New fuzzy extra dimensions from SU(N) gauge theories

We start with an SU(N) Yang-Mills theory on a manifold M, suitably coupled to scalar fields in the adjoint representation of SU(N), which are forming a doublet and a triplet, respectively, under a global SU(2) symmetry. We show that a direct sum of fuzzy spheres S-F(2 Int) := S-F(2)(l) circle plus S-F(2)(l) circle plus S-F(2)(l + 1/2) circle plus S-F(2)(l - 1/2) emerges as the vacuum solution after the spontaneous breaking of the gauge symmetry and paves the way for us to interpret the spontaneously broken model as a U(n) gauge theory over M x S-F(2 Int) . Focusing on a U(2) gauge theory, we present complete parametrizations of the SU(2)-equivariant, scalar, spinor and vector fields characterizing the effective low energy features of this model. Next, we direct our attention to the monopole bundles S-F(2 +/-) := S-F(2)(l) circle plus S-F(2)(l +/- 1/2) over S-F(2)(l) with winding numbers +/- 1, which naturally come forth through certain projections of S-F(2 Int), and give the parametrizations of the SU(2)-equivariant fields of the U(2) gauge theory over M x S-F(2 +/-) as a projected subset of those of the parent model. Referring to our earlier work [1], we explain the essential features of the low energy effective action that ensues from this model after dimensional reduction. Replacing the doublet with a k-component multiplet of the global SU(2), we provide a detailed study of vacuum solutions that appear as direct sums of fuzzy spheres as a consequence of the spontaneous breaking of SU(N) gauge symmetry in these models and obtain a class of winding number +/-(k - 1) is an element of Z monopole bundles S-F(2,+/-(k-1)) over S-F(2)(l) as certain projections of these vacuum solutions and briefly discuss their equivariant field content. We make the observation that S-F(2 Int) is indeed the bosonic part of the N = 2 fuzzy supersphere with OSP(2, 2) supersymmetry and construct the generators of the osp(2, 2) Lie superalgebra in two of its irreducible representations using the matrix content of the vacuum solution S-F(2 Int). Finally, we show that our vacuum solutions are stable by demonstrating that they form mixed states with nonzero von Neumann entropy.

Citation Formats
S. Kürkcüoğlu, “New fuzzy extra dimensions from SU(N) gauge theories,” PHYSICAL REVIEW D, vol. 92, pp. 0–0, 2015, Accessed: 00, 2020. [Online]. Available: