On the continuity of the commutative limit of the 4d N=4 non-commutative super Yang-Mills theory
arXiv:1410.4503 · doi:10.1016/j.nuclphysb.2015.01.016
Abstract
We study the commutative limit of the non-commutative maximally supersymmetric Yang-Mills theory in four dimensions (N=4 SYM). The commutative limits of non-commutative spaces are important in particular in the applications of non-commutative spaces for regularisation of supersymmetric theories (such as the use of non-commutative spaces as alternatives to lattices for supersymmetric gauge theories and interpretations of some matrix models as regularised supermembrane or superstring theories), which in turn can play a prominent role in the study of quantum gravity via the gauge/gravity duality. In general, the commutative limits are known to be singular and non-smooth due to UV/IR mixing effects. We give a direct proof that UV effects do not break the continuity of the commutative limit of the non-commutative N=4 SYM to all order in perturbation theory, including non-planar contributions. This is achieved by establishing the uniform convergence (with respect to the non-commutative parameter) of momentum integrals associated with all Feynman diagrams appearing in the theory, using the same tools involved in the proof of finiteness of the commutative N=4 SYM.
v1: 27 pages, 3 figures. v2: References updated
References in corpus (8)
- Integrability of classical strings dual for noncommutative gauge theories
- N=4 Super Yang-Mills from the Plane Wave Matrix Model
- Deconfinement phase transition in N=4 super Yang-Mills theory on RxS^3 from supersymmetric matrix quantum mechanics
- Restoration of supersymmetry on the lattice: Two-dimensional supersymmetric Yang-Mills theory
- Testing a novel large-N reduction for N=4 super Yang-Mills theory on RxS^3
- N=4 Supersymmetry on a Space-Time Lattice
- Proof of ultra-violet finiteness for a planar non-supersymmetric Yang-Mills theory
- A Proposal for a Non-Perturbative Regularization of {\cal N}=2 SUSY 4D Gauge Theory