On the continuity of the commutative limit of the 4d N=4 non-commutative super Yang-Mills theory
Abstract
We study the commutative limit of the non-commutative maximally supersymmetric Yang-Mills theory in four dimensions (N=4SYM), 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 N=4SYM 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=4SYM.
Journal
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- Nuclear Physics B
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Nuclear Physics B 892 449-474, 2015-03
Elsevier
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Details 詳細情報について
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- CRID
- 1050001335835573248
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- NII Article ID
- 120005766974
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- ISSN
- 05503213
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- HANDLE
- 2433/215112
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- Text Lang
- en
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- Article Type
- journal article
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- Data Source
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- IRDB
- CiNii Articles