nLab quaternionic Seiberg-Witten theory

Idea

Quaternionic Seiberg-Witten theory is the transfer of Seiberg-Witten theory from Riemannian 4-manifolds with spinᶜ structure to Riemannian 4-manifolds with a spinʰ structure.

Description

While usual Seiberg-Witten theory is based on the Lie group $Spin^\mathrm{c}(4)=U(2)\times_{U(1)}U(2)$, quaternionic Seiberg-Witten theory is based on the Lie group:

$$Spin^\mathrm{h}(4) \coloneqq\big(Spin(4)\times SU(2)\big)/\mathbb{Z}_2 \cong\big(SU(2)\times SU(2)\times SU(2)\big)/\{\pm(\mathbf{1}_2,\mathbf{1}_2,\mathbf{1}_2 )\}.$$

Related concepts

Articles about Seiberg-Witten theory:

• Ordinary theory: Seiberg-Witten equations, linearized Seiberg-Witten equations, Seiberg-Witten invariant, Seiberg-Witten moduli space, Seiberg-Witten flow
• Adapted theory: D=6 Seiberg-Witten theory, D=7 Seiberg-Witten theory (over G₂ manifolds), D=8 Seiberg-Witten theory (over Spin(7) manifolds), quaternionic Seiberg-Witten theory, pseudo-Riemannian Seiberg-Witten theory