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Register a new userN=2 supersymmetric gauge theory on connected sums of $S^2times S^2$
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We construct 4D $mathcal{N}=2$ theories on an infinite family of 4D toric manifolds with the topology of connected sums of $S^2 times S^2$. These theories are constructed through the dimensional reduction along a non-trivial $U(1)$-fiber of 5D theories on toric Sasaki-Einstein manifolds. We discuss the conditions under which such reductions can be carried out and give a partial classification result of the resulting 4D manifolds. We calculate the partition functions of these 4D theories and they involve both instanton and anti-instanton contributions, thus generalizing Pestuns famous result on $S^4$.
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A solution to the infinite coupling problem for N=2 conformal supersymmetric gauge theories in four dimensions is presented. The infinitely-coupled theories are argued to be interacting superconformal field theories (SCFTs) with weakly gauged flavor groups. Consistency checks of this proposal are found by examining some low-rank examples. As part of these checks, we show how to compute new exact quantities in these SCFTs: the central charges of their flavor current algebras. Also, the isolated rank 1 E_6 and E_7 SCFTs are found as limits of Lagrangian field theories.
We investigate the Wilson line correlators dual to supergravity multiplets in N=4 non-commutative gauge theory on S^2 x S^2. We find additional non-analytic contributions to the correlators due to UV/IR mixing in comparison to ordinary gauge theory. Although they are no longer BPS off shell, their renormalization effects are finite as long as they carry finite momenta. We propose a renormalization procedure to obtain local operators with no anomalous dimensions in perturbation theory. We reflect on our results from dual supergravity point of view. We show that supergravity can account for both IR and UV/IR contributions.
Strings in $mathcal{N}=2$ supersymmetric ${rm U}(1)^N$ gauge theories with $N$ hypermultiplets are studied in the generic setting of an arbitrary Fayet-Iliopoulos triplet of parameters for each gauge group and an invertible charge matrix. Although the string tension is generically of a square-root form, it turns out that all existing BPS (Bogomolnyi-Prasad-Sommerfield) solutions have a tension which is linear in the magnetic fluxes, which in turn are linearly related to the winding numbers. The main result is a series of theorems establishing three different kinds of solutions of the so-called constraint equations, which can be pictured as orthogonal directions to the magnetic flux in ${rm SU}(2)_R$ space. We further prove for all cases, that a seemingly vanishing Bogomolnyi bound cannot have solutions. Finally, we write down the most general vortex equations in both master form and Taubes-like form. Remarkably, the final vortex equations essentially look Abelian in the sense that there is no trace of the ${rm SU}(2)_R$ symmetry in the equations, after the constraint equations have been solved.
In this paper we apply the previously derived formalism of permutation orbifold conformal field theories to N=2 supersymmetric minimal models. By interchanging extensions and permutations of the factors we find a very interesting structure relating various conformal field theories that seems not to be known in literature. Moreover, unexpected exceptional simple currents arise in the extended permuted models, coming from off-diagonal fields. In a few situations they admit fixed points that must be resolved. We determine the complete CFT data with all fixed point resolution matrices for all simple currents of all Z_2-permutations orbifolds of all minimal N=2 models with k eq 2 mod 4.
Holographic CFTs and holographic RG flows on space-time manifolds which are $d$-dimensional products of spheres are investigated. On the gravity side, this corresponds to Einstein-dilaton gravity on an asymptotically $AdS_{d+1}$ geometry, foliated by a product of spheres. We focus on holographic theories on $S^2times S^2$, we show that the only regular five-dimensional bulk geometries have an IR endpoint where one of the sphere shrinks to zero size, while the other remains finite. In the $Z_2$-symmetric limit, where the two spheres have the same UV radii, we show the existence of a infinite discrete set of regular solutions, satisfying an Efimov-like discrete scaling. The $Z_2$-symmetric solution in which both spheres shrink to zero at the endpoint is singular, whereas the solution with lowest free energy is regular and breaks $Z_2$ symmetry spontaneously. We explain this phenomenon analytically by identifying an unstable mode in the bulk around the would-be $Z_2$-symmetric solution. The space of theories have two branches that are connected by a conifold transition in the bulk, which is regular and correspond to a quantum first order transition. Our results also imply that $AdS_5$ does not admit a regular slicing by $S^2times S^2$.
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