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

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.


Equivariant Reduction of Gauge Theories over Fuzzy Extra Dimensions
Kürkcüoğlu, Seçkin (IOP Publishing, 2012-2-8)
In SU(N) Yang-Mills theories on a manifold M, which are suitably coupled to a set of scalars, fuzzy spheres may be generated as extra dimensions by spontaneous symmetry breaking. This process results in gauge theories over the product space of the manifold M and the fuzzy spheres with smaller gauge groups. Here we present the SU(2)- and SU(2) x SU(2)-equivariant parametrization of U(2) and U(4) gauge fields on S-F(2), and S-F(2), x S-F(2), respectively and outline the dimensional reduction of these theories...
New fuzzy extra dimensions from SU(N) gauge theories
Kürkcüoğlu, Seçkin (2015-07-16)
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 ...
Energy spectrum of extended Hubbard model with spin-dependent hopping and related spin ladder model
Cheranovskii, VO; Ezerskaya, EV; Özkan, İlker (2002-06-15)
We studied the energy spectrum of the 1-D extended Hubbard model with spin-dependent hopping and related spin ladder system formed by two coupled XXZ spin 1/2 chains with the interchain interaction of Ising type. It was proved that the model excitation spectrum has no gap excepting some special values of z-projection of the ground-state total spin. The thorough analytic consideration of two-magnon states was given. The existence tip to five bound states at specified value of quasimomentum of the pair of inv...
Hermitian and gauge-covariant Hamiltonians for a particle in a magnetic field on cylindrical and spherical surfaces
Shikakhwa, M. S.; Chair, N. (IOP Publishing, 2017-01-01)
We construct the Hermitian Schrodinger Hamiltonian of spin-less particles and the gauge-covariant Pauli Hamiltonian of spin one-half particles in a magnetic field, which are confined to cylindrical and spherical surfaces. The approach does not require the use of involved differential-geometrical methods and is intuitive and physical, relying on the general requirements of Hermicity and gauge-covariance. The surfaces are embedded in the full three-dimensional space and confinement to the surfaces is achieved...
Entangled Harmonic Oscillators and Space-Time Entanglement
Başkal, Sibel; Kim, Young S.; Noz, Marilyn E. (MDPI AG, 2016-6-28)
The mathematical basis for the Gaussian entanglement is discussed in detail, as well as its implications in the internal space-time structure of relativistic extended particles. It is shown that the Gaussian entanglement shares the same set of mathematical formulas with the harmonic oscillator in the Lorentz-covariant world. It is thus possible to transfer the concept of entanglement to the Lorentz-covariant picture of the bound state, which requires both space and time separations between two constituent p...
Citation Formats
S. Kürkcüoğlu, “Equivariant fields in an SU(N) gauge theory with new spontaneously generated fuzzy extra dimensions,” PHYSICAL REVIEW D, pp. 0–0, 2016, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/38894.