110 research outputs found
Scaling Behaviour of Quiver Quantum Mechanics
We explore vacuum degeneracy of Kronecker quiver with large ranks, by
computing Witten index of corresponding 1d gauged linear sigma model. For
quivers with the intersection number , we actually counted index
of its mutation equivalent, , and find exponentially large
behaviour whenever . We close with speculation on more general ranks of
Kronecker quiver including the nonprimitive cases.Comment: 28 pages, 5 figures, minor typo correcte
Comments on twisted indices in 3d supersymmetric gauge theories
We study three-dimensional supersymmetric gauge theories on
with a topological twist along , a genus-
Riemann surface. The twisted supersymmetric index at genus and the
correlation functions of half-BPS loop operators on can be computed
exactly by supersymmetric localization. For , this gives a simple UV
computation of the 3d Witten index. Twisted indices provide us with a clean
derivation of the quantum algebra of supersymmetric Wilson loops, for any
Yang-Mills-Chern-Simons-matter theory, in terms of the associated Bethe
equations for the theory on . This also provides a
powerful and simple tool to study 3d Seiberg dualities.
Finally, we study A- and B-twisted indices for supersymmetric
gauge theories, which turns out to be very useful for quantitative studies of
three-dimensional mirror symmetry. We also briefly comment on a relation
between the twisted indices and the Hilbert series of
moduli spaces.Comment: 66 pages plus appendix; v2: corrected typos and added reference
Witten Index and Wall Crossing
We compute the Witten index of one-dimensional gauged linear sigma models
with at least supersymmetry. In the phase where the gauge
group is broken to a finite group, the index is expressed as a certain residue
integral. It is subject to a change as the Fayet-Iliopoulos parameter is varied
through the phase boundaries. The wall crossing formula is expressed as an
integral at infinity of the Coulomb branch. The result is applied to many
examples, including quiver quantum mechanics that is relevant for BPS states in
theories.Comment: 123 pages, v3: the discussion on the smooth transition (Section 4.4)
is improved, more minor corrections made; v2: references added, minor
corrections mad
Supersymmetric partition functions and the three-dimensional A-twist
We study three-dimensional supersymmetric gauge theories on
, an oriented circle bundle of degree over a closed
Riemann surface, . We compute the supersymmetric
partition function and correlation functions of supersymmetric loop operators.
This uncovers interesting relations between observables on manifolds of
different topologies. In particular, the familiar supersymmetric partition
function on the round can be understood as the expectation value of a
so-called "fibering operator" on with a topological twist.
More generally, we show that the 3d supersymmetric partition
functions (and supersymmetric Wilson loop correlation functions) on
are fully determined by the two-dimensional A-twisted
topological field theory obtained by compactifying the 3d theory on a circle.
We give two complementary derivations of the result. We also discuss
applications to F-maximization and to three-dimensional supersymmetric
dualities.Comment: 84 pages plus appendix, 8 figures; v2: added reference
supersymmetric indices and the four-dimensional A-model
We compute the supersymmetric partition function of
supersymmetric gauge theories with an -symmetry on , a principal elliptic fiber bundle of degree
over a genus- Riemann surface, . Equivalently, we compute the
generalized supersymmetric index , with the
supersymmetric three-manifold as the spatial slice. The
ordinary supersymmetric index on the round three-sphere is
recovered as a special case. We approach this computation from the point of
view of a topological -model for the abelianized gauge fields on the base
. This -model---or -twisted two-dimensional
gauge theory---encodes all the information about the
generalized indices, which are viewed as expectations values of some
canonically-defined surface defects wrapped on inside . Being defined by compactification on the torus, the -model also enjoys
natural modular properties, governed by the four-dimensional 't Hooft
anomalies. As an application of our results, we provide new tests of Seiberg
duality. We also present a new evaluation formula for the three-sphere index as
a sum over two-dimensional vacua.Comment: 91 pages including appendices; v2: corrected typos and added
references, JHEP versio
Exact Partition Functions on RP2 and Orientifolds
We consider gauged linear sigma models (GLSM) on , obtained
from a parity projection of . The theories admit squashing deformation,
much like GLSM on , which allows us to interpret the partition function as
the overlap amplitude between the vacuum state and crosscap states. From these,
we extract the central charge of Orientifold planes, and observe that the Gamma
class makes a prominent appearance as in the recent D-brane counterpart. We
also repeat the computation for the mirror Landau-Ginzburg theory, which
naturally brings out the -dependence as a relative sign between two
holonomy sectors on . We also show how our results are
consistent with known topological properties of D-brane and Orientifold plane
world-volumes, and discuss what part of the wrapped D-brane/Orientifold central
charge should be attributed to the quantum volumes.Comment: 55 pages, 1 figure, published version: discussions on role of theta
angle and on r-charge dependent normalization calrified; typos corrected; one
reference adde
Three-Dimensional Topological Field Theories and Non-Unitary Minimal Models
We find an intriguing relation between a class of 3-dimensional non-unitary
topological field theories (TFTs) and Virasoro minimal models with
. The TFTs are constructed by topologically twisting superconformal field theories (SCFTs) of rank-0, i.e. having
zero-dimensional Coulomb and Higgs branches. We present ultraviolet (UV) field
theory descriptions of the SCFTs with manifest supersymmetry,
which we argue is enhanced to in the infrared. From the UV
description, we compute various partition functions of the TFTs and reproduce
some basic properties of the minimal models, such as their characters and
modular matrices. We expect more general correspondence between topologically
twisted rank-0 SCFTs and non-unitary rational
conformal field theories.Comment: 6 page
Where in Health Sector Do We See ODA Being Effective? With Special Reference to Eight Health Indicators
Analysis for aid effectiveness has become a hot topic of Millennium Development Goal area. While many studies seek to evaluate ODA effectiveness at macro-level or micro-level, this paper attempts to
fill the gap by reproducing the analysis at meso-level. The authors tested aid effectiveness in health
sector with special reference to eight health indicators. Comparing the effect of the same aid on
various health indicators, we found interesting results that the statistical degree and the significance of
aid vary in health indicators
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