5D N=1 super QFT: symplectic quivers

TL;DR

This paper introduces a method to construct 5D N=1 super quantum field theories with symplectic gauge symmetry using Sasaki-Einstein manifolds and M-theory compactifications, expanding the class of known gauge models.

Contribution

It develops a novel approach to build 5D super QFTs with symplectic gauge groups from geometric and quiver symmetry considerations, extending existing models based on unitary groups.

Findings

Constructed 5D super QFTs with symplectic SP(2r,R) gauge symmetry.

Embedded these models in M-theory on specific Calabi-Yau threefolds.

Used outer-automorphism symmetries to derive BPS quivers with symplectic gauge invariance.

Abstract

We develop a method to build new 5D $\mathcal{N}=1$ gauge models based on Sasaki-Einstein manifolds $Y^{p,q}.$ These models extend the standard 5D ones having a unitary SU$\left( p\right) _{q}$ gauge symmetry based on $% Y^{p,q}$. Particular focus is put on the building of a gauge family with symplectic SP$\left( 2r,\mathbb{R}\right) $ symmetry. These super QFTs are embedded in M-theory compactified on folded toric Calabi-Yau threefolds $% \hat{X}(Y^{2r,0})$ constructed from conical $Y^{2r,0}$. By using outer-automorphism symmetries of 5D $\mathcal{N}=1$\textbf{\ }BPS quivers with unitary SU$\left( 2r\right) $ gauge invariance, we also construct BPS quivers with symplectic SP$\left( 2r,\mathbb{R}\right) $ gauge symmetry. Other related aspects are discussed. Keywords: SCFT$_{5}$, 5D $\mathcal{N}=1$ super QFT on a finite circle, Sasaki-Einstein manifolds, BPS quivers, outer-automorphisms.