Renormalization on noncommutative torus

Abstract

We study a self-interacting scalar ${\phi }^4$ theory on the $d$-dimensional noncommutative torus. We determine, for the particular cases $d=2$ and $d=4$, the counterterms required by one-loop renormalization. We discuss higher loops in two dimensions and two-loop contributions to the self-energy in four dimensions. Our analysis points toward the absence of any problems related to the UV/IR mixing and thus to renormalizability of the theory. However, we find another potentially troubling phenomenon which is a wild behavior of the two-point amplitude as a function of the noncommutativity matrix $\theta$.

v2: comments and references added, v3: typos corrected; matches published version

References in corpus (6)

• A translation-invariant renormalizable non-commutative scalar model
• Heat kernel and number theory on NC-torus
• The ultraviolet infrared mixing problem on the noncommutative Moyal space
• Heat kernel expansion and induced action for the matrix model Dirac operator
• Nilpotent noncommutativity and renormalization
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Cited by in corpus (7)

• Tachyonic instabilities in 2+1 dimensional Yang-Mills theory and its connection to Number Theory
• On the Physics of the Minimal Length: The Question of Gauge Invariance
• $U(N)$ Yang-Mills in non-commutative space time
• Perturbative effective action for the photon in noncommutative QED${}_2$ and exactness of the Schwinger mass
• One-loop $\beta$ function of noncommutative scalar $QE{D}_4$
• Three-dimensional noncommutative Yukawa theory: Induced effective action and propagating modes
• Energy momentum tensor for translation invariant renormalizable noncommutative field theory