Non–Commutative Gauge Theories and the Cosmological Constant

Explaining the small observed value of the cosmological constant is one of the crucial problems in contemporary theoretical physics (see [1–3] for reviews). Although classically the value of the cosmological constant can be tuned to an arbitrarily small value, one cannot do so in a quantum theory. In general quantum fluctuations force one to relate the vacuum energy density to the UV cut-off scale in the theory, ρ ∼ Λ. From the theoretical point of view, the most natural thing is to identify Λ with the Planck scale. However, this yields a cosmological constant which is enormously bigger than the estimated value. In supersymmetric theories the vacuum energy is exactly zero, due to the cancellation of fermionic and bosonic fluctuations. However, once supersymmetry is broken, “mixed” contributions of the form ΛP ∑ (mB −mF ) arise (where mB and mF are bosonic and fermionic masses respectively). Thus, although supersymmetry might reduce the value of the vacuum energy, the problem remains unsolved. It was suggested that certain non-supersymmetric theories, called “orbifold field theories” [4], might lead to a small value of the vacuum energy. From the field theory point of view the reason