Related papers: Singular Instantons and Painlev\'e VI
We test the $\mathbb{C}P^{N-1}$ sigma models for the Painlev\'e property. While the construction of finite action solutions ensures their meromorphicity, the general case requires testing. The test is performed for the equations in the…
The integrability (solvability via an associated single-valued linear problem) of a differential equation is closely related to the singularity structure of its solutions. In particular, there is strong evidence that all integrable…
Concordance invariants of knots are derived from the instanton homology groups with local coefficients, as introduced in earlier work of the authors. These concordance invariants include a 1-parameter family of homomorphisms $f_{r}$, from…
According to a recent classification of 6d (1,0) theories within F-theory there are only six "pure" 6d gauge theories which have a UV superconformal fixed point. The corresponding gauge groups are $SU(3),SO(8),F_4,E_6,E_7$, and $E_8$. These…
The critical and asymptotic behaviors of solutions of the sixth Painlev\'e equation, an their parametrization in terms of monodromy data, are synthetically reviewed. The explicit formulas are given. This paper has been withdrawn by the…
We classify $G_2$-instantons admitting $SU(2)^3$-symmetries, and construct a new family of examples on the spinor bundle of the 3-sphere, equipped with the asymptotically conical, co-homogeneity one $G_2$-metric of Bryant-Salamon. We also…
Instanton bundles on $\mathbb{P}^3$ have been at the core of the research in Algebraic Geometry during the last thirty years. Motivated by the recent extension of their definition to other Fano threefolds of Picard number one, we develop…
We construct instanton solutions on noncommutative Euclidean 4-space which are deformations of instanton solutions on commutative Euclidean 4-space. We show that the instanton numbers of these noncommutative instanton solutions coincide…
Mathematical instanton bundles on $ P_3$ have their analogues in rank--$2n$ instanton bundles on odd dimensional projective spaces $ P_{2n+1}$. The families of special instanton bundles on these spaces generalize the special 'tHooft bundles…
We study movable singularities of Garnier systems using the connection of the latter with isomonodromic deformations of Fuchsian systems. Questions on the existence of solutions for some inverse monodromy problems are also considered.
In this paper, we present new, unstable solutions, which we call quicksilver solutions, of a $q$-difference Painlev\'e equation in the limit as the independent variable approaches infinity. The specific equation we consider in this paper is…
This paper is an addendum to earlier papers \cite{R1,R2} in which it was shown that the unstable separatrix solutions for Painlev\'e I and II are determined by $PT$-symmetric Hamiltonians. In this paper unstable separatrix solutions of the…
We extend the instanton calculus for N=1/2 U(2) supersymmetric gauge theory by including one massless flavor. We write the equations of motion at leading order in the coupling constant and we solve them exactly in the non(anti)commutativity…
The sixth Painlev\'e equation is a basic equation among the non-linear differential equations with three fixed singularities, corresponding to Gauss's hypergeometric differential equation among the linear differential equations. It is known…
Gravitational instantons ''Lambda-instantons'' are defined here for any given value Lambda of the cosmological constant. A multiple of the Euler characteristic appears as an upper bound for the de Sitter action and as a lower bound for a…
We find a new class of N=2 massive IIA solutions whose internal spaces are S^2 fibrations over S^2 x S^2. These solutions appear naturally as massive deformations of the type IIA reduction of Sasaki-Einstein manifolds in M-theory, including…
We consider a family of four-dimensional non-linear sigma models based on an O(5) symmetric group, whose fields take their values on the 4-sphere S4. An SO(4)-subgroup of the model is gauged. The solutions of the model are characterised by…
On P3, we show that mathematical instantons in characteristic two are unobstructed. We produce upper bounds for the dimension of the moduli space of stable rank two bundles on P3 in characteristic two. In cases where there is a phenomenon…
We study self-dual SU(N) gauge field configurations on the 4 torus with twisted boundary conditions, known as fractional instantons. Focusing on the minimum non-zero action case, we generalize the constant field strength solutions…
Instantons, localised saddle points of the action, play an important role in describing non-perturbative aspects of quantum field theories, for example vacuum decay or violation of conservation laws associated with anomalous symmetries.…