Exact Results in 5D from Instantons and Deconstruction

All five-dimensional non-abelian gauge theories have a $U(1)_I$ global symmetry associated with instantonic particles. We describe an obstruction to coupling $U(1)_I$ to a classical background gauge field that occurs whenever the theory has a one-form center symmetry. This is a finite-order mixed 't Hooft anomaly between the two symmetries. We also show that a similar obstruction takes place in gauge theories with fundamental matter by studying twisted bundles for the ordinar...

We explore quantum states of instanton solitons in five dimensional noncommutative Yang-Mills theories. We start with maximally supersymmetric U(N) theory compactified on a circle S^1, and derive the low energy dynamics of instanton solitons, or calorons, which is no longer singular. Quantizing the low energy dynamics, we find N physically distinct ground states with a unit Pontryagin number and no electric charge. These states have a natural D-string interpretation. The conc...

We relate the non-perturbative exact results in supersymmetry to perturbation theory using several different methods: instanton calculations at weak or strong coupling, a method using gaugino condensation and another method relating strong and weak coupling. This allows many precise numerical checks of the consistency of these methods, especially the amplitude of instanton effects, and of the network of exact solutions in supersymmetry. However, there remain difficulties with...

Instantons and W-bosons in 5d maximally supersymmetric Yang-Mills theory arise from a circle compactification of the 6d (2,0) theory as Kaluza-Klein modes and winding self-dual strings, respectively. We study an index which counts BPS instantons with electric charges in Coulomb and symmetric phases. We first prove the existence of unique threshold bound state of (noncommutative) U(1) instantons for any instanton number, and also show that charged instantons in the Coulomb pha...

We refine a previous proposal for obtaining the multi-instanton partition function from the supersymmetric index of the 1d supersymmetric gauge theory on the worldline of D0-branes. We provide examples where the refinements are crucial for obtaining the correct result.

We discuss instanton operators in five-dimensional gauge theories. These are defined as disorder operators which create a non-vanishing second Chern class on a four-sphere surrounding their insertion point. As such they may be thought of as higher-dimensional analogues of three-dimensional monopole (or `t Hooft) operators. We argue that they play an important role in the enhancement of the Lorentz symmetry for maximally supersymmetric Yang-Mills to SO(1,5) at strong coupling.

Supersymmetric configurations of type II D-branes with nonzero gauge field strengths in general supersymmetric backgrounds with nonzero B fields are analyzed using the kappa-symmetric worldvolume action. It is found in dimension four or greater that the usual instanton equation for the gauge field obtains a nonlinear deformation. The deformation is parameterized by the topological data of the B-field, the background geometry and the cycle wrapped by the brane. In the appropri...

We describe a procedure for finding Kaluza-Klein monopole solutions in deconstructed four and five dimensional supersymmetric gauge theories. In the deconstruction of a four dimensional theory, the KK monopoles are finite-action solutions of the Euclidean equations of motion of the finite lattice spacing theory. The "lattice" KK monopoles can be viewed as constituents of continuum-limit four dimensional instantons. In the five dimensional case, the KK monopoles are static fin...

We discuss instantons in dimensions higher than four. A generalized self-dual or anti-self-dual instanton equation in n-dimensions can be defined in terms of a closed (n-4) form $\Omega$ and it was recently employed as a topological gauge fixing condition in higher dimensional generalizations of cohomological Yang-Mills theory. When $\Omega$ is a calibration which is naturally introduced on the manifold of special holomony, we argue that higher dimensional instanton may be lo...

It has recently been suggested that, in a large N limit, a particular four dimensional gauge theory is indistinguishable from the six dimensional CFT with (0,2) supersymmetry compactified on a torus. We give further evidence for this correspondence by studying the Seiberg-Witten curve for the "deconstructed" theory and demonstrating that along the reduced Coulomb branch of moduli space (on the intersection of the Higgs and Coulomb branches) it describes the low energy physics...