1,911 research outputs found
On the crossing relation in the presence of defects
The OPE of local operators in the presence of defect lines is considered both
in the rational CFT and the Virasoro (Liouville) theory. The duality
transformation of the 4-point function with inserted defect operators is
explicitly computed. The two channels of the correlator reproduce the
expectation values of the Wilson and 't Hooft operators, recently discussed in
Liouville theory in relation to the AGT conjecture.Comment: TEX file with harvmac; v3: JHEP versio
Wall-Crossing in Coupled 2d-4d Systems
We introduce a new wall-crossing formula which combines and generalizes the
Cecotti-Vafa and Kontsevich-Soibelman formulas for supersymmetric 2d and 4d
systems respectively. This 2d-4d wall-crossing formula governs the
wall-crossing of BPS states in an N=2 supersymmetric 4d gauge theory coupled to
a supersymmetric surface defect. When the theory and defect are compactified on
a circle, we get a 3d theory with a supersymmetric line operator, corresponding
to a hyperholomorphic connection on a vector bundle over a hyperkahler space.
The 2d-4d wall-crossing formula can be interpreted as a smoothness condition
for this hyperholomorphic connection. We explain how the 2d-4d BPS spectrum can
be determined for 4d theories of class S, that is, for those theories obtained
by compactifying the six-dimensional (0,2) theory with a partial topological
twist on a punctured Riemann surface C. For such theories there are canonical
surface defects. We illustrate with several examples in the case of A_1
theories of class S. Finally, we indicate how our results can be used to
produce solutions to the A_1 Hitchin equations on the Riemann surface C.Comment: 170 pages, 45 figure
\Omega-deformation of B-twisted gauge theories and the 3d-3d correspondence
We study \Omega-deformation of B-twisted gauge theories in two dimensions. As
an application, we construct an \Omega-deformed, topologically twisted
five-dimensional maximally supersymmetric Yang-Mills theory on the product of a
Riemann surface and a three-manifold , and show that when
is a disk, this theory is equivalent to analytically continued Chern-Simons
theory on . Based on these results, we establish a correspondence between
three-dimensional superconformal theories and analytically
continued Chern-Simons theory. Furthermore, we argue that there is a mirror
symmetry between {\Omega}-deformed two-dimensional theories.Comment: 26 pages. v2: the discussion on the boundary condition for vector
multiplet improved, and other minor changes mad
Towards a 4d/2d correspondence for Sicilian quivers
We study the 4d/2d AGT correspondence between four-dimensional instanton
counting and two-dimensional conformal blocks for generalized SU(2) quiver
gauge theories coming from punctured Gaiotto curves of arbitrary genus. We
propose a conformal block description that corresponds to the elementary SU(2)
trifundamental half-hypermultiplet, and check it against Sp(1)-SO(4) instanton
counting.Comment: 39 pages, 11 figure
Genus-one correction to asymptotically free Seiberg-Witten prepotential from Dijkgraaf-Vafa matrix model
We find perfect agreements on the genus-one correction to the prepotential of
SU(2) Seiberg-Witten theory with N_f=2, 3 between field theoretical and
Dijkgraaf-Vafa-Penner type matrix model results.Comment: 12 pages; v2: minor revision; v3: more structured, submitted versio
The Virtue of Defects in 4D Gauge Theories and 2D CFTs
We advance a correspondence between the topological defect operators in
Liouville and Toda conformal field theories - which we construct - and loop
operators and domain wall operators in four dimensional N=2 supersymmetric
gauge theories on S^4. Our computation of the correlation functions in
Liouville/Toda theory in the presence of topological defect operators, which
are supported on curves on the Riemann surface, yields the exact answer for the
partition function of four dimensional gauge theories in the presence of
various walls and loop operators; results which we can quantitatively
substantiate with an independent gauge theory analysis. As an interesting
outcome of this work for two dimensional conformal field theories, we prove
that topological defect operators and the Verlinde loop operators are different
descriptions of the same operators.Comment: 59 pages, latex; v2 corrections to some formula
Unicellular cyanobacteria are important components of phytoplankton communities in Australia's northern oceanic ecoregions
© 2019 Moore, Huang, Ostrowski, Mazard, Kumar, Gamage, Brown, Messer, Seymour and Paulsen. The tropical marine environments of northern Australia encompasses a diverse range of geomorphological and oceanographic conditions and high levels of productivity and nitrogen fixation. However, efforts to characterize phytoplankton assemblages in these waters have been restricted to studies using microscopic and pigment analyses, leading to the current consensus that this region is dominated by large diatoms, dinoflagellates, and the marine cyanobacterium Trichodesmium. During an oceanographic transect from the Arafura Sea through the Torres Strait to the Coral Sea, we characterized prokaryotic and eukaryotic phytoplankton communities in surface waters using a combination of flow cytometry and Illumina based 16S and 18S ribosomal RNA amplicon sequencing. Similar to observations in other marine regions around Australian, phytoplankton assemblages throughout this entire region were rich in unicellular picocyanobacterial primary producers while picoeukaryotic phytoplankton formed a consistent, though smaller proportion of the photosynthetic biomass. Major taxonomic groups displayed distinct biogeographic patterns linked to oceanographic and nutrient conditions. Unicellular picocyanobacteria dominated in both flow cytometric abundance and carbon biomass, with members of the Synechococcus genus dominating in the shallower Arafura Sea and Torres Strait where chlorophyll a was relatively higher (averaging 0.4 ± 0.2 mg m-3), and Prochlorococcus dominating in the oligotrophic Coral Sea where chlorophyll a averaged 0.13 ± 0.07 mg m-3. Consistent with previous microscopic and pigment-based observations, we found from sequence analysis that a variety of diatoms (Bacillariophyceae) exhibited high relative abundance in the Arafura Sea and Torres Strait, while dinoflagellates (Dinophyceae) and prymnesiophytes (Prymnesiophyceae) were more abundant in the Coral Sea. Ordination analysis identified temperature, nutrient concentrations and water depth as key drivers of the region's assemblage composition. This is the first molecular and flow cytometric survey of the abundance and diversity of both prokaryotic and picoeukaryotic phytoplankton in this region, and points to the need to include the picocyanobacterial populations as an essential oceanic variable for sustained monitoring in order to better understand the health of these important coastal waters as global oceans change
Affine sl(N) conformal blocks from N=2 SU(N) gauge theories
Recently Alday and Tachikawa proposed a relation between conformal blocks in
a two-dimensional theory with affine sl(2) symmetry and instanton partition
functions in four-dimensional conformal N=2 SU(2) quiver gauge theories in the
presence of a certain surface operator. In this paper we extend this proposal
to a relation between conformal blocks in theories with affine sl(N) symmetry
and instanton partition functions in conformal N=2 SU(N) quiver gauge theories
in the presence of a surface operator. We also discuss the extension to
non-conformal N=2 SU(N) theories.Comment: 40 pages. v2: minor changes and clarification
Classical conformal blocks from TBA for the elliptic Calogero-Moser system
The so-called Poghossian identities connecting the toric and spherical
blocks, the AGT relation on the torus and the Nekrasov-Shatashvili formula for
the elliptic Calogero-Moser Yang's (eCMY) functional are used to derive certain
expressions for the classical 4-point block on the sphere. The main motivation
for this line of research is the longstanding open problem of uniformization of
the 4-punctured Riemann sphere, where the 4-point classical block plays a
crucial role. It is found that the obtained representation for certain 4-point
classical blocks implies the relation between the accessory parameter of the
Fuchsian uniformization of the 4-punctured sphere and the eCMY functional.
Additionally, a relation between the 4-point classical block and the ,
twisted superpotential is found and further used to re-derive the
instanton sector of the Seiberg-Witten prepotential of the , supersymmetric gauge theory from the classical block.Comment: 25 pages, no figures, latex+JHEP3, published versio
't Hooft Operators in Gauge Theory from Toda CFT
We construct loop operators in two dimensional Toda CFT and calculate with
them the exact expectation value of certain supersymmetric 't Hooft and dyonic
loop operators in four dimensional \Ncal=2 gauge theories with SU(N) gauge
group. Explicit formulae for 't Hooft and dyonic operators in \Ncal=2^* and
\Ncal=2 conformal SQCD with SU(N) gauge group are presented. We also briefly
speculate on the Toda CFT realization of arbitrary loop operators in these
gauge theories in terms of topological web operators in Toda CFT.Comment: 49 pages, LaTeX. Typos fixed, references adde
- …