Perturbative Instabilities on the Non-Commutative Torus, Morita Duality and Twisted Boundary Conditions
Abstract
We study one-loop corrections in scalar and gauge field theories on the non-commutative torus. For rational theta, Morita equivalence allows these theories to be reformulated in terms of ordinary theories on a commutative torus with twisted boundary conditions. UV/IR mixing does not lead to singularities, however there can be large corrections. In particular, gauge theories show tachyonic instabilities for some of the modes. We discuss their relevance to spontaneous ZN x ZN symmetry breaking in the Morita dual SU(N) theory due to electric flux condensation.
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