On the continuity of the commutative limit of the 4d N=4 non-commutative super Yang–Mills theory
Volume
892
Pagination
449 - 474
Publisher
DOI
10.1016/j.nuclphysb.2015.01.016
Journal
Nuclear Physics B
ISSN
0550-3213
Metadata
Show full item recordAbstract
We study the commutative limit of the non-commutative maximally supersymmetric Yang–Mills theory in four dimensions (
), where non-commutativity is introduced in the two spacelike directions. 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
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
.
Authors
Hanada, M; Shimada, HCollections
- Mathematics [1686]