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.


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