相关论文: Three Applications of Instanton Numbers
There exists a recursive algorithm for constructing BPST-type multi-instantons on commutative R^4. When deformed noncommutatively, however, it becomes difficult to write down non-singular instanton configurations with topological charge…
An instanton homology is constructed for webs and foams, using gauge theory with structure group SU(3), adapting previous work of the authors for the SO(3) case. Skein exact triangles are established, and using an eigenspace decomposition…
I prove connectedness of the moduli space $\mathcal M_n$ of $SU(2)$ instantons on $S^3\times S^1$ with charge $n$.
We study generalized anti-self-dual instantons defined over Riemannian manifolds equipped with a parallel codimension-$4$ differential form. In particular, for product Riemannian manifolds possessing such a form, we study dimension…
Extreme events play a crucial role in fluid turbulence. Inspired by methods from field theory, these extreme events, their evolution and probability can be computed with help of the instanton formalism as minimizers of a suitable action…
We develop a monotone, two-scale discretization for a class of integrodifferential operators of order $2s$, $s \in (0,1)$. We apply it to develop numerical schemes, and derive pointwise convergence rates, for linear and obstacle problems…
We present calculations of the size distribution of instantons in the 2d O(3) non-linear sigma-model, and briefly discuss the effects cooling has upon the configurations and the topological objects. (This preprint is also available via…
In order to optimize cooling as a technique to study the instanton content of the QCD vacuum, we have studied the effects of alternative algorithms, improved actions and boundary conditions on the evolution of single instantons and…
This paper is devoted to the study of the uniformization of the moduli space of pairs (X, E) consisting of an algebraic curve and a vector bundle on it. For this goal, we study the moduli space of 5-tuples (X, x, z, E, \phi), consisting of…
We generalize Nakajima-Yoshioka blowup equations to arbitrary gauge group with hypermultiplets in arbitrary representations. Using our blowup equations, we compute the instanton partition functions for 4d N=2 and 5d N=1 gauge theories for…
We investigate the distribution of instanton sizes in the framework of a simplified model for ensembles of instantons. This model takes into account the non-diluteness of instantons. The infrared problem for the integration over instanton…
We study aspects of worldsheet instantons relevant to a heterotic standard model. The non-simply connected Calabi-Yau threefold used admits Z_3 x Z_3 Wilson lines, and a more detailed investigation shows that the homology classes of curves…
We construct a conformally invariant vector bundle connection such that its equation of parallel transport is a first order system that gives a prolongation of the conformal Killing equation on differential forms. Parallel sections of this…
We compute the instanton partition function for ${\cal N}=4$ U(N) gauge theories living on toric varieties, mainly of type $\R^4/\Gamma_{p,q}$ including $A_{p-1}$ or $O_{\PP_1}(-p)$ surfaces. The results provide microscopic formulas for the…
We use the approach used by Eguchi-Hanson in constructing four-dimensional instanton metrics and construct a class of regular six-dimensional instantons which are nothing but $S^2\times S^2$ resolved conifolds. We then also obtain D3-brane…
We use stable maps, and their stable lifts to the Semple bundle variety of second-order curvilinear data, to calculate certain characteristic numbers for rational plane curves. These characteristic numbers involve first-order (tangency) and…
We review how instanton solutions at finite temperature can be seen as boundstates of constituent monopoles, discuss some speculations concerning their physical relevance and the lattice evidence for their presence in a dynamical context.
We study Lelong numbers and integrability indices for $S^1$-invariant singular metrics on vector bundles over the disk.
Building on our previous work [2109.01110], we will compute a new kind of $G_2$ instanton partition function. By doing so, we complete a set of building blocks of the instanton partition function associated with a large class of $G_2$…
We use mirror symmetry to determine and sum up a class of membrane instanton corrections to the hypermultiplet moduli space metric arising in Calabi-Yau threefold compactifications of type IIA strings. These corrections are mirror to the D1…