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We find new spontaneously generated fuzzy extra dimensions emerging from acertain deformation of $N=4$ supersymmetric Yang-Mills (SYM) theory with cubicsoft supersymmetry breaking and mass deformation terms. First, we determine aparticular four dimensional fuzzy vacuum that may be expressed in terms of adirect sum of product of two fuzzy spheres, and denote it in short as $S_F^{2\,Int}\times S_F^{2\, Int}$. The direct sum structure of the vacuum is revealedby a suitable splitting of the scalar fields in the model in a manner thatgeneralizes our approach in \cite{Seckinson}. Fluctuations around this vacuumhave the structure of gauge fields over $S_F^{2\, Int}\times S_F^{2\, Int}$,and this enables us to conjecture the spontaneous broken model as an effective$U(n)$ $(n < {\cal N})$ gauge theory on the product manifold $M^4 \timesS_F^{2\, Int} \times S_F^{2\, Int}$. We support this interpretation byexamining the $U(4)$ theory and determining all of the $SU(2)\times SU(2)$equivariant fields in the model, characterizing its low energy degrees offreedom. Monopole sectors with winding numbers $(\pm1,0),\,(0,\pm1),\,(\pm1,\pm 1)$ are accessed from $S_F^{2\, Int}\times S_F^{2\,Int}$ after suitable projections and subsequently equivariant fields in thesesectors are obtained. We indicate how Abelian Higgs type models with vortexsolutions emerge after dimensionally reducing over the fuzzy monopole sectorsas well. A family of fuzzy vacua is determined by giving a systematic treatmentfor the splitting of the scalar fields and it is made manifest that suitableprojections of these vacuum solutions yield all higher winding number fuzzymonopole sectors. We observe that the vacuum configuration $S_F^{2\, Int}\timesS_F^{2\, Int}$ identifies with the bosonic part of the product of two fuzzysuperspheres with $OSP(2,2)\times OSP(2,2)$ supersymmetry and elaborate on thisfeature.

Equivariant Fields in an $SU({\cal N})$ Gauge Theory with new Spontaneously Generated Fuzzy Extra Dimensions