The IR/UV connection in the non-commutative gauge theories

By Alec Matusis, L. Susskind, N. Toumbas. 2000

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Quantum field theory on non-commutative spaces does not enjoy the usual ultraviolet-infrared decoupling that forms the basis for conventional renormalization. The high momentum contributions to loop integrations can lead to unfamiliar long distance behavior which can potentially undermine naive expectations for the IR behavior of the theory. These ``anomalies" involve non-analytic behavior in the noncommutativity parameter θ making the limit θ→0 singular. In this paper we will analyze such effects in the one loop approximation to gauge theories on non-commutative space. We will see that contrary to expectations poles in θ do occur and lead to large discrepancies between the expected and actual infrared behavior. We find that poles in θ are absent in supersymmetric theories. The ``anomalies" are generally still present, but only at the logarithmic level. A notable exception is non-commutative super Yang-Mills theory with 16 real supercharges in which anomalous effects seem to be absent altogether.

Subfields: Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/0695ca4cdf19739b5d1d49721e0946c7dde4f0ae

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Citations in the corpus

Modern Tests of Lorentz Invariance (2005, methodology): “Supersymmetry is currently the only known symmetry (other than Lorentz symmetry itself) that can protect Lorentz violating operators of dimension four or less [137, 159, 65], much as SUSY protects some lower dimension operators in non-commutative field theory [216].”
Non-commutative solitons (2000, background): “Perturbative aspects of noncommutative field theories have been analyzed in [2-27].”
Quantum-Spacetime Phenomenology (2008, background): “For the “canonical noncommutative spacetimes” one does obtain a plausible-looking field theory [213], but the results actually show that it is not possible to rely on an ordinary effective low-energy quantum-field-theory description because of the presence of “UV/IR mixing”[213, 397] (a mechanism su”
Emergent geometry and gravity from matrix models: an introduction (2010, methodology): “ gauge elds should not be interpreted as photons. These \strange" terms will be understood as induced gravitational terms. A notable exception is the N= 4 SUSY case, which contains no such terms [25]. Eq. (24) says that translations on R4 are nothing but particular gauge transformations. Thus ”
Quantum field theory on noncommutative spaces (2001, background): “34) we see that both linear and logarithmic infrared singularities arise [105].”
Comments on perturbative dynamics of non-commutative Yang–Mills theory (2000, neutral): “It cannot be written as a sum of a SU(N) and a U(1) theories as the ordinary YM theory, since there are interaction terms between the SU(N) gluons and the U(1) ’photon’.”
Exact Solution of Quantum Field Theory on Noncommutative Phase Spaces (2003, background): “Coupling scalar field theories to fermionic field theories with enough supersymmetry is known to be a way to rid the noncommutative quantum field theory of UV/IR mixing [52, 53].”
Planck-scale modified dispersion relations and Finsler geometry (2006, background): “Moreover attempts to develop a quantum field theory associated with different forms of noncommutativity, a much needed step in order to be able to effectively cast phenomenological constraints, led to highly non-trivial quantum field theories (possibly with problematic features as the IR/UV-mixing [”
Invasion of the giant gravitons from Anti-de Sitter space (2000, neutral): “∗mcgreevy@stanford.edu, susskind@sewerrat.stanford.edu”
Nonassociative Star Product Deformations for D-Brane World-Volumes in Curved Backgrounds (2001, background): “physics is therefore captured within a quantum field theory (which is renormalizable, de- spite appearances [7, 8 ]).”