Abstract
New solutions of SU(N) N=4 SYM on R4 interpreted as spinning self-intersecting extra dimensions are discussed. Remarkably, these backgrounds lead to a low-energy sector with 3 generations of chiral fermions coupled to scalar and gauge fields, with standard Lorentz-invariant kinematics. This sector arises from zero modes localized on the rotation axes, which are oblivious to the background rotation. The remaining modes are not described by a Lorentz-invariant field theory and are mostly “heavy”, but there is one sextet of tachyonic excitations. Assuming that the latter get stabilized, e.g. by quantum effects, we argue that different rotation frequencies would induce a VEV for some of the low-energy scalar fields. We discuss configurations which may lead to a low-energy physics not far from the broken phase of the standard model.
Highlights
Simplicity has always been a central guiding principle in theoretical physics
KN is some approximation to a compact space K ⊂ R6, such as a fuzzy sphere, or some more complicated fuzzy manifold. This mechanism of dynamically generating fuzzy extra dimensions has been studied in various guises and examples, see, e.g., [1,2,3,4,5,6,7,8,9,10,11,12]
To get some insight into the low-energy physics which may emerge on such a background, we start exploring the structure of the Yukawa couplings between the lowenergy Higgs modes and the chiral fermions, as well as the couplings between the low-energy fermionic currents and the gauge fields
Summary
Simplicity has always been a central guiding principle in theoretical physics. In the theory of fundamental interactions, this leads naturally to the idea of grand unified models. A interesting and non-trivial example was found in [17], where KN ∼= CN [μ] is a fuzzy version of a squashed (or projected) self-intersecting coadjoint orbit of SU(3) This leads to 3 generations of chiral fermions in the low-energy theory, localized at the origin of the extra dimensions. These solutions can be stabilized by a cubic soft SUSY breaking term in the potential, which is added by hand. To get some insight into the low-energy physics which may emerge on such a background, we start exploring the (rather complicated) structure of the Yukawa couplings between the lowenergy Higgs modes and the chiral fermions, as well as the couplings between the low-energy fermionic currents and the gauge fields This is interesting for stacks of such branes.
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