Related papers: HyperK\"ahler quotients and N=4 gauge theories in …
We consider N=2 and N=4 supersymmetric gauge theories in two-dimensions, coupled to matter multiplets. In analogy with the N=2 case also in the N=4 case one can introduce Fayet-Iliopoulos terms.The associated three-parameters have the…
We present theories of N=2 hypermultiplets in four spacetime dimensions that are invariant under rigid or local superconformal symmetries. The target spaces of theories with rigid superconformal invariance are (4n)-dimensional {\it special}…
An overview of matter-coupled ${\cal N}=2$ supergravity theories with 8 real supercharges, in 4,5 and 6 dimensions is given. The construction of the theories by superconformal methods is explained from basic principles. Special geometry is…
Using superspace techniques we construct the general theory describing D=4, N=2 supergravity coupled to an arbitrary number of vector and scalar--tensor multiplets. The scalar manifold of the theory is the direct product of a special…
We consider a general class of symmetries of hyper-Kahler quotients which can be interpreted as classical analogs of Seiberg duality for N=2 supersymmetric quiver gauge theories in the baryonic Higgs branch. Along the way we find that a…
The geometric models of N=4 supersymmetric mechanics with $(2d.2d)_{\DC}$-dimensional phase space are proposed, which can be viewed as one-dimensional counterparts of two-dimensional N=2 supersymmetric sigma-models by Alvarez-Gaum\'e and…
The properties of supersymmetric gauge theories in the Higgs phase at low energies can appropriately be studied by means of a non-linear sigma model, which has the target space being Kahler for N=1 supersymmetric models and hyperKahler for…
According to the proposal of Hanany and Witten, Coulomb branches of N=4 SU(n) gauge theories in three dimensions are isometric to moduli spaces of BPS monopoles. We generalize this proposal to gauge theories with matter, which allows us to…
In this note we construct rigidly supersymmetric gauged sigma models and gauge theories on certain Einstein four-manifolds, and discuss constraints on these theories. In work elsewhere, it was recently shown that on some nontrivial Einstein…
Due to its rich structure and close connection with gauge theory, hyperk\"ahler manifolds have attracted increasing interest. Using infinite dimensional hyperk\"ahler reduction, Kronheimer proved that certain adjoint orbits of complexified…
Non-compact hyperk\"ahler spaces arise frequently in gauge theory. The 4-dimensional hyperk\"ahler ALE spaces are a special class of non-compact hyperk\"ahler spaces. They are in one-to-one correspondence with the finite subgroups of SU(2)…
We construct novel $7d$ supersymmetric gauge theories which include a Chern-Simons-like term on curved spaces. In order to so, we examine the supersymmetry constraints for E7-branes in type IIA$^*$ theory, rather than making use of an…
We construct N=1 supersymmetric versions of four-dimensional Freedman-Townsend models and generalizations thereof found recently by Henneaux and Knaepen, with couplings between 1-form and 2-form gauge potentials. The models are presented…
We present the exact effective superpotentials in $4d$, $N=1$ supersymmetric $SU(2)$ gauge theories with $N_3$ triplets and $N_2$ doublets of matter superfields. For the theories with a single triplet matter superfield we present the exact…
We develop a graphical representation of polynomial invariants of unitary gauge groups, and use it to find the algebraic curve corresponding to a hyperkahler quotient of a linear space. We apply this method to four dimensional ALE spaces,…
Using the N=4, 1D harmonic superspace approach, we construct a new type of N=4 supersymmetric mechanics involving 4n-dimensional Quaternion-K\"ahler (QK) 1D sigma models as the bosonic core. The basic ingredients of our construction are…
The two-dimensional gauged linear sigma model has provided a physical model for the quantum cohomology of a K\"ahler manifold, $X$. A three-dimensional version of such construction has recently been shown to shed light on models of quantum…
We use the manifestly N=2 supersymmetric, off-shell, harmonic (or twistor) superspace approach to solve the constraints implied by four-dimensional N=2 superconformal symmetry on the N=2 non-linear sigma-model target space, known as the…
As shown by Witten the N=1 supersymmetric gauged WZW model based on a group G has an extended N=2 supersymmetry if the gauged subgroup H is so chosen that G/H is Kahler. We extend Witten's result and prove that the N=1 supersymmetric gauged…
We analyse the geometry of four-dimensional bosonic manifolds arising within the context of $N=4, D=1$ supersymmetry. We demonstrate that both cases of general hyper-K\"ahler manifolds, i.e. those with translation or rotational isometries,…