Emergent π©=3 and Frozen π©=2 SCFTs from π©=1 Gauge Theory
Abstract
Four-dimensional π©=3 superconformal field theories (SCFTs) are an exotic class of quantum field theories that admit no conventional Lagrangian description. In this Letter, we construct an π©=1 supersymmetric gauge theory and argue that its infrared fixed point exhibits supersymmetry enhancement to an π©=3 SCFT. The ultraviolet theory has gauge group SU(2)3, a set of chiral multiplets, and a suitable superpotential. By performing a-maximization, we obtain infrared central charges a=c=5/4, matching those of the rank-one π©=3 β€3 S-fold SCFT. The ultraviolet gauge-theory description allows us to compute the full superconformal index with four independent fugacities. We then examine various limits of the full index and further propose a closed-form expression for the Macdonald index, reproducing all known results for the proposed π©=3 theory. More remarkably, we argue that further gauging the π©=3 theory yields the frozen rank-one π©=2 SCFT conjectured from Seiberg--Witten geometry, providing strong evidence for its existence and unlocking its previously inaccessible full superconformal index. Our construction thus opens a systematic route to exploring the refined protected structure of these exotic, intrinsically strongly coupled theories using conventional π©=1 Lagrangian techniques.
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BibTeX
@misc{jiang2026emergent,
title = {{Emergent $\mathcal N=3$ and Frozen $\mathcal N=2$ SCFTs from $\mathcal N=1$ Gauge Theory}},
author = {Hongliang Jiang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.09504},
eprint = {2610.09504},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.09504},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Emergent π©=3 and Frozen π©=2 SCFTs from π©=1 Gauge Theory
AU - Hongliang Jiang
PY - 2026
DA - 2026/10/07
PB - arXiv
DO - 10.48550/arxiv.2610.09504
UR - https://arxiv.org/abs/2610.09504
AB - Four-dimensional π©=3 superconformal field theories (SCFTs) are an exotic class of quantum field theories that admit no conventional Lagrangian description. In this Letter, we construct an π©=1 supersymmetric gauge theory and argue that its infrared fixed point exhibits supersymmetry enhancement to an π©=3 SCFT. The ultraviolet theory has gauge group SU(2)^3, a set of chiral multiplets, and a suitable superpotential. By performing a-maximization, we obtain infrared central charges a=c=5/4, matching those of the rank-one π©=3 β€_3 S-fold SCFT. The ultraviolet gauge-theory description allows us to compute the full superconformal index with four independent fugacities. We then examine various limits of the full index and further propose a closed-form expression for the Macdonald index, reproducing all known results for the proposed π©=3 theory. More remarkably, we argue that further gauging the π©=3 theory yields the frozen rank-one π©=2 SCFT conjectured from Seiberg--Witten geometry, providing strong evidence for its existence and unlocking its previously inaccessible full superconformal index. Our construction thus opens a systematic route to exploring the refined protected structure of these exotic, intrinsically strongly coupled theories using conventional π©=1 Lagrangian techniques.
ER -