230 research outputs found
Localization of supersymmetric field theories on non-compact hyperbolic three-manifolds
We study supersymmetric gauge theories with an R-symmetry, defined on
non-compact, hyperbolic, Riemannian three-manifolds, focusing on the case of a
supersymmetry-preserving quotient of Euclidean AdS. We compute the exact
partition function in these theories, using the method of localization, thus
reducing the problem to the computation of one-loop determinants around a
supersymmetric locus. We evaluate the one-loop determinants employing three
different techniques: an index theorem, the method of pairing of eigenvalues,
and the heat kernel method. Along the way, we discuss aspects of supersymmetry
in manifolds with a conformal boundary, including supersymmetric actions and
boundary conditions.Comment: v3:79p, minor clarifications and references adde
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
\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
A topologically twisted index for three-dimensional supersymmetric theories
We provide a general formula for the partition function of three-dimensional (formula presented) gauge theories placed on S2
7S1 with a topological twist along S2, which can be interpreted as an index for chiral states of the theories immersed in background magnetic fields. The result is expressed as a sum over magnetic fluxes of the residues of a meromorphic form which is a function of the scalar zero-modes. The partition function depends on a collection of background magnetic fluxes and fugacities for the global symmetries. We illustrate our formula in many examples of 3d Yang-Mills-Chern-Simons theories with matter, including Aharony and Giveon-Kutasov dualities. Finally, our formula generalizes to \u3a9-backgrounds, as well as two-dimensional theories on S2 and four-dimensional theories on S2
7 T2. In particular this provides an alternative way to compute genus-zero A-model topological amplitudes and Gromov-Witten invariants
Exact Results in D=2 Supersymmetric Gauge Theories
We compute exactly the partition function of two dimensional N=(2,2) gauge
theories on S^2 and show that it admits two dual descriptions: either as an
integral over the Coulomb branch or as a sum over vortex and anti-vortex
excitations on the Higgs branches of the theory. We further demonstrate that
correlation functions in two dimensional Liouville/Toda CFT compute the S^2
partition function for a class of N=(2,2) gauge theories, thereby uncovering
novel modular properties in two dimensional gauge theories. Some of these gauge
theories flow in the infrared to Calabi-Yau sigma models - such as the conifold
- and the topology changing flop transition is realized as crossing symmetry in
Liouville/Toda CFT. Evidence for Seiberg duality in two dimensions is exhibited
by demonstrating that the partition function of conjectured Seiberg dual pairs
are the same.Comment: 78 pages, LaTeX; v2: small corrections and references added; v3: JHEP
version, discussing factorization further in new appendix F; v4: sign
corrected for non simply-connected gauge grou
Generalized Toda Theory from Six Dimensions and the Conifold
Recently, a physical derivation of the Alday-Gaiotto-Tachikawa correspondence
has been put forward. A crucial role is played by the complex Chern-Simons
theory arising in the 3d-3d correspondence, whose boundary modes lead to Toda
theory on a Riemann surface. We explore several features of this derivation and
subsequently argue that it can be extended to a generalization of the AGT
correspondence. The latter involves codimension two defects in six dimensions
that wrap the Riemann surface. We use a purely geometrical description of these
defects and find that the generalized AGT setup can be modeled in a pole region
using generalized conifolds. Furthermore, we argue that the ordinary conifold
clarifies several features of the derivation of the original AGT
correspondence.Comment: 27+2 pages, 3 figure
Higgs branch localization in three dimensions
We show that the supersymmetric partition function of three-dimensional N =2 R-symmetric Chern-Simons-matter theories on the squashed S 3 and on S 2
7 S 1 can be computed with the so-called Higgs branch localization method, alternative to the more standard Coulomb branch localization. For theories that could be completely Higgsed by Fayet-Iliopoulos terms, the path integral is dominated by BPS vortex strings sitting at two circles in the geometry. In this way, the partition function directly takes the form of a sum, over a finite number of points on the classical Coulomb branch, of a vortex-string times an antivortex-string partition functions. \ua9 2014 The Author(s)
Refined Checks and Exact Dualities in Three Dimensions
We discuss and provide nontrivial evidence for a large class of dualities in
three-dimensional field theories with different gauge groups. We match the full
partition functions of the dual phases for any value of the couplings to
underpin our proposals. We focus on two classes of models. The first class,
motivated by the AdS/CFT conjecture, consists of necklace U(N) quiver gauge
theories with non chiral matter fields. We also consider orientifold
projections and establish dualities among necklace quivers with alternating
orthogonal and symplectic groups. The second class consists of theories with
tensor matter fields with free theory duals. In most of these cases the
R-symmetry mixes with IR accidental symmetries and we develop the prescription
to include their contribution into the partition function and the extremization
problem accordingly.Comment: 38 pages, 3 figure, using jheppu
High expression of CXCR4 may predict poor survival in resected pancreatic adenocarcinoma
Chemokines and their receptors are involved in tumourigenicity and clinicopathological significance of chemokines receptor expression in pancreatic adenocarcinoma (PA) is not fully understood. This study was conducted to determine patients' outcome according to the expressions of CXCR4, CXCR7 and HIF-1α after resection of PA. Immunohistochemistry for CXCR4, CXCR7 and HIF-1α expressions as well as cell proliferative index (Ki-67) was conducted in 71 resected (R0) PA and their 48 related lymph nodes (LN) using tissue microarray. CXCR4 and CXCR7 expressions were positively correlated to HIF-1α suggesting a potential role of HIF-1α in CXCR4 and CXCR7 transcription activation. Patients with CXCR4high tumour expression had shorter OS than those with low expression (median survival: 9.7 vs 43.2 months, P=0.0006), a higher risk of LN metastases and liver recurrence. In multivariate analysis, high CXCR4 expression, LN metastases and poorly differentiated tumour are independent negative prognosis factors. In a combining analysis, patients with CXCR4low/CXCR7low tumour had a significantly shorter DFS and OS than patients with a CXCR7high/CXCR4high tumour. CXCR4 in resected PA may represent a valuable prognostic factor as well as an attractive target for therapeutic purpose
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