New fuzzy extra dimensions from SU(N) gauge theories

Download

index.pdf

Date

2015-07-16

Author

Kürkcüoğlu, Seçkin

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

175
views

94
downloads

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.

Subject Keywords

Non-abelian vortices, Spectrum

URI

https://hdl.handle.net/11511/37250

Journal

PHYSICAL REVIEW D

DOI

https://doi.org/10.1103/physrevd.92.025022

Collections

Department of Physics, Article

Suggestions

OpenMETU
Core

A novel approach to chemical resemblance of alternant hydrocarbons Türker, Burhan Lemi (2002-02-14) Within the constraints of the Huckel molecular orbital theory, a topological approach has been developed for the resemblance of alternant hydrocarbons. Four topological variables are considered which categorize alternant hydrocarbons having some resemblance of certain degree between them. Depending on variations of these topological variables, various groups of the compounds, including the identity case, various isomers and nonresembling systems have been investigated.
Stabilization of integral-equation formulations for the accurate solution of scattering problems involving low-contrast dielectric objects Ergül, Özgür Salih (Institute of Electrical and Electronics Engineers (IEEE), 2008-03-01) The solution of scattering problems involving low-contrast dielectric objects with three-dimensional arbitrary shapes is considered. Using the traditional forms of the surface integral equations, scattered fields cannot be calculated accurately if the contrast of the object is low. Therefore, we consider the stabilization of the formulations by extracting the nonradiating parts of the equivalent currents. We also investigate various types of stable formulations and show that accuracy can be improved systema...
Approximate Stable Diagonalization of the Green's Function for Low Frequencies Ergül, Özgür Salih (Institute of Electrical and Electronics Engineers (IEEE), 2014-01-01) We present an approximate diagonalization of the Green's function that is stable at arbitrarily short distances with respect to wavelength. The diagonalization is based on scaled spherical functions and plane waves, where a scaling factor is used to stabilize special functions with small arguments. Optimization of the scaling factor leads to accurate diagonalizations, which can be used to implement the multilevel fast multipole algorithm for low-frequency problems.
Efficient solution of the electric-field integral equation using the iterative LSQR algorithm Ergül, Özgür Salih (Institute of Electrical and Electronics Engineers (IEEE), 2008-01-01) In this letter, we consider iterative solutions of the three-dimensional electromagnetic scattering problems formulated by surface integral equations. We show that solutions of the electric-field integral equation (EFIE) can be improved by employing an iterative least-squares QR (LSQR) algorithm. Compared to many other Krylov subspace methods, LSQR provides faster convergence and it becomes an alternative choice to the time-efficient no-restart generalized minimal residual (GMRES) algorithm that requires la...
Efficient Surface Integral Equation Methods for the Analysis of Complex Metamaterial Structures Yla-Oijala, Pasi; Ergül, Özgür Salih; Gurel, Levent; Taskinen, Matti (2009-03-27) Two approaches, the multilevel fast multipole algorithm with sparse approximate inverse preconditioner and the surface equivalence principle algorithm, are applied to analyze complex three-dimensional metamaterial structures. The efficiency and performance of these methods are studied and discussed.

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: https://hdl.handle.net/11511/37250.