Related papers: Exceptional SW Geometry from ALE Fibrations

Vafa-Witten (VW) theory is a topologically twisted version of N=4 supersymmetric Yang-Mills theory. S-duality suggests that the partition function of VW theory with gauge group SU(N) transforms as a modular form under duality…

We survey some of the AGT relations between N=2 gauge theories in four dimensions and geometric representations of symmetry algebras of two-dimensional conformal field theory on the equivariant cohomology of their instanton moduli spaces.…

We generalize S-duality to N=2 superconformal field theories (SCFTs) with Coulomb branch operators of non-integer scaling dimension. As simple examples, we find minimal generalizations of the S-dualities discovered in SU(2) gauge theory…

We present a self-contained review of the Plane-wave/super-Yang-Mills duality, which states that strings on a plane-wave background are dual to a particular large R-charge sector of N=4, D=4 superconformal U(N) gauge theory. This duality is…

We review the generalization of the work of Seiberg and Witten on N=2 supersymmetric SU(2) Yang-Mills theory to SU(n) gauge groups. The quantum moduli spaces of the effective low energy theory parametrize a special family of hyperelliptic…

The effective action of N=2 Yang-Mills theory with adjoint matter is shown to be governed by an integrable spin model with spectral parameter on an elliptic curve. We sketch a route to deriving this effective dynamics from the underlying…

We give a new description of classical Yang-Mills theory by coupling a two-dimensional chiral CFT (which gives the tree-level S-matrix of Yang-Mills theory at genus zero) to a background non-abelian gauge field. The resulting model is…

Starting with minimal requirements from the physical experience with higher gauge theories, i.e. gauge theories for a tower of differential forms of different form degrees, we discover that all the structural identities governing such…

We study the quantum Seiberg-Witten (SW) curves for $(A_1, G)$-type Argyres-Douglas (AD) theory by taking the scaling limit of the quantum SW curve of $N=2$ gauge theory with gauge group $G$. For $G=A_r$, the quantum SW curve of the AD…

We derive an effective Abelian gauge theory (EAGT) of a modified SU(2) Yang-Mills theory. The modification is made by explicitly introducing mass terms of the off-diagonal gluon fields into pure SU(2) Yang-Mills theory, in order that…

A class of new nonabelian gauge theories for vector fields on three manifolds is presented. The theories describe a generalization of three-dimensional Yang-Mills theory featuring a novel nonlinear gauge symmetry and field equations for…

Recently Alday, Gaiotto and Tachikawa have proposed relation between 2- and 4-dimensional conformal field theories. The relation implies that the Nekrasov partition functions of N=2 superconformal gauge theories are equal to conformal…

We show that recently formulated four-dimensional self-dual supersymmetric Yang-Mills theory, which is consistent background for open $~N=2$~ superstring, generates two-dimensional $~N=(1,1),~\, N=(1,0) $~ and $~N=(2,0)$~ supersymmetric…

Employing the nonabelian duality transformation, I derive the Gauge String form of certain D>=3 lattice Yang-Mills (YM_{D}) theories in the strong coupling (SC) phase. With the judicious choice of the actions, in D>=3 our construction…

We study the topologically twisted compactification of the 6d $(2,0)$ M5-brane theory on an elliptically fibered K\"ahler three-fold preserving two supercharges. We show that upon reducing on the elliptic fiber, the 4d theory is…

Using simple symmetry arguments we classify the ungauged $D=4$, $\mathcal{N}=2$ supergravity theories, coupled to both vector and hyper multiplets through homogeneous scalar manifolds, that can be built as the product of $\mathcal{N}=2$ and…

We show how Higgs mechanism for non-abelian N=2 gauge theories in four dimensions is geometrically realized in the context of type II strings as transitions among compactifications of Calabi-Yau threefolds. We use this result and T-duality…

We consider the global aspects of the 6-dimensional $\mathcal{N}=(1, 0)$ theory arising from the coupling of the vector multiplet to the tensor multiplet. We show that the Yang-Mills field and its dual, when both are abelianized, combine to…

We conjecture that $W$ gravity can be interpreted as the gauge theory of $\phi$ diffeomorphisms in the space of dimensionally-reduced $D=2+2$ $SU^*(\infty)$ Yang-Mills instantons. These $\phi$ diffeomorphisms preserve a volume-three form…

Lie algebroid Yang-Mills theories are a generalization of Yang-Mills gauge theories, replacing the structural Lie algebra by a Lie algebroid E. In this note we relax the conditions on the fiber metric of E for gauge invariance of the action…