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Equivariant fields in an SU(N) gauge theory with new spontaneously generated fuzzy extra dimensions

Kürkcüoğlu, Seçkin
Ünal, Gönül
We find new spontaneously generated fuzzy extra dimensions emerging from a certain deformation of N = 4 supersymmetric Yang-Mills theory with cubic soft supersymmetry breaking and mass deformation terms. First, we determine a particular four-dimensional fuzzy vacuum that may be expressed in terms of a direct sum of product of two fuzzy spheres, and denote it in short as S-F(2Int) x S-F(2Int) . The direct sum structure of the vacuum is clearly revealed by a suitable splitting of the scalar fields in the model in a manner that generalizes our approach in [Phys. Rev. D 92, 025022 (2015)]. Fluctuations around this vacuum have the structure of gauge fields over S-F(2Int) x S-F(2Int), and this enables us to conjecture the spontaneous broken model as an effective U(n) (n < N) gauge theory on the product manifold M-4 x S-F(2Int) x S-F(2Int). We support this interpretation by examining the U(4) theory and determining all of the SU(2) x SU(2) equivariant fields in the model, characterizing its low energy degrees of freedom. Monopole sectors with winding numbers (+/- 1,0), (0, +/- 1), (+/- 1,+/- 1) are accessed from S-F(2Int) x S-F(2Int) after suitable projections, and subsequently equivariant fields in these sectors are obtained. We indicate how Abelian Higgs type models with vortex solutions emerge after dimensionally reducing over the fuzzy monopole sectors as well. A family of fuzzy vacua is determined by giving a systematic treatment for the splitting of the scalar fields, and it is made manifest that suitable projections of these vacuum solutions yield all higher winding number fuzzy monopole sectors. We observe that the vacuum configuration S-F(2Int) x S-F(2Int) identifies with the bosonic part of the product of two fuzzy superspheres with OSP(2,2) x OSP(2,2) supersymmetry and elaborate on this unexpected and intriguing feature.