Mirror symmetry by O3-planes

TL;DR

This work derives three-dimensional N=4 mirror pairs for orthogonal and symplectic gauge groups using O3-plane brane constructions, leveraging brane splitting and S-duality to map Coulomb and Higgs branches. It introduces precise splitting rules for D5- and NS-branes on O3-planes, which lead to nontrivial strong-coupling predictions for certain IR fixed points and reveal hidden FI-terms and symmetry enhancements. The authors present detailed mirrors for Sp(k), Sp'(k), SO(2k), and SO(2k+1), including elliptic and non-elliptic two-gauge-factor models, and demonstrate cases where different theories share the same infrared mirror. These results expand the catalog of 3d N=4 mirror pairs and provide testable predictions, notably via Seiberg-Witten curves, and illuminate subtle IR dualities beyond known U(N) cases.

Abstract

We construct the three dimensional mirror theory of SO(2k) and SO(2k+1) gauge groups by using O3-planes. An essential ingredient in constructing the mirror is the splitting of a physical brane (NS-brane or D5-brane) on O3-planes. In particular, matching the dimensions of moduli spaces of mirror pair (for example, the SO(2k+1) and its mirror) there is a D3-brane creation or annihilation accompanying the splitting. This novel dynamical process gives a nontrivial prediction for strongly coupled field theories, which will be very interesting to check by Seiberg-Witten curves. Furthermore, applying the same idea, we revisit the mirror theory of Sp(k) gauge group and find new mirrors which differ from previously known results. Our new result for Sp(k) gives another example to a previously observed fact, which shows that different theories can be mirror to the same theory. We also discussed the phenomena such as "hidden FI-parameters" when the number of flavors and the rank of the gauge group satisfy certain relations, ``incomplete Higgsing'' for the mirror of SO(2k+1) and the ``hidden global symmetry''. After discussing the mirror for a single Sp or SO gauge group, we extend the study to a product of two gauge groups in two different models, namely the elliptic and the non-elliptic models.