The Volume of the Quiver Vortex Moduli Space
Kazutoshi Ohta, Norisuke Sakai

TL;DR
This paper derives an exact formula for the volume of vortex moduli spaces in quiver gauge theories on Riemann surfaces using supersymmetric localization and graph theory, revealing bounds and properties of these spaces.
Contribution
It introduces a novel contour integral formula for the moduli space volume in quiver gauge theories, generalizing Jeffrey-Kirwan residues and connecting to Bradlow bounds.
Findings
Exact volume formula derived via localization
Generalization of Jeffrey-Kirwan residue formula
Application to gauged non-linear sigma models
Abstract
We study the moduli space volume of BPS vortices in quiver gauge theories on compact Riemann surfaces. The existence of BPS vortices imposes constraints on the quiver gauge theories. We show that the moduli space volume is given by a vev of a suitable cohomological operator (volume operator) in a supersymmetric quiver gauge theory, where BPS equations of the vortices are embedded. In the supersymmetric gauge theory, the moduli space volume is exactly evaluated as a contour integral by using the localization. Graph theory is useful to construct the supersymmetric quiver gauge theory and to derive the volume formula. The contour integral formula of the volume (generalization of the Jeffrey-Kirwan residue formula) leads to the Bradlow bounds (upper bounds on the vorticity by the area of the Riemann surface divided by the intrinsic size of the vortex). We give some examples of various…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
