Bubbling solutions of mixed type for a general non-Abelian Chern–Simons–Higgs system of rank 2 over a torus

We show that self-dual Nielsen-Olesen (NO) vortices in three dimensions give rise to a class of exact solutions when coupled to Einstein-Maxwell-Dilaton gravity obeying the Majumdar-Papapetrou (MP) relation between gravitational and Maxwell couplings, provided certain types of Chern-Simons interactions are present. The metric may be solved explicitly in terms of the NO vortex function and becomes degenerate at scales [Formula: see text] where lS is the vortex core size and lp the Planck length. For typical lS≥104lp the horizon is thus pushed out to exponentially large scales. In the intermediate asymptotic region (IAR) lS≪r≪rH there is a logarithmic deviation of the metric from the flat metric and of the electric field from that of a point charge (which makes it decrease slower than r−1: hence the prefix hyper). In the IAR, the ADM energy and charge integrals increase logarithmically with the distance from the core region and finally diverge at the signature change horizon. String solutions in 4+p dimensions are obtained by replacing the Maxwell field with an antisymmetric tensor field (of rank 2+p) and have essentially similar properties with [Formula: see text] and with the antisymmetric charge playing the role of the topological electric charge.

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Bootstrapping BPS spectra of 5d/6d field theories

Journal of High Energy Physics ◽

10.1007/jhep04(2021)161 ◽

2021 ◽

Vol 2021 (4) ◽

Author(s):

Hee-Cheol Kim ◽

Minsung Kim ◽

Sung-Soo Kim ◽

Ki-Hong Lee

Keyword(s):

Gauge Theory ◽

Systematic Approach ◽

Field Theories ◽

Geometric Description ◽

Superconformal Field Theories ◽

Significant Generalization ◽

Rank 2 ◽

Bps Spectrum ◽

Chern Simons ◽

Kaluza Klein

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 $$ \hat{\mathrm{\mathbb{C}}} $$ 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 $$ \mathcal{N} $$ 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.

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