217 research outputs found
S-duality and 2d Topological QFT
We study the superconformal index for the class of N=2 4d superconformal
field theories recently introduced by Gaiotto. These theories are defined by
compactifying the (2,0) 6d theory on a Riemann surface with punctures. We
interpret the index of the 4d theory associated to an n-punctured Riemann
surface as the n-point correlation function of a 2d topological QFT living on
the surface. Invariance of the index under generalized S-duality
transformations (the mapping class group of the Riemann surface) translates
into associativity of the operator algebra of the 2d TQFT. In the A_1 case, for
which the 4d SCFTs have a Lagrangian realization, the structure constants and
metric of the 2d TQFT can be calculated explicitly in terms of elliptic gamma
functions. Associativity then holds thanks to a remarkable symmetry of an
elliptic hypergeometric beta integral, proved very recently by van de Bult.Comment: 25 pages, 11 figure
Hilbert Series for Moduli Spaces of Two Instantons
The Hilbert Series (HS) of the moduli space of two G instantons on C^2, where
G is a simple gauge group, is studied in detail. For a given G, the moduli
space is a singular hyperKahler cone with a symmetry group U(2) \times G, where
U(2) is the natural symmetry group of C^2. Holomorphic functions on the moduli
space transform in irreducible representations of the symmetry group and hence
the Hilbert series admits a character expansion. For cases that G is a
classical group (of type A, B, C, or D), there is an ADHM construction which
allows us to compute the HS explicitly using a contour integral. For cases that
G is of E-type, recent index results allow for an explicit computation of the
HS. The character expansion can be expressed as an infinite sum which lives on
a Cartesian lattice that is generated by a small number of representations.
This structure persists for all G and allows for an explicit expressions of the
HS to all simple groups. For cases that G is of type G_2 or F_4, discrete
symmetries are enough to evaluate the HS exactly, even though neither ADHM
construction nor index is known for these cases.Comment: 53 pages, 9 tables, 24 figure
M5-branes from gauge theories on the 5-sphere
We use the 5-sphere partition functions of supersymmetric Yang-Mills theories
to explore the (2,0) superconformal theory on S^5 x S^1. The 5d theories can be
regarded as Scherk-Schwarz reductions of the 6d theory along the circle. In a
special limit, the perturbative partition function takes the form of the
Chern-Simons partition function on S^3. With a simple non-perturbative
completion, it becomes a 6d index which captures the degeneracy of a sector of
BPS states as well as the index version of the vacuum Casimir energy. The
Casimir energy exhibits the N^3 scaling at large N. The large N index for U(N)
gauge group also completely agrees with the supergravity index on AdS_7 x S^4.Comment: 44 pages, 1 figure, v4: ref added, clarified weak/strong coupling
behaviors of large N free energy, minor improvements, version to be published
in JHE
Localization of N=4 Superconformal Field Theory on S^1 x S^3 and Index
We provide the geometrical meaning of the superconformal index.
With this interpretation, the superconformal index can be realized
as the partition function on a Scherk-Schwarz deformed background. We apply the
localization method in TQFT to compute the deformed partition function since
the deformed action can be written as a -exact form. The
critical points of the deformed action turn out to be the space of flat
connections which are, in fact, zero modes of the gauge field. The one-loop
evaluation over the space of flat connections reduces to the matrix integral by
which the superconformal index is expressed.Comment: 42+1 pages, 2 figures, JHEP style: v1.2.3 minor corrections, v4 major
revision, conclusions essentially unchanged, v5 published versio
On instantons as Kaluza-Klein modes of M5-branes
Instantons and W-bosons in 5d maximally supersymmetric Yang-Mills theory
arise from a circle compactification of the 6d (2,0) theory as Kaluza-Klein
modes and winding self-dual strings, respectively. We study an index which
counts BPS instantons with electric charges in Coulomb and symmetric phases. We
first prove the existence of unique threshold bound state of (noncommutative)
U(1) instantons for any instanton number, and also show that charged instantons
in the Coulomb phase correctly give the degeneracy of SU(2) self-dual strings.
By studying SU(N) self-dual strings in the Coulomb phase, we find novel
momentum-carrying degrees on the worldsheet. The total number of these degrees
equals the anomaly coefficient of SU(N) (2,0) theory. We finally show that our
index can be used to study the symmetric phase of this theory, and provide an
interpretation as the superconformal index of the sigma model on instanton
moduli space.Comment: 54 pages, 2 figures. v2: references added, figure improved, added
comments on self-dual string anomaly, added new materials on the symmetric
phase index, other minor correction
Quivers, YBE and 3-manifolds
We study 4d superconformal indices for a large class of N=1 superconformal
quiver gauge theories realized combinatorially as a bipartite graph or a set of
"zig-zag paths" on a two-dimensional torus T^2. An exchange of loops, which we
call a "double Yang-Baxter move", gives the Seiberg duality of the gauge
theory, and the invariance of the index under the duality is translated into
the Yang-Baxter-type equation of a spin system defined on a "Z-invariant"
lattice on T^2. When we compactify the gauge theory to 3d, Higgs the theory and
then compactify further to 2d, the superconformal index reduces to an integral
of quantum/classical dilogarithm functions. The saddle point of this integral
unexpectedly reproduces the hyperbolic volume of a hyperbolic 3-manifold. The
3-manifold is obtained by gluing hyperbolic ideal polyhedra in H^3, each of
which could be thought of as a 3d lift of the faces of the 2d bipartite
graph.The same quantity is also related with the thermodynamic limit of the BPS
partition function, or equivalently the genus 0 topological string partition
function, on a toric Calabi-Yau manifold dual to quiver gauge theories. We also
comment on brane realization of our theories. This paper is a companion to
another paper summarizing the results.Comment: 61 pages, 16 figures; v2: typos correcte
The air quality impacts of road closures associated with the 2004 Democratic National Convention in Boston
BACKGROUND: The Democratic National Convention (DNC) in Boston, Massachusetts in 2004 provided an opportunity to evaluate the impacts of a localized and short-term but potentially significant change in traffic patterns on air quality, and to determine the optimal monitoring approach to address events of this nature. It was anticipated that the road closures associated with the DNC would both influence the overall air pollution level and the distribution of concentrations across the city, through shifts in traffic patterns. METHODS: To capture these effects, we placed passive nitrogen dioxide badges at 40 sites around metropolitan Boston before, during, and after the DNC, with the goal of capturing the array of hypothesized impacts. In addition, we continuously measured elemental carbon at three sites, and gathered continuous air pollution data from US EPA fixed-site monitors and traffic count data from the Massachusetts Highway Department. RESULTS: There were significant reductions in traffic volume on the highway with closures north of Boston, with relatively little change along other highways, indicating a more isolated traffic reduction rather than an across-the-board decrease. For our nitrogen dioxide samples, while there was a relatively small change in mean concentrations, there was significant heterogeneity across sites, which corresponded with our a priori classifications of road segments. The median ratio of nitrogen dioxide concentrations during the DNC relative to non-DNC sampling periods was 0.58 at sites with hypothesized traffic reductions, versus 0.88 for sites with no changes hypothesized and 1.15 for sites with hypothesized traffic increases. Continuous monitors measured slightly lower concentrations of elemental carbon and nitrogen dioxide during road closure periods at monitors proximate to closed highway segments, but not for PM(2.5 )or further from major highways. CONCLUSION: We conclude that there was a small but measurable influence of DNC-related road closures on air quality patterns in the Boston area, and that a low-cost monitoring study combining passive badges for spatial heterogeneity and continuous monitors for temporal heterogeneity can provide useful insight for community air quality assessments
Holographic renormalization and supersymmetry
Holographic renormalization is a systematic procedure for regulating
divergences in observables in asymptotically locally AdS spacetimes. For dual
boundary field theories which are supersymmetric it is natural to ask whether
this defines a supersymmetric renormalization scheme. Recent results in
localization have brought this question into sharp focus: rigid supersymmetry
on a curved boundary requires specific geometric structures, and general
arguments imply that BPS observables, such as the partition function, are
invariant under certain deformations of these structures. One can then ask if
the dual holographic observables are similarly invariant. We study this
question in minimal N = 2 gauged supergravity in four and five dimensions. In
four dimensions we show that holographic renormalization precisely reproduces
the expected field theory results. In five dimensions we find that no choice of
standard holographic counterterms is compatible with supersymmetry, which leads
us to introduce novel finite boundary terms. For a class of solutions
satisfying certain topological assumptions we provide some independent tests of
these new boundary terms, in particular showing that they reproduce the
expected VEVs of conserved charges.Comment: 70 pages; corrected typo
Superconformal Index with Duality Domain Wall
We study a superconformal index for super Yang-Mills on with a half BPS duality domain wall inserted at the great
two-sphere in . The index is obtained by coupling the 3d generalized
superconformal index on the duality domain wall with 4d half-indices. We
further consider insertions of line operators to the configuration and propose
integral equations which express that the 3d index on duality domain wall is a
duality kernel relating half indices of two line operators related by the
duality map. We explicitly check the proposed integral equations for various
duality domain walls and line operators in the SU(2) theory. We
also briefly comment on a generalization to Gaiotto
theories with a simple example, SU(2) SYM with four flavors.Comment: v1: 25 pages, 4 figures. v2: comments and a reference added, minor
corrections. v3: 30 pages, new results and discussions added to sec 4.5 and
sec 5.1, eq 49 and eq 51 corrected, text improved; to appear in JHE
Depression and sickness behavior are Janus-faced responses to shared inflammatory pathways
It is of considerable translational importance whether depression is a form or a consequence of sickness behavior. Sickness behavior is a behavioral complex induced by infections and immune trauma and mediated by pro-inflammatory cytokines. It is an adaptive response that enhances recovery by conserving energy to combat acute inflammation. There are considerable phenomenological similarities between sickness behavior and depression, for example, behavioral inhibition, anorexia and weight loss, and melancholic (anhedonia), physio-somatic (fatigue, hyperalgesia, malaise), anxiety and neurocognitive symptoms. In clinical depression, however, a transition occurs to sensitization of immuno-inflammatory pathways, progressive damage by oxidative and nitrosative stress to lipids, proteins, and DNA, and autoimmune responses directed against self-epitopes. The latter mechanisms are the substrate of a neuroprogressive process, whereby multiple depressive episodes cause neural tissue damage and consequent functional and cognitive sequelae. Thus, shared immuno-inflammatory pathways underpin the physiology of sickness behavior and the pathophysiology of clinical depression explaining their partially overlapping phenomenology. Inflammation may provoke a Janus-faced response with a good, acute side, generating protective inflammation through sickness behavior and a bad, chronic side, for example, clinical depression, a lifelong disorder with positive feedback loops between (neuro)inflammation and (neuro)degenerative processes following less well defined triggers
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