust fungal candidate effectors in the model plant Nicotiana benthamiana. This pipeline involves selecting candidate effectors in silico and performing cell biology and protein-protein interaction assays in planta to gain insight into the putative functions of candidate effectors. In this study, we used this pipeline to identify and characterize sixteen candidate effectors from the wheat yellow rust fungal pathogen Puccinia striiformis f sp tritici. Nine candidate effectors targeted a specific plant subcellular compartment or protein complex, providing valuable information on their putative functions in plant cells. One candidate effector, PST02549, accumulated in processing bodies (P-bodies), protein complexes involved in mRNA decapping, degradation, and storage. PST02549 also associates with the P-body-resident ENHANCER OF mRNA DECAPPING PROTEIN 4 (EDC4) from N. benthamiana and wheat. We propose that P-bodies are a novel plant cell compartment targeted by pathogen effectors
Quiver Structure of Heterotic Moduli
We analyse the vector bundle moduli arising from generic heterotic
compactifications from the point of view of quiver representations. Phenomena
such as stability walls, crossing between chambers of supersymmetry, splitting
of non-Abelian bundles and dynamic generation of D-terms are succinctly encoded
into finite quivers. By studying the Poincar\'e polynomial of the quiver moduli
space using the Reineke formula, we can learn about such useful concepts as
Donaldson-Thomas invariants, instanton transitions and supersymmetry breaking.Comment: 38 pages, 5 figures, 1 tabl
Mixed Hodge polynomials of character varieties
We calculate the E-polynomials of certain twisted GL(n,C)-character varieties
M_n of Riemann surfaces by counting points over finite fields using the
character table of the finite group of Lie-type GL(n,F_q) and a theorem proved
in the appendix by N. Katz. We deduce from this calculation several geometric
results, for example, the value of the topological Euler characteristic of the
associated PGL(n,C)-character variety. The calculation also leads to several
conjectures about the cohomology of M_n: an explicit conjecture for its mixed
Hodge polynomial; a conjectured curious Hard Lefschetz theorem and a conjecture
relating the pure part to absolutely indecomposable representations of a
certain quiver. We prove these conjectures for n = 2.Comment: with an appendix by Nicholas M. Katz; 57 pages. revised version: New
definition for homogeneous weight in Definition 4.1.6, subsequent arguments
modified. Some other minor changes. To appear in Invent. Mat
From Black Holes to Quivers
Middle cohomology states on the Higgs branch of supersymmetric quiver quantum
mechanics - also known as pure Higgs states - have recently emerged as possible
microscopic candidates for single-centered black hole micro-states, as they
carry zero angular momentum and appear to be robust under wall-crossing. Using
the connection between quiver quantum mechanics on the Coulomb branch and the
quantum mechanics of multi-centered black holes, we propose a general algorithm
for reconstructing the full moduli-dependent cohomology of the moduli space of
an arbitrary quiver, in terms of the BPS invariants of the pure Higgs states.
We analyze many examples of quivers with loops, including all cyclic Abelian
quivers and several examples with two loops or non-Abelian gauge groups, and
provide supporting evidence for this proposal. We also develop methods to count
pure Higgs states directly.Comment: 56 pages; v2: added Eqs 4.28-30, 5.35-36, 5.55; v3: journal version;
v4: Misprints corrected, improved discussion of Higgs branch for non-Abelian
3-node quiver, see around Eq. (6.22) and (6.37
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