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Non-Commutative Yang-Mills and the AdS/CFT Correspondence

Akikazu Hashimoto, N. Itzhaki

Abstract

We study the non-commutative supersymmetric Yang-Mills theory at strong coupling using the AdS/CFT correspondence. The supergravity description and the UV/IR relation confirms the expectation that the non-commutativity affects the ultra-violet but not the infra-red of the Yang-Mills dynamics. We show that the supergravity solution dual to the non-commutative N=4 SYM in four dimensions has no boundary and defines a minimal scale. We also show that the relation between the B field and the scale of non-commutativity is corrected at large coupling and determine its dependence on the 't Hooft coupling λ.

Non-Commutative Yang-Mills and the AdS/CFT Correspondence

Abstract

We study the non-commutative supersymmetric Yang-Mills theory at strong coupling using the AdS/CFT correspondence. The supergravity description and the UV/IR relation confirms the expectation that the non-commutativity affects the ultra-violet but not the infra-red of the Yang-Mills dynamics. We show that the supergravity solution dual to the non-commutative N=4 SYM in four dimensions has no boundary and defines a minimal scale. We also show that the relation between the B field and the scale of non-commutativity is corrected at large coupling and determine its dependence on the 't Hooft coupling λ.

Paper Structure

This paper contains 2 sections, 14 equations, 1 figure.

Table of Contents

  1. Note Added
  2. Acknowledgments

Figures (1)

  • Figure 1: D$(p-2)$-branes in square torus of radius $R \ll \sqrt{\alpha'}$ and B-field flux and its T-dual D$(p-1)$-branes on a skewed torus. Skewed geometry of the torus gives rise to non-locality in the open string excitations living on the D$(p-1)$-brane.