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

N1 - Publisher Copyright:
© 2016 The Author(s).
Copyright:
Copyright 2016 Elsevier B.V., All rights reserved.

PY - 2016/4

Y1 - 2016/4

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.

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U2 - 10.1093/ptep/ptw014

DO - 10.1093/ptep/ptw014

M3 - Article

AN - SCOPUS:84997611059

VL - 2016

JO - Progress of Theoretical and Experimental Physics

JF - Progress of Theoretical and Experimental Physics

SN - 2050-3911

IS - 4

M1 - 043B01

ER -