A roadmap for bootstrapping critical gauge theories: decoupling operators of conformal field theories in $d>2$ dimensions
Yin-Chen He, Junchen Rong, Ning Su
SciPost Phys. 11, 111 (2021) · published 22 December 2021
- doi: 10.21468/SciPostPhys.11.6.111
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Abstract
We propose a roadmap for bootstrapping conformal field theories (CFTs) described by gauge theories in dimensions $d>2$. In particular, we provide a simple and workable answer to the question of how to detect the gauge group in the bootstrap calculation. Our recipe is based on the notion of \emph{decoupling operator}, which has a simple (gauge) group theoretical origin, and is reminiscent of the null operator of $2d$ Wess-Zumino-Witten CFTs in higher dimensions. Using the decoupling operator we can efficiently detect the rank (i.e. color number) of gauge groups, e.g., by imposing gap conditions in the CFT spectrum. We also discuss the physics of the equation of motion, which has interesting consequences in the CFT spectrum as well. As an application of our recipes, we study a prototypical critical gauge theory, namely the scalar QED which has a $U(1)$ gauge field interacting with critical bosons. We show that the scalar QED can be solved by conformal bootstrap, namely we have obtained its kinks and islands in both $d=3$ and $d=2+\epsilon$ dimensions.
Cited by 9
Authors / Affiliations: mappings to Contributors and Organizations
See all Organizations.- 1 Yin-Chen He,
- 2 Junchen Rong,
- 3 Ning Su
- 1 Institut Périmètre de physique théorique / Perimeter Institute [PI]
- 2 Deutsches Elektronen-Synchrotron / Deutsche Elektronen-Synchrotron DESY [DESY]
- 3 Università di Pisa / University of Pisa [UniPi]