On the unitarity of quantum gauge theories on non-commutative spaces

Abstract

We study the perturbative unitarity of non-commutative quantum Yang-Mills theories, extending previous investigations on scalar field theories to the gauge case where non-locality mingles with the presence of unphysical states. We concentrate our efforts on two different aspects of the problem. We start by discussing the analytical structure of the vacuum polarization tensor, showing how Cutkoski's rules and positivity of the spectral function are realized when non-commutativity does not affect the temporal coordinate. When instead non-commutativity involves time, we find the presence of extra troublesome singularities on the $p_0^2$-plane that seem to invalidate the perturbative unitarity of the theory. The existence of new tachyonic poles, with respect to the scalar case, is also uncovered. Then we turn our attention to a different unitarity check in the ordinary theories, namely time exponentiation of a Wilson loop. We perform a $O(g^4)$ generalization to the (spatial) non-commutative case of the familiar results in the usual Yang-Mills theory. We show that exponentiation persists at $O(g^4)$ in spite of the presence of Moyal phases reflecting non-commutativity and of the singular infrared behaviour induced by UV/IR mixing.

RevTeX, 27 pages, 8 eps-figures; report number and references added; minor changes

References in corpus (3)

• Instability of Non-Commutative SYM Theories at Finite Temperature
• Hard Non-commutative Loops Resummation
• A Note on Unitarity of Non-Relativistic Non-Commutative Theories

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• General structure of the photon self-energy in non-commutative QED
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• Perturbative Wilson loop in two-dimensional non-commutative Yang-Mills theory
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• IR Dynamics from UV Divergences: UV/IR Mixing, NCFT, and the Hierarchy Problem
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• The covariant form of the gauge anomaly on noncommutative R2n
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