Daniela Zanon

Exact anomalous dimensions of N=4 Yang–Mills operators with large R charge

Abstract In a N =1 superspace formulation of N =4 Yang–Mills theory we obtain the anomalous dimensions of chiral operators with large R charge J→∞ keeping g2N/J2 finite, to all orders of perturbation theory in the planar limit. Our result proves the conjecture that the anomalous dimensions are indeed finite in the above limit. This amounts to an exact check of the proposed duality between a sector of N =4 Yang–Mills theory with large R charge J and string theory in a pp-wave background.

Perturbative computation of glueball superpotentials

Abstract Using N =1 superspace techniques in four dimensions we show how to perturbatively compute the superpotential generated for the glueball superfield upon integrating out massive charged fields. The technique applies to arbitrary gauge groups and representations. Moreover, we show that for U ( N ) gauge theories admitting a large N expansion the computation dramatically simplifies and we prove the validity of the recently proposed recipe for computation of this quantity in terms of planar diagrams of matrix integrals.

Wrapping at four loops in N=4 SYM

Abstract We present the planar four-loop anomalous dimension of the composite operator tr ( ϕ [ Z , ϕ ] Z ) in the flavour SU ( 2 ) sector of the N = 4 SYM theory. At this loop order wrapping interactions are present: they give rise to contributions proportional to ζ ( 5 ) increasing the level of transcendentality of the anomalous dimension. In a sequel of this Letter all the details of our calculation will be reported.

Exact results in planar Script N = 1 superconformal Yang-Mills theory

In the β-deformed = 4 supersymmetric SU(N) Yang-Mills theory we study the class of operators J = Tr(ΦiJΦk), i≠k and compute their exact anomalous dimensions for N,J→∞. This leads to a prediction for the masses of the corresponding states in the dual string theory sector. We test the exact formula perturbatively up to two loops. The consistency of the perturbative calculation with the exact result indicates that in the planar limit the one-loop condition g2 = h for superconformal invariance is indeed sufficient to insure the exact superconformal invariance of the theory. We present a direct proof of this point in perturbation theory. The J sector of this theory shares many similarities with the BMN sector of the = 4 theory in the large R-charge limit.

Anomalous dimension with wrapping at four loops in N=4 SYM

Abstract In this paper we give all the details of the calculation that we presented in our previous paper [F. Fiamberti, A. Santambrogio, C. Sieg, D. Zanon, Wrapping at four loops in N = 4 SYM, arXiv: 0712.3522 ], concerning the four-loop anomalous dimension of the Konishi descendant tr ( ϕ Z ϕ Z − ϕ ϕ Z Z ) in the SU ( 2 ) sector of the N = 4 planar SYM theory. We explicitly consider all the wrapping diagrams that we compute using an N = 1 superspace approach and Gegenbauer polynomial x-space techniques.

EXACT S-MATRICES FOR NONSIMPLY-LACED AFFINE TODA THEORIES

Abstract We derive exact, factorized, purely elastic scattering matrices for the affine Toda theories based on the nonsimply-laced Lie algebras a 2 n −1 (2) , b n (1) , c c (1) , d n (2) , and g n (1) , as well as the superalgebras A (4) (0, 2 n ) and B (1) (0, n ).

Two-point correlators in the beta-deformed N=4 SYM at the next-to-leading order.

We compute two-point functions of lowest weight operators at the next-to-leading order in the couplings for the β-deformed = 4SU(N) SYM. In particular we focus on the CPO Tr(Φ12) and the operator Tr(Φ1Φ2) not presently listed as BPS. We find that for both operators no anomalous dimension is generated at this order, then confirming the results recently obtained at lowest order in [5]. However, in both cases a finite correction to the two-point function appears.

Two point functions of chiral operators in N=4 SYM at order g**4

We compute two-point functions of chiral operators Tr Φ3 in = 4 SU(N) supersymmetric Yang-Mills theory to the order g4 in perturbation theory. We perform explicit calculations using = 1 superspace techniques and find that perturbative corrections to the correlators vanish for all N. While at order g2 the cancellations can be ascribed to the nonrenormalization theorem valid for correlators of operators in the same multiplet as the stress tensor, at order g4 this argument no longer applies and the actual cancellation occurs in a highly nontrivial way. Our result is obtained in complete generality, without the need of additional conjectures or assumptions. It gives further support to the belief that such correlators are not renormalized to all orders in g and to all orders in N.

More on correlators and contact terms in N=4 SYM at order g(4)

We compute two-point functions of chiral operators Tr(\Phi^k) for any k, in {\cal N}=4 supersymmetric SU(N) Yang-Mills theory. We find that up to the order g^4 the perturbative corrections to the correlators vanish for all N. The cancellation occurs in a highly non trivial way, due to a complicated interplay between planar and non planar diagrams. In complete generality we show that this same result is valid for any simple gauge group. Contact term contributions signal the presence of ultraviolet divergences. They are arbitrary at the tree level, but the absence of perturbative renormalization in the non singular part of the correlators allows to compute them unambiguously at higher orders. In the spirit of the AdS/CFT correspondence we comment on their relation to infrared singularities in the supergravity sector.We compute two-point functions of chiral operators TrΦk for any k, in N=4 supersymmetric SU(N) Yang–Mills theory. We find that up to the order g4 the perturbative corrections to the correlators vanish for all N. The cancellation occurs in a highly non trivial way, due to a complicated interplay between planar and non planar diagrams. In complete generality we show that this same result is valid for any simple gauge group. Contact term contributions signal the presence of ultraviolet divergences. They are arbitrary at the tree level, but the absence of perturbative renormalization in the non singular part of the correlators allows to compute them unambiguously at higher orders. In the spirit of the AdS/CFT correspondence we comment on their relation to infrared singularities in the supergravity sector.

β-functions for the Green-Schwarz superstring

Abstract We describe the calculation of one- and two-loop radiative corrections for the heterotic superstring σ-model described by the Green-Schwarz action in a supergravity-Yang-Mills background. The corresponding β-functions vanish when the superspace equations of motion for the coupled supergravity-Yang-Mills system are satisfied.