Abstract
We propose a systematic approach to computing the BPS spectrum of any 5d/6d supersymmetric quantum field theory in Coulomb phases, which admits either gauge theory descriptions or geometric descriptions, based on the Nakajima-Yoshioka’s blowup equations. We provide a significant generalization of the blowup equation approach in terms of both properly quantized magnetic fluxes on the blowup hat{mathrm{mathbb{C}}} 2 and the effective prepotential for 5d/6d field theories on the Omega background which is uniquely determined by the Chern-Simons couplings on their Coulomb branches. We employ our method to compute BPS spectra of all rank-1 and rank-2 5d Kaluza-Klein (KK) theories descending from 6d mathcal{N} = (1, 0) superconformal field theories (SCFTs) compactified on a circle with/without twist. We also discuss various 5d SCFTs and KK theories of higher ranks, which include a few exotic cases such as new rank-1 and rank-2 5d SCFTs engineered with frozen singularity as well as the 5d SU(3)8 gauge theory currently having neither a brane web nor a smooth shrinkable geometric description. The results serve as non-trivial checks for a large class of non-trivial dualities among 5d theories and also as independent evidences for the existence of certain exotic theories.
Highlights
Supersymmetric theories with eight supercharges in five and six dimensions are a very rich subject that has been investigated over the past decades
We propose a systematic approach to computing the BPS spectrum of any 5d/6d supersymmetric quantum field theory in Coulomb phases, which admits either gauge theory descriptions or geometric descriptions, based on the Nakajima-Yoshioka’s blowup equations
We provide a significant generalization of the blowup equation approach in terms of both properly quantized magnetic fluxes on the blowup C 2 and the effective prepotential for 5d/6d field theories on the Omega background which is uniquely determined by the Chern-Simons couplings on their Coulomb branches
Summary
Supersymmetric theories with eight supercharges in five and six dimensions are a very rich subject that has been investigated over the past decades. There exist some 5d/6d gauge theories, for instance, the 5d SU(3) gauge theory, that currently have neither ADHM constructions nor shrinkable geometric descriptions nor associated 5brane webs, so that all the computational methods introduced above including the blowup method cannot be used to compute their BPS partition functions. We will generalize the Nakajima-Yoshioka’s blowup equations in [80] to arbitrary 5d/6d gauge theories (including quiver gauge theories and twisted circle compactifications of 6d theories) with matter fields in arbitrary representations, and extend the work of [85, 86] for a geometric application of the blowup equations to any local Calabi-Yau 3-folds (including elliptic and non-toric ones) based on novel geometric constructions of 5d SCFTs/KK theories introduced in [11, 17].
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
