We study theories with sixteen supercharges and a discrete energy spectrum. One class of theories has symmetry group SU(2|4). They arise as truncations of N = 4 super Yang Mills. They include the plane wave matrix model, 2+1 super Yang Mills on R × S2 and N = 4 super Yang Mills on R × S/Zk. We explain how to obtain their gravity duals in a unified way. We explore the regions of the geometry tha...

We proved a uniqueness theorem of tangent connections for a Yang–Mills connection with an isolated singularity with a quadratic growth of the curvature at the singularity. We also obtained control over the rate of the asymptotic convergence of the connection to the tangent connection if furthermore the connection is stationary or the tangent connection is integrable, with a stronger result in t...

We consider the Einstein/Yang-Mills equations in 3 + 1 space time dimensions with SU(2) gauge group and prove rigorously the existence of a globally defined smooth static solution. We show that the associated Einstein metric is asymp-totically flat and the total mass is finite. Thus, for non-abelian gauge fields the Yang/Mills repulsive force can balance the gravitational attractive force and p...

Perturbiner, that is, the solution of field equations which is a generating function for tree form-factors in N = 3 (N = 4) supersymmetric Yang-Mills theory, is studied in the framework of twistor formulation of the N = 3 superfield equations. In the case, when all one-particle asymptotic states belong to the same type of N = 3 supermultiplets (without any restriction on kinematics), the soluti...

We show that the QCD vacuum (without dynamical quarks) is a dual supercon-ductor at least in the low-energy region in the sense that monopole condensation does really occur. In fact, we derive the dual Ginzburg-Landau theory (i.e., dual Abelian Higgs model) directly from the SU(2) Yang-Mills theory by adopting the maximal Abelian gauge. The dual superconductor can be on the border between type ...

We present a lattice formulation of noncommutative Yang-Mills theory in arbitrary even dimensionality. The UV/IR mixing characteristic of noncommutative field theories is demonstrated at a completely nonperturbative level. We prove a discrete Morita equivalence between ordinary Yang-Mills theory with multi-valued gauge fields and noncommutative Yang-Mills theory with periodic gauge fields. Usin...

We show that a recently proposed Yang-Mills matrix model with an auxiliary field, which is a candidate for a non-perturbative description of type IIB superstrings, captures the Euler characteristic of moduli space of Riemann surfaces. This happens at the saddle point for the Yang-Mills field. It turns out that the large-n limit in this matrix model corresponds to a double scaling limit in the P...

We consider SU(N) Yang-Mills theory on the space R×S3 with Minkowski signature (−+++). The condition of SO(4)-invariance imposed on gauge fields yields a bosonic matrix model which is a consistent truncation of the plane wave matrix model. For matrices parametrized by a scalar φ, the Yang-Mills equations are reduced to the equation of a particle moving in the double-well potential. The classica...

Perturbiner, that is, the solution of field equations which is a generating function for tree form-factors in N = 3 (N = 4) supersymmetric Yang-Mills theory, is studied in the framework of twistor formulation of the N = 3 superfield equations. In the case, when all one-particle asymptotic states belong to the same type of N = 3 supermultiplets (without any restriction on kinematics), the soluti...

We study a class of lattice field theories in two dimensions that includes gauge theories. Given a two dimensional orientable surface of genus g, the partition function Z is defined for a triangulation consisting of n triangles of area ǫ. The reason these models are called quasi-topological is that Z depends on g, n and ǫ but not on the details of the triangulation. They are also soluble in the...