Fermions on spontaneously generated spherical extra dimensions

Abstract

We include fermions to the model proposed in hep-th/0606021, and obtain a renormalizable 4-dimensional SU(N) gauge theory which spontaneously generates fuzzy extra dimensions and behaves like Yang-Mills theory on M^4 \times S^2. We find a truncated tower of fermionic Kaluza-Klein states transforming under the low-energy gauge group, which is found to be either SU(n), or SU(n_1) x SU(n_2) x U(1). The latter case implies a nontrivial U(1) flux on S^2, leading to would-be zero modes for the bifundamental fermions. In the non-chiral case they may pair up to acquire a mass, and the emerging picture is that of mirror fermions. We discuss the possible implementation of a chirality constraint in 6 dimensions, which is nontrivial at the quantum level due to the fuzzy nature of the extra dimensions.

34 pages. V2: references added, minor corrections V3: discussion added, final version

References in corpus (28)

• (De)Constructing Dimensions
• Towards the large N limit of pure N=1 super Yang Mills
• Non-Abelian BPS Monopoles in N=4 Gauged Supergravity
• Quantized Gauge Theory on the Fuzzy Sphere as Random Matrix Model
• Emergent Gravity from Noncommutative Gauge Theory
• Noncommutative Geometry and Gauge Theory on Fuzzy Sphere
• Non-Abelian Solitons in N=4 Gauged Supergravity and Leading Order String Theory
• Scaling Limits of the Fuzzy Sphere at one Loop
• The Fermion Doubling Problem and Noncommutative Geometry
• Chirality and Dirac Operator on Noncommutative Sphere
• Nonperturbative studies of fuzzy spheres in a matrix model with the Chern-Simons term
• Finite Gauge Theory on Fuzzy CP^2
• The Fuzzy Ginsparg-Wilson Algebra: A Solution of the Fermion Doubling Problem
• Dynamical generation of fuzzy extra dimensions, dimensional reduction and symmetry breaking
• Dimensional Reduction over Fuzzy Coset Spaces
• Deconstruction of the Maldacena-Nunez Compactification
• Spherical Deconstruction
• Dynamical aspects of the fuzzy CP${}^2$ in the large $N$ reduced model with a cubic term
• Dynamical generation of a nontrivial index on the fuzzy 2-sphere
• Dynamical generation of gauge groups in the massive Yang-Mills-Chern-Simons matrix model
• Gauge Theory on Fuzzy S^2 x S^2 and Regularization on Noncommutative R^4
• Ginsparg-Wilson Dirac operator in the monopole backgrounds on the fuzzy 2-sphere
• Noncommutativity, Extra Dimensions, and Power Law Running in the Infrared
• Renormalizable Theories from Fuzzy Higher Dimensions
• The Standard Model Fermion Spectrum From Complex Projective spaces
• Fuzzy Extra Dimensions: Dimensional Reduction, Dynamical Generation and Renormalizability
• Non-commutative Complex Projective Spaces and the Standard Model
• Gauge Theory on the Fuzzy Sphere and Random Matrices

Cited by in corpus (36)

• Emergent Gravity from Noncommutative Gauge Theory
• Emergent Gravity and Noncommutative Branes from Yang-Mills Matrix Models
• Orbifolds, fuzzy spheres and chiral fermions
• Chiral Fermions and the Standard Model from the Matrix Model Compactified on a Torus
• Fermions and Emergent Noncommutative Gravity
• On the fermion spectrum of spontaneously generated fuzzy extra dimensions with fluxes
• Evidence for F(uzz) Theory
• Noncommutative gauge theory and symmetry breaking in matrix models
• Four-dimensional Gravity on a Covariant Noncommutative Space
• Dimensional Reduction, Monopoles and Dynamical Symmetry Breaking
• Equivariant reduction of Yang-Mills theory over the fuzzy sphere and the emergent vortices
• Higher-Dimensional Unified Theories with Fuzzy Extra Dimensions
• Self-intersecting fuzzy extra dimensions from squashed coadjoint orbits in $\mathcal{N}=4$ SYM and matrix models
• Spinning squashed extra dimensions and chiral gauge theory from $\mathcal{N}=4$ SYM
• Higher-Dimensional Unification with continuous and fuzzy coset spaces as extra dimensions
• Probability distribution of the index in gauge theory on 2d non-commutative geometry
• Noncommutative Vortices and Flux-Tubes from Yang-Mills Theories with Spontaneously Generated Fuzzy Extra Dimensions
• Index theorem in spontaneously symmetry-broken gauge theories on a fuzzy 2-sphere
• Finite-matrix formulation of gauge theories on a non-commutative torus with twisted boundary conditions
• Gravity as a Gauge Theory on Three-Dimensional Noncommutative spaces
• Probability of the Standard Model Appearance from a Matrix Model
• Intertwining noncommutativity with gravity and particle physics
• Equivariant Reduction of U(4) Gauge Theory over S_F^2 x S_F^2 and the Emergent Vortices
• Construction of a topological charge on fuzzy S^2 x S^2 via Ginsparg-Wilson relation
• Unified Gauge Theories and Reduction of Couplings: from Finiteness to Fuzzy Extra Dimensions
• Ginsparg-Wilson relation on a fuzzy 2-sphere for adjoint matter
• The instability of intersecting fuzzy spheres
• New Fuzzy Extra Dimensions from $SU(\mathcal{N})$ Gauge Theories
• Dominance of a single topological sector in gauge theory on non-commutative geometry
• Equivariant Fields in an $SU(\mathcal{N})$ Gauge Theory with new Spontaneously Generated Fuzzy Extra Dimensions
• A Solvable Model for Fermion Masses on a Warped 6D World with the Extra 2D Sphere
• Noncommutative Gauge Theories and Gravity
• Chiral low-energy physics from squashed branes in deformed $\mathcal{N}=4$ SYM
• Fermions Coupled to Emergent Noncommutative Gravity
• Towards realistic models from Higher-Dimensional theories with Fuzzy extra dimensions
• Non-commutativity in Unified Theories and Gravity