On β–deformations and Noncommutativity

We elucidate the connection between the N = 1 β–deformed SYM theory and noncommutativity. Our starting point is the T–duality generating transformation involved in constructing the gravity duals of both β–deformed and noncommutative gauge theories. We show that the two methods can be identified provided that a particular submatrix of the O(3, 3,R) group element employed in the former case, is interpreted as the noncommutativity parameter associated with the deformation of the transverse space. It is then explained how to construct the matrix in question, relying solely on information extracted from the gauge theory Lagrangian and basic notions of AdS/CFT. This result may provide an additional tool in exploring deformations of the N = 4 SYM theory. Finally we use the uncovered relationship between β–deformations and noncommutativity to find the gravity background dual to a noncommutative gauge theory with β–type noncommutativity parameter.