Journal
SCIPOST PHYSICS
Volume 11, Issue 6, Pages -Publisher
SCIPOST FOUNDATION
DOI: 10.21468/SciPostPhys.11.6.111
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Funding
- Government of Canada through the Department of Innovation, Science and Industry Canada
- Province of Ontario through the Ministry of Colleges and Universities
- European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme [758903]
- DFG through the Emmy Noether research group The Conformal Bootstrap Program [400570283]
- Swiss National Science Foundation [PP00P2-163670]
- Swiss National Science Foundation (SNF) [PP00P2_163670] Funding Source: Swiss National Science Foundation (SNF)
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The researchers propose a roadmap for bootstrapping conformal field theories described by gauge theories in dimensions d > 2. They offer a simple way to detect the gauge group in the bootstrap calculation using the notion of a decoupling operator, and discuss the physical implications of the equation of motion in the CFT spectrum. As an application, they study a critical gauge theory, scalar QED, using conformal bootstrap to obtain its properties in different dimensions.
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 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.
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