Related papers: A Compact Expression for Periodic Instantons
We construct a large class of periodic instantons. Conjecturally we produce all periodic instantons. This confirms a conjecture of Garland and Murray that relates periodic instantons to orbits of the loop group acting on an extension of its…
We reconsider the large $N$ asymptotics of Harish-Chandra-Itzykson-Zuber integrals. We provide, using Dyson's Brownian motion and the method of instantons, an alternative, transparent derivation of the Matytsin formalism for the unitary…
We continue our study of the noncommutative algebraic and differential geometry of a particular class of deformations of toric varieties, focusing on aspects pertinent to the construction and enumeration of noncommutative instantons on…
This thesis is designed for a comprehensive review of noncommutative (BPS) solitons with applications to D-brane dynamics including our works. We focus on noncommutative instantons and monopoles and study various aspects of the exact…
Self-dual Yang-Mills instantons on $R^4$ correspond to algebraic ADHM data. The ADHM equations for $S^1$-symmetric instantons give a one-dimensional integrable lattice system, which may be viewed as an discretization of the Nahm equations.…
We construct all instantons for the \nlsig\ on a cylinder, known not to exist on a finite time interval. We show that the widest instantons go through sphalerons. A re-interpretation of moduli-space transforms the scale parameter $\rho$ to…
We present a systematic derivation of multi-instanton amplitudes in terms of ADHM equivariant cohomology. The results rely on a supersymmetric formulation of the localization formula for equivariant forms. We examine the cases of N=4 and…
The Hermitian Yang-Mills equations on certain vector bundles over Calabi-Yau cones can be reduced to a set of matrix equations; in fact, these are Nahm-type equations. The latter can be analysed further by generalising arguments of…
We introduce a general method to engineer arbitrary Hamiltonians in the Floquet phase space of a periodically driven oscillator, based on the non-commutative Fourier transformation (NcFT) technique. We establish the relationship between an…
It is shown that periodic instanton solutions may have bifurcations which qualitatively change the behaviour of the finite temperature transition rate. These bifurcations are studied numerically in a quantum mechanical model and in the…
Gravitational instantons of Bianchi type IX space are constructed in Ashtekar's canonical formalism. Instead of solving the self-duality condition, we fully solve the constraint on the ``initial surface'' and ``Hamiltonian equations''. This…
We study the moduli space of self-dual instantons on $\mathbb{C}P^2$. These are described by an ADHM-like construction which allows to compute the Hilbert series of the moduli space. The latter has been found to be blind to certain compact…
The instanton equations on vector bundles over Calabi-Yau and hyper-K\"ahler cones can be reduced to matrix equations resembling Nahm's equations. We complement the discussion of Hermitian Yang-Mills (HYM) equations on Calabi-Yau cones,…
This is a mini-review about generalized instantons of noncommutative gauge theories in dimensions 4, 6 and 8, with emphasis on their realizations in type II string theory, their geometric interpretations, and their applications to the…
Quantum properties of a (1+1)-dimensional scalar theory on a cylinder with a compact spatial part, namely, $0\leq x\leq L$, are considered. In particular, quantum theory around the classical periodic field configurations is studied and the…
We develop a worldline-instanton approach for calculating the momentum spectrum of particles produced by gravitational fields which depend on both space and time. The instantons are open. The middle part is complex and describes the…
We consider an eight-dimensional local octonionic theory with the seven-sphere playing the role of the gauge group. Duality conditions for two- and four-forms in eight dimensions are related. Dual fields--octonionic instantons--solve an 8D…
We provide a step-by-step method to construct skyrmions from instanton ADHM data, including when the exact ADHM data is unknown. The configurations look like clusters of smaller skyrmions, and can be used to build manifolds of skyrmions…
We study doubly-periodic instantons, i.e. instantons on the product of a 1-dimensional complex torus T with a complex line C, with quadratic curvature decay. We determine the asymptotic behaviour of these instantons, constructing new…
We generalise recent results on Hopf instantons in a Chern--Simons and Fermion theory in a fixed background magnetic field. We find that these instanton solutions have to obey the Liouville equation in target space. As a consequence, these…