Three ways to solve critical ${\varphi }^4$ theory on $4-\epsilon$ dimensional real projective space: perturbation, bootstrap, and Schwinger-Dyson equation

Abstract

We solve the two-point function of the lowest dimensional scalar operator in the critical ${\varphi }^4$ theory on $4-\epsilon$ dimensional real projective space in three different methods. The first is to use the conventional perturbation theory, and the second is to impose the crosscap bootstrap equation, and the third is to solve the Schwinger-Dyson equation under the assumption of conformal invariance. We find that the three methods lead to mutually consistent results but each has its own advantage.

arXiv comment24 pages; v2: some references added; v3: Typos corrected

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Cited by in corpus (9)

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• The Conformal Bootstrap at Finite Temperature
• Selected Topics in Analytic Conformal Bootstrap: A Guided Journey
• Aspects of CFTs on Real Projective Space
• A dispersion relation for defect CFT
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• Recursive structure of the Gauß hypergeometric function and boundary/crosscap conformal block
• Boundary anomalous dimensions from BCFT: O($N$)-symmetric ${\varphi }^{2n}$ theories with a boundary and higher-derivative generalizations