A roadmap for bootstrapping critical gauge theories: decoupling operators of conformal field theories in $d>2$ dimensions

He, Yin-Chen; Rong, Junchen; Su, Ning

doi:10.21468/SciPostPhys.11.6.111

SciPost Physics

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.

TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.11.6.111
TI  - A roadmap for bootstrapping critical gauge theories: decoupling operators of conformal field theories in $d>2$ dimensions
PY  - 2021/12/22
UR  - https://scipost.org/SciPostPhys.11.6.111
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 11
IS  - 6
SP  - 111
A1  - He, Yin-Chen
AU  - Rong, Junchen
AU  - Su, Ning
AB  - 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.
ER  -

@Article{10.21468/SciPostPhys.11.6.111,
	title={{A roadmap for bootstrapping critical gauge theories: decoupling operators of conformal field theories in $d>2$ dimensions}},
	author={Yin-Chen He and Junchen Rong and Ning Su},
	journal={SciPost Phys.},
	volume={11},
	pages={111},
	year={2021},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.11.6.111},
	url={https://scipost.org/10.21468/SciPostPhys.11.6.111},
}

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¹ Yin-Chen He,
² Junchen Rong,
³ Ning Su

Funders for the research work leading to this publication