59 citations · 223 across the 20 of their papers we have counts for
13 papers · 1 filter
The Kapustin-Witten equations and nonabelian Hodge theory
Chih-Chung Liu, Steven Rayan, Yuuji Tanaka
Arising from a topological twist of super Yang-Mills theory are the Kapustin-Witten equations, a family of gauge-theoretic equations on a four-manifold parametriz…
On orientations for gauge-theoretic moduli spaces
Dominic Joyce, Yuuji Tanaka, Markus Upmeier
Let be a compact manifold, a real elliptic operator on , a Lie group, a principal -bundle, and the infinite-dimensional moduli space of…
On the singular sets of solutions to the Kapustin-Witten equations and the Vafa-Witten ones on compact Kähler surfaces
Yuuji Tanaka
This article finds a structure of singular sets on compact Kahler surfaces, which Taubes introduced in the studies of the asymptotic analysis of solutions to the Kapustin-Witten eq…
A perturbation and generic smoothness of the Vafa-Witten moduli spaces on closed symplectic four-manifolds
Yuuji Tanaka
We prove a Freed-Uhlenbeck style generic smoothness theorem for the moduli space of solutions to the Vafa--Witten equations on a closed symplectic four-manifold by using a method d…
Seiberg-Witten type equations on compact symplectic 6-manifolds
Yuuji Tanaka
In this article, we consider a gauge-theoretic equation on compact symplectic 6-manifolds, which forms an elliptic system after gauge fixing. This can be thought of as a higher-dim…
Stable sheaves with twisted sections and the Vafa-Witten equations on smooth projective surfaces
Yuuji Tanaka
This article describes a Hitchin-Kobayashi style correspondence for the Vafa-Witten equations on smooth projective surfaces. This is an equivalence between a suitable notion of sta…
Some boundedness properties of solutions to the Vafa-Witten equations on closed four-manifolds
Yuuji Tanaka
We consider a set of gauge-theoretic equations on closed oriented four-manifolds, which was introduced by Vafa and Witten. The equations involve a triple consisting of a connection…
A stability of vector bundles with twisted sections and the Donaldson-Thomas instantons on compact Kähler threefolds
Yuuji Tanaka
We consider a version of Hermitian-Einstein equation but perturbed by a Higgs field with a solution called a Donaldson-Thomas instanton on compact Kähler threefolds. The equation c…
A removal singularity theorem of the Donaldson-Thomas instantons on compact Kähler threefolds
Yuuji Tanaka
We consider a perturbed Hermitian-Einstein equation, which we call the Donaldson-Thomas equation, on compact Kähler threefolds. In arXiv:0805.2195, we analysed some analytic proper…
A construction of Spin(7)-instantons
Yuuji Tanaka
Joyce constructed examples of compact eight-manifolds with holonomy Spin(7), starting with a Calabi-Yau four-orbifold with isolated singular points of a special kind. That construc…
The Donaldson-Thomas instantons on compact Kahler threefolds and a convergence
Yuuji Tanaka
The contents of this article are now presented in the appendix of arXiv:0805.2195v2.
A weak compactness theorem of the Donaldson-Thomas instantons on compact Kähler threefolds
Yuuji Tanaka
In arXiv:0805.2192, we set up a gauge-theoretic equation on symplectic 6-manifolds, which is a version of the Hermitian-Einstein equation perturbed by Higgs fields, and call Donald…
On the moduli space of Donaldson-Thomas instantons
Yuuji Tanaka
In alignment with a programme by Donaldson and Thomas [DT], Thomas [Th] constructed a deformation invariant for smooth projective Calabi-Yau threefolds, which is now called the Don…