PP-wave string interactions from perturbative Yang-Mills theory

By N. Constable, D. Freedman, M. Headrick, Shiraz Minwalla, L. Motl, Alexander Postnikov, W. Skiba. 2002

300 citations recorded by the source corpus.

Recently, Berenstein et al. have proposed a duality between a sector of = 4 super-Yang-Mills theory with large R-charge J, and string theory in a pp-wave background. In the limit considered, the effective 't Hooft coupling has been argued to be ?' = gYM2N/J2 = 1/(?p+?')2. We study Yang-Mills theory at small ?' (large ?) with a view to reproducing string interactions. We demonstrate that the effective genus counting parameter of the Yang-Mills theory is g22 = J4/N2 = (4?gs)2(?p+?')4, the effective two-dimensional Newton constant for strings propagating on the pp-wave background. We identify g2(?')1/2 as the effective coupling between a wide class of excited string states on the pp-wave background. We compute the anomalous dimensions of BMN operators at first order in g22 and ?' and interpret our result as the genus one mass renormalization of the corresponding string state. We postulate a relation between the three-string vertex function and the gauge theory three-point function and compare our proposal to string field theory. We utilize this proposal, together with quantum mechanical perturbation theory, to recompute the genus one energy shift of string states, and find precise agreement with our gauge theory computation.

Subfields: Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/dfa44b9c1543848f671a13affc4731c4acf725e6

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Citations in the corpus

Rotating string solutions: AdS/CFT duality in non-supersymmetric sectors (2003, background): “[9] and [13]), where similar discussion applied to excited states near a BPS state.”
Giant Gravitons - with Strings Attached (III) (2007, background): “The advantage of this decomposition is that it is known that at one loop, the D term contributions cancel with the gauge boson exchange and the scalar self energies[35].”
More comments on superstring interactions in the pp-wave background (2002, unknown): “The structure of the interaction vertex for large μ, in particular subleading corrections which are important in trying to generalize the proposal of [11] to the interacting gauge theory were studied in [21, 22].”
The Dilatation Operator of N=4 Super Yang-Mills Theory and Integrability (2004, background): “This is yet another confirmation of the AdS/CFT correspondence, but for the first time within an interacting string theory! In the study of the BMN correspondence, the attention has been shifted away from lower dimensional operators to operators with a large number of constituent fields [18,19, 21,2”
The dilatation operator of conformal N=4 super-Yang–Mills theory (2003, background): “The full one-loop contribution D2 was first worked out, in the disguise of an “effective vertex”, in appendix C of [25] (but see also [22, 23, 26, 20, 37, 34]): 3 D2 = −:Tr[Φm, Φn][Φ̌m, Φ̌n]:− 12 :Tr[Φm, Φ̌n][Φm, Φ̌n]:.”
On type IIA Penrose limit and = 6 Chern-Simons theories (2008, background): “It is also useful to remember that in the original analysis of BMN operators there are two different coupling constants: one is the rescaled ’t Hooft coupling λ J2 and the other is the effective string coupling J 2 N [57].”
A New Double-Scaling Limit of N = 4 Super Yang-Mills Theory and PP-Wave Strings (2002, result): “After that, the paper [ 14 ] appeared, which contained the correct treatment of this correction.”
Superstring interactions in a pp -wave background (2002, methodology): “xpansion parameters λ′ = g 2 YMN J2 = 1 (µp+α′)2 and g 2 = J2 N = 4πgs(µp+α′)2, so there exists the intriguing possibility that there is a regime in which both sides of the ‘duality’ are perturbative [7]. The authors of [1] obtained the light-cone gauge worldsheet action for a single free string in ”
Giant gravitons—with strings attached (I) (2007, unknown): “The advantage of this decomposition is that it is known that at one loop, the D term contributions cancel with the gauge boson exchange and the scalar self energies[35].”
The Complete One-Loop Dilatation Operator of N=4 Super Yang-Mills Theory (2003, unknown): “ way have been investigated in [28,29,30]. With the advent of the BMN correspondence [5] the attention has been shifted away from lower dimensional operators to operators with a large number of ﬁelds [31,32,33, 34,35]. There, the complications are mostly of combinatorial nature. It was therefore des”
Stringing Spins and Spinning Strings (2003, background): “The result for this particular [J, 0, J ] operator is smaller than the anomalous dimension derived by Frolov and Tseytlin [hep-th/0304255] for a semiclassical string configuration which is the dual of a gauge invariant operator in the same representation.”
D-branes in Yang-Mills theory and emergent gauge symmetry (2004, unknown): “VF = 2tr(|[X, Y ]|(2) + |[X, Z]|(2) + |[Y, Z]|(2)) (19) According to the argument in Appendix B in [21], The D-term and gluon exchange cancel at one loop order (this is based on techniques in previous papers [22, 23] ), so to this order we only need to consider the contributions from F-term.”
Operator mixing and the BMN correspondence (2002, methodology): “eter g2 = J2/N. These quantities can be expressed in terms of the string scale α′ and coupling gs, light-cone momentum p+, and transverse string mass µas λ′ = 1 (µp+α′)2 , g2 = 4πgs(µp+α′)2. (1.1) In [4] we proposed that free three-point functions of the BMN operators OJ n≡ 1 √ JNJ+2 XJ l=0 e2πinl/J”
BMN Correlators and Operator Mixing in N=4 Super Yang-Mills Theory (2002, methodology): “As a consequence, the reported agreement of these “bare” three-point functions with string field theory calculations [10, 15, 4, 17] seem to indicate that the latter have to be reconsidered as well.”