The β-function in duality-covariant noncommutative ϕ^4-theory

Abstract

We compute the one-loop β-functions describing the renormalisation of the coupling constant λand the frequency parameter Ωfor the real four-dimensional duality-covariant noncommutative ϕ^4-model, which is renormalisable to all orders. The contribution from the one-loop four-point function is reduced by the one-loop wavefunction renormalisation, but the β_λ-function remains non-negative. Both β_λand β_Ωvanish at the one-loop level for the duality-invariant model characterised by Ω=1. Moreover, β_Ωalso vanishes in the limit Ω\to 0, which defines the standard noncommutative ϕ^4-quantum field theory. Thus, the limit Ω\to 0 exists at least at the one-loop level.

11 pages, LaTeX

References in corpus (4)

• Noncommutative Perturbative Dynamics
• Duality in Scalar Field Theory on Noncommutative Phase Spaces
• Renormalisation of ϕ^4-theory on noncommutative R^2 in the matrix base
• Exact Solution of Quantum Field Theory on Noncommutative Phase Spaces

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