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. July 1999Classical supersymmetric Yang-Mills theory (SYM) in (p + 1)-dimensional space can be generalized to SYM on non-commutative spaces [1]. Since the generalization involves infinitely many higher order terms, it is very hard to provide a pure field theory proof that such a theory is consistent at the quantum level. String theory provides a way to obtain these theories by considering the decoupling limit of D(p−2)-branes in type II string theories on T 2 with a background NSNS 2-form field B µν polarized along the plane of the torus [2,3]. The fact that non-commutative SYM is obtained from string theory, in a limit which does not involve gravity, suggests (if string theory with constant B field is consistent) that the non-commutative SYM, at least with sixteen supercharges, is a consistent theory at the quantum level.
Recently it was suggested that a graviton in AdS 5 × S 5 with a large momentum along the sphere can blow up into a spherical D-brane in S 5 . In this paper we show that the same graviton can also blow up into a spherical D-brane in AdS 5 with exactly the same quantum numbers (angular momentum and energy). These branes are BPS, preserving 16 of the 32 supersymmetries. We show that there is a BPS classical solution for SYM on S 3 × R with exactly the same quantum numbers. The solution has non-vanishing Higgs expectation values and hence is dual to the large brane in AdS.
We consider the spectra of excitations around diagonal and intersecting D-brane configurations on tori. These configurations are described by constant curvature connections in a dual gauge theory description. The low-energy string fluctuation spectrum is reproduced exactly by the gauge theory in the case of vanishing field strength; however, this correspondence breaks down for fixed nonzero field strength. We show that in many cases the full Born-Infeld action correctly captures the low-energy spectrum in the case of non-vanishing field strength. This gives a field theory description of the low-energy physics of systems of diagonally wound branes and branes at angles as considered by Berkooz, Douglas and Leigh. This description extends naturally to non-supersymmetric configurations, where the tachyonic instability associated with brane-anti-brane systems appears as an instability around a saddle point solution of the corresponding Yang-Mills/Born-Infeld theory. In some cases, the field theory description requires a non-abelian generalization of the Born-Infeld action. We follow Tseytlin's recent proposal for formulating such an action. In the case of intersecting branes, the non-abelian Born-Infeld theory produces a transcendental relation which comes tantalizingly close to reproducing the correct spectrum; however, a discrepancy remains which indicates that a further clarification of the non-abelian Born-Infeld action may be necessary. March 1997A particularly interesting class of systems of the type considered here are those corresponding to non-supersymmetric D-brane configurations. On T 4 constant gauge field backgrounds are stable if and only if the gauge field is (anti)-self-dual. In [9] it was argued that the (anti)-self-dual condition is equivalent to the condition that the dual D-brane configuration preserve enough supersymmetry to be a BPS state. Considering non-supersymmetric D-brane configurations, we find that the tachyonic instability of the string ground state appears naturally in the field theory language as an instability of a saddle point configuration in the Yang-Mills/Born-Infeld theory. This provides a natural framework for studying aspects of brane-anti-brane interactions in the context of field theory.The organization of this paper is as follows: In section 2 we consider D-brane configurations which are tilted with respect to the torus; these configurations correspond to gauge theory backgrounds with constant field strengths in the central U(1) part of U(N). The necessity for replacing the Yang-Mills action with the Born-Infeld action in order to exactly reproduce the fluctuation spectrum emerges from this analysis. We also discuss the issue of fractional quantization from the gauge theory point of view in this section. In section 3 we consider systems of intersecting D-branes which correspond to reducible connections in the dual gauge theory. We discuss the discrepancy between the spectra and its possible resolution by the non-abelian Born-Infeld action. We also discuss here the D-brane/Bo...
We construct gauge invariant operators in non-commutative gauge theories which in the IR reduce to the usual operators of ordinary field theories (e.g. Tr F 2 ). We show that in the deep UV the two-point functions of these operators admit a universal exponential behavior which fits neatly with the dual supergravity results. We also consider the ratio between n-point functions and two-point functions to find exponential suppression in the UV which we compare to the high energy fixed angle scattering of string theory.
We calculate the leading order interactions of massless D-brane excitations. Their 4-point functions are found to be identical to those found in type I theory. The amplitude for two massless D-brane fluctuations to produce a massless closed string is found to possess interesting new structure. As a function of its single kinematic invariant, it displays an infinite sequence of alternating zeros and poles. At high transverse momenta, this amplitude decays exponentially, indicating a growing effective thickness of the D-brane. This amplitude is the leading process by which non-extrtemal D-branes produce Hawking radiation.
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