### Abstract

As a perturbative check of the construction of 4D N = 4 supersymmetric Yang-Mills theory (SYM) from mass-deformed N = (8, 8) SYM on the 2D lattice, the one-loop effective action for scalar kinetic terms is computed in N = 4 U(k) SYM on R^{2}× (fuzzy S2), which is obtained by expanding 2D N = (8, 8) U(N) SYM with mass deformation around its fuzzy-sphere classical solution. The radius of the fuzzy sphere is proportional to the inverse of the mass. We consider two successive limits: (1) decompactify the fuzzy sphere to a noncommutative (Moyal) plane and (2) turn off the noncommutativity of the Moyal plane. It is straightforward at the classical level to obtain the ordinary N = 4 SYM on R^{4} in the limits, while it is nontrivial at the quantum level. The one-loop effective action for the SU(k) sector of the gauge group U(k) coincides with that of the ordinary 4D N = 4 SYM in the above limits. Although a "noncommutative anomaly" appears in the overall U(1) sector of the U(k) gauge group, this can be expected to be a gauge artifact not affecting gauge-invariant observables.

Original language | English |
---|---|

Article number | 043B01 |

Journal | Progress of Theoretical and Experimental Physics |

Volume | 2016 |

Issue number | 4 |

DOIs | |

Publication status | Published - 2016 Apr 1 |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*Progress of Theoretical and Experimental Physics*,

*2016*(4), [043B01]. https://doi.org/10.1093/ptep/ptw014

**A one-loop test for construction of 4D N = 4 SYM from 2D SYM via fuzzy-sphere geometry.** / Matsuura, So; Sugino, Fumihiko.

Research output: Contribution to journal › Article

*Progress of Theoretical and Experimental Physics*, vol. 2016, no. 4, 043B01. https://doi.org/10.1093/ptep/ptw014

}

TY - JOUR

T1 - A one-loop test for construction of 4D N = 4 SYM from 2D SYM via fuzzy-sphere geometry

AU - Matsuura, So

AU - Sugino, Fumihiko

PY - 2016/4/1

Y1 - 2016/4/1

N2 - As a perturbative check of the construction of 4D N = 4 supersymmetric Yang-Mills theory (SYM) from mass-deformed N = (8, 8) SYM on the 2D lattice, the one-loop effective action for scalar kinetic terms is computed in N = 4 U(k) SYM on R2× (fuzzy S2), which is obtained by expanding 2D N = (8, 8) U(N) SYM with mass deformation around its fuzzy-sphere classical solution. The radius of the fuzzy sphere is proportional to the inverse of the mass. We consider two successive limits: (1) decompactify the fuzzy sphere to a noncommutative (Moyal) plane and (2) turn off the noncommutativity of the Moyal plane. It is straightforward at the classical level to obtain the ordinary N = 4 SYM on R4 in the limits, while it is nontrivial at the quantum level. The one-loop effective action for the SU(k) sector of the gauge group U(k) coincides with that of the ordinary 4D N = 4 SYM in the above limits. Although a "noncommutative anomaly" appears in the overall U(1) sector of the U(k) gauge group, this can be expected to be a gauge artifact not affecting gauge-invariant observables.

AB - As a perturbative check of the construction of 4D N = 4 supersymmetric Yang-Mills theory (SYM) from mass-deformed N = (8, 8) SYM on the 2D lattice, the one-loop effective action for scalar kinetic terms is computed in N = 4 U(k) SYM on R2× (fuzzy S2), which is obtained by expanding 2D N = (8, 8) U(N) SYM with mass deformation around its fuzzy-sphere classical solution. The radius of the fuzzy sphere is proportional to the inverse of the mass. We consider two successive limits: (1) decompactify the fuzzy sphere to a noncommutative (Moyal) plane and (2) turn off the noncommutativity of the Moyal plane. It is straightforward at the classical level to obtain the ordinary N = 4 SYM on R4 in the limits, while it is nontrivial at the quantum level. The one-loop effective action for the SU(k) sector of the gauge group U(k) coincides with that of the ordinary 4D N = 4 SYM in the above limits. Although a "noncommutative anomaly" appears in the overall U(1) sector of the U(k) gauge group, this can be expected to be a gauge artifact not affecting gauge-invariant observables.

UR - http://www.scopus.com/inward/record.url?scp=84997611059&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84997611059&partnerID=8YFLogxK

U2 - 10.1093/ptep/ptw014

DO - 10.1093/ptep/ptw014

M3 - Article

VL - 2016

JO - Progress of Theoretical and Experimental Physics

JF - Progress of Theoretical and Experimental Physics

SN - 2050-3911

IS - 4

M1 - 043B01

ER -