Abstract
It is argued that the one-loop effective action for space-like noncommutative (i) λφ4 scalar field theory and (ii) U(1) gauge theory does not exist. This indicates that such theories are not renormalizable already at one-loop order and suggests supersymmetrization and reinvestigating other types of noncommutativity.
Highlights
It is argued that the one-loop effective action for space-like noncommutative (i) λφ4 scalar field theory and (ii) U (1) gauge theory does not exist
As is well-known, in a noncommutative field theory with superficial UV divergences, one-loop radiative corrections to 1PI Green functions consist of a planar part and a nonplanar part
In this paper we show that this is the case for a real scalar field theory and U (1) gauge theory, and discuss the connections with other issues in the literature
Summary
It is argued that the one-loop effective action for space-like noncommutative (i) λφ4 scalar field theory and (ii) U (1) gauge theory does not exist. As is well-known, in a noncommutative field theory with superficial UV divergences, one-loop radiative corrections to 1PI Green functions consist of a planar part and a nonplanar part.
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