\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 $\Sigma$ and a three-manifold $M$, and show that when $\Sigma$ is a disk, this theory is equivalent to analytically continued Chern-Simons theory on $M$. Based on these results, we establish a correspondence between three-dimensional $\mathcal{N} = 2$ 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

Anomaly-Free Supersymmetric SO(2N+2)/U(N+1) sigma-Model Based on the SO(2N+1) Lie Algebra of the Fermion Operators

The extended supersymmetric (SUSY) sigma-model has been proposed on the bases of SO(2N+1) Lie algebra spanned by fermion annihilation-creation operators and pair operators. The canonical transformation, extension of an SO(2N) Bogoliubov transformation to an SO(2N+1) group, is introduced. Embedding the SO(2N+1) group into an SO(2N+2) group and using SO(2N+2)/U(N+1) coset variables, we have investigated the SUSY sigma-model on the Kaehler manifold, the coset space SO(2N+2)/U(N+1). We have constructed the Killing potential, extension of the potential in the SO(2N)/U(N) coset space to that in the SO(2N+2)/U(N+1) coset space. It is equivalent to the generalized density matrix whose diagonal-block part is related to a reduced scalar potential with a Fayet-Ilipoulos term. The f-deformed reduced scalar potential is optimized with respect to vacuum expectation value of the sigma-model fields and a solution for one of the SO(2N+1) group parameters has been obtained. The solution, however, is only a small part of all solutions obtained from anomaly-free SUSY coset models. To construct the coset models consistently, we must embed a coset coordinate in an anomaly-free spinor representation (rep) of SO(2N+2) group and give corresponding Kaehler and Killing potentials for an anomaly-free SO(2N+2)/U(N+1) model based on each positive chiral spinor rep. Using such mathematical manipulation we construct successfully the anomaly-free SO(2N+2)/U(N+1) SUSY sigma-model and investigate new aspects which have never been seen in the SUSY sigma-model on the Kaehler coset space SO(2N)/U(N). We reach a f-deformed reduced scalar potential. It is minimized with respect to the vacuum expectation value of anomaly-free SUSY sigma-model fields. Thus we find an interesting f-deformed solution very different from the previous solution for an anomaly-free SO(2.5+2)/(SU(5+1)*U(1)) SUSY sigma-model.Comment: 24 pages, no fiure

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 $c>25$ 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

The partition bundle of type A_{N-1} (2, 0) theory

Six-dimensional (2, 0) theory can be defined on a large class of six-manifolds endowed with some additional topological and geometric data (i.e. an orientation, a spin structure, a conformal structure, and an R-symmetry bundle with connection). We discuss the nature of the object that generalizes the partition function of a more conventional quantum theory. This object takes its values in a certain complex vector space, which fits together into the total space of a complex vector bundle (the `partition bundle') as the data on the six-manifold is varied in its infinite-dimensional parameter space. In this context, an important role is played by the middle-dimensional intermediate Jacobian of the six-manifold endowed with some additional data (i.e. a symplectic structure, a quadratic form, and a complex structure). We define a certain hermitian vector bundle over this finite-dimensional parameter space. The partition bundle is then given by the pullback of the latter bundle by the map from the parameter space related to the six-manifold to the parameter space related to the intermediate Jacobian.Comment: 15 pages. Minor changes, added reference

Stringy Instantons in SU(N) N=2 Non-Conformal Gauge Theories

In this paper we explicitly obtain the leading corrections to the SU(N) N=2 prepotential due to stringy instantons both in flat space-time and in the presence of a non-trivial graviphoton background field. We show that the stringy corrections to the prepotential are expressible in terms of the elementary symmetric polynomials. For N>2 the theory is not conformal; we discuss the introduction of an explicit dependence on the string scale \alpha' in the low-energy effective action through the stringy non-perturbative sector.Comment: 22 pages, 1 figur

Continuity properties of measurable group cohomology

A version of group cohomology for locally compact groups and Polish modules has previously been developed using a bar resolution restricted to measurable cochains. That theory was shown to enjoy analogs of most of the standard algebraic properties of group cohomology, but various analytic features of those cohomology groups were only partially understood. This paper re-examines some of those issues. At its heart is a simple dimension-shifting argument which enables one to `regularize' measurable cocycles, leading to some simplifications in the description of the cohomology groups. A range of consequences are then derived from this argument. First, we prove that for target modules that are Fr\'echet spaces, the cohomology groups agree with those defined using continuous cocycles, and hence they vanish in positive degrees when the acting group is compact. Using this, we then show that for Fr\'echet, discrete or toral modules the cohomology groups are continuous under forming inverse limits of compact base groups, and also under forming direct limits of discrete target modules. Lastly, these results together enable us to establish various circumstances under which the measurable-cochains cohomology groups coincide with others defined using sheaves on a semi-simplicial space associated to the underlying group, or sheaves on a classifying space for that group. We also prove in some cases that the natural quotient topologies on the measurable-cochains cohomology groups are Hausdorff.Comment: 52 pages. [Nov 22, 2011:] Major re-write with Calvin C. Moore as new co-author. Results from previous version strengthened and several new results added. [Nov 25, 2012:] Final version now available at springerlink.co

Refined topological amplitudes in N=1 flux compactification

We study the implication of refined topological string amplitudes in the supersymmetric N=1 flux compactification. They generate higher derivative couplings among the vector multiplets and graviphoton with generically non-holomorphic moduli dependence. For a particular term, we can compute them by assuming the geometric engineering. We claim that the Dijkgraaf-Vafa large N matrix model with the beta-ensemble measure directly computes the higher derivative corrections to the supersymmetric effective action of the supersymmetric N=1$ gauge theory.Comment: 16 pages, v2: reference adde

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

The effect of regional citrate anti-coagulation on the coagulation system in critically ill patients receiving continuous renal replacement therapy for acute kidney injury - An observational cohort study

BACKGROUND: Regional anticoagulation with citrate is the recommended first line treatment for patients receiving continuous renal replacement therapy (CRRT). There is wide variability in filter patency which may be due to differences in patient characteristics and local practice. It is also possible that citrate has effects on primary and secondary haemostasis, fibrinolysis and platelet function that are still unknown. The primary aim of the study is to describe the effect of citrate on coagulation and fibrinolysis pathways in both the patient and the haemodialysis circuit. METHODS: The study will recruit 12 adult patients admitted to the intensive care unit, requiring CRRT with regional citrate anticoagulation for acute kidney injury. Patients with pre-existing thrombotic or bleeding tendencies will be excluded. Thrombin generation, clot lysis and platelet function will be measured at baseline and at 12, 24, 36, 48 and 72 h after commencing CRRT (from the patient and from the circuit). We will describe the evolution of parameters over time as well as the differences in parameters between the patient and the circuit. DISCUSSION: The study will provide new data on the effects of citrate during continuous renal replacement therapy which is not currently available. We will minimise confounding factors through the use of tight exclusion criteria and accept that this will slow down recruitment. Depending on the results, we hope to incorporate the findings into existing clinical guidelines and clinical practice with the aim to prevent premature filter clotting and interruptions in treatment. TRIAL REGISTRATION: The study was registered with clinicaltrials.gov on 10th June 2015 (NCT02486614)

GLSMs for non-Kahler Geometries

We identify a simple mechanism by which H-flux satisfying the modified Bianchi identity arises in garden-variety (0,2) gauged linear sigma models. Taking suitable limits leads to effective gauged linear sigma models with Green-Schwarz anomaly cancellation. We test the quantum-consistency of a class of such effective theories by constructing an off-shell superconformal algebra, providing evidence that these models run to good CFTs in the deep IR.Comment: 37 pages, Minor updates for v