Mixed field theory

Journal Article · Tue Dec 17 00:00:00 UTC 2019 · Journal of High Energy Physics (Online)

DOI: https://doi.org/10.1007/jhep12(2019)136 · OSTI ID:1800749

Gubser, Steven S. ^[1]; Jepsen, Christian ^[2]; Ji, Ziming ^[2]; Trundy, Brian ^[2]

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1. Princeton Univ., NJ (United States). Joseph Henry Labs.; OSTI
2. Princeton Univ., NJ (United States). Joseph Henry Labs.

We consider scalar field theory defined over a direct product of the real and p-adic numbers. An adjustable dynamical scaling exponent z enters into the microscopic lagrangian, so that the Gaussian theories provide a line of fixed points. We argue that at z = 1/3, a branch of Wilson-Fisher fixed points joins onto the line of Gaussian theories. We compute standard critical exponents at the Wilson-Fisher fixed points in the region where they are perturbatively accessible, including a loop correction to the dynamical critical exponent. We show that the classical propagator contains oscillatory behavior in the real direction, though the amplitude of these oscillations can be made exponentially small without fine-tuning parameters of the theory. Similar oscillatory behavior emerges in Fourier space from two-loop corrections, though again it can be highly suppressed. We also briefly consider compact p-adic extra dimensions, showing in non-linear, classical, scalar field theories that a form of consistent truncation allows us to retain only finitely many Kaluza-Klein modes in an effective theory formulated on the non-compact directions.

• Research Organization: Princeton Univ., NJ (United States)
• Sponsoring Organization: USDOE Office of Science (SC)
• Grant/Contract Number: FG02-91ER40671
• OSTI ID: 1800749
• Journal Information: Journal of High Energy Physics (Online), Journal Name: Journal of High Energy Physics (Online) Journal Issue: 12 Vol. 2019; ISSN 1029-8479
• Publisher: Springer BerlinCopyright Statement
• Country of Publication: United States
• Language: English