On beta-deformations and Noncommutativity

Abstract

We elucidate the connection between the N=1 beta-deformed SYM theory and noncommutativity. Our starting point is the T-duality generating transformation involved in constructing the gravity duals of both beta-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 beta-deformations and noncommutativity to find the gravity background dual to a noncommutative gauge theory with beta-type noncommutativity parameter.

16 pages, no figures

References in corpus (40)

• Deformation quantization of Poisson manifolds, I
• Noncommutative Field Theory
• Supergravity and The Large N Limit of Theories With Sixteen Supercharges
• Duality in the Type--II Superstring Effective Action
• Space-Time Noncommutative Field Theories And Unitarity
• Large N Limit of Non-Commutative Gauge Theories
• Space/Time Non-Commutativity and Causality
• Strings in a Time-Dependent Orbifold
• Non-commutative superspace from string theory
• Strings in Time-Dependent Orbifolds
• Generalized Duality in Curved String-Backgrounds
• On Theories With Light-Like Noncommutativity
• Deformations of N=4 SYM and integrable spin chain models
• Marginal and Relevant Deformations of N=4 Field Theories and Non-Commutative Moduli Spaces of Vacua
• Supergravity and Large N Noncommutative Field Theories
• Gauge-string duality for (non)supersymmetric deformations of N=4 Super Yang-Mills theory
• On Noncommutative Open String Theories
• Holography and String Dynamics in Time-dependent Backgrounds
• Dipole Deformations of N=1 SYM and Supergravity backgrounds with U(1) X U(1) global symmetry
• Amplitudes in the beta-deformed Conformal Yang-Mills
• Dualities, Twists, and Gauge Theories with Non-Constant Non-Commutativity
• Lunin-Maldacena Deformations With Three Parameters
• Construction of Gauge Theories on Curved Noncommutative Spacetime
• The Hagedorn transition in non-commutative open string theory
• New results in the deformed N=4 SYM theory
• Non-Commutative Moduli Spaces, Dielectric Tori and T-duality
• Spacetime decay of cones at strong coupling
• Decay of C/Z_n: exact supergravity solutions
• Graviton Scattering on D6 Branes with B Fields
• Conformal invariance of the planar beta-deformed N=4 SYM theory requires beta real
• Generalizations of Lunin-Maldacena transformation on the $AdSsub5xSsup5$ background
• Effective action of beta-deformed N=4 SYM theory and AdS/CFT
• On the all-order perturbative finiteness of the deformed N=4 SYM theory
• Supergravity Dual of Noncommutative N=1 SYM
• The Seiberg-Witten Map for a Time-dependent Background
• Noncommutative Supersymmetric/Integrable Models and String Theory
• The large M limit of Non-Commutative Open Strings at strong coupling
• The Coulomb branch of the Leigh-Strassler deformation and matrix models
• On Supergravity Solutions of Branes in Melvin Universes
• Winding String Dynamics in a Time-Dependent Beta Deformed Background

Cited by in corpus (3)

• Melvin Twists of global AdS_5 \times S_5 and their Non-Commutative Field Theory Dual
• (Non)-supersymmetric Marginal Deformations from Twistor String Theory
• Integrable Hopf twists, marginal deformations and generalised geometry