Search

For three-dimensional ABJ(M) theories and N= 4 Chern-Simons-matter quiver theories, we construct two sets of 1/2 BPS Wilson loop operators by applying the Higgsing procedure along independent directions of the moduli space, and choosing different massive modes. For theories whose dual M-theory description is known, we also determine the corresponding spectrum of 1/2 BPS M2-brane solutions. We identify the supercharges in M-theory and field theory, as well as the supercharges preserved by M2-/anti-M2-branes and 1/2 BPS Wilson loops. In particular, in N= 4 orbifold ABJM theory we find pairs of different 1/2 BPS Wilson loops that preserve exactly the same set of supercharges. In field theory they arise by Higgsing with the choice of either particles or antiparticles, whereas in the dual description they correspond to a pair of M2-/anti-M2-branes localized at different positions in the compact space. This result enlightens the origin of classical Wilson loop degeneracy in these theories, already discussed in arXiv:1506.07614. A discussion on possible scenarios that emerge by comparison with localization results is included.

In three dimensional N= 4 Chern-Simons-matter theories two independent fermionic Wilson loop operators can be defined, which preserve half of the supersymmetry charges and are cohomologically equivalent at classical level. We compute their three-loop expectation value in a convenient color sector and prove that the degeneracy is uplifted by quantum corrections. We expand the matrix model prediction in the same regime and by comparison we conclude that the quantum 1/2 BPS Wilson loop is the average of the two operators. We provide an all-loop argument to support this claim at any order. As a by-product, we identify the localization result at three loops as a correction to the framing factor induced by matter interactions. Finally, we comment on the quantum properties of the non-1/2 BPS Wilson loop operator defined as the difference of the two fermionic ones.

Supersymmetric localization provides exact results that should match QFT computations in some regularization scheme. The agreement is particularly subtle in three dimensions where complex answers from localization procedure sometimes arise. We investigate this problem by studying the expectation value of the 1/6 BPS Wilson loop in planar ABJ(M) theory at three loops in perturbation theory. We reproduce the corresponding term in the localization result and argue that it originates entirely from a non-trivial framing of the circular contour. Contrary to pure Chern-Simons theory, we point out that for ABJ(M) the framing phase is a non-trivial function of the couplings and that it potentially receives contributions from vertex-like diagrams. Finally, we briefly discuss the intimate link between the exact framing factor and the Bremsstrahlung function of the 1/2-BPS cusp.

For three-dimensional N=4 super-Chern-Simons-matter theories associated to necklace quivers U(N0)×U(N1)×.U(N2r-1), we study at quantum level the two kinds of 1/2 BPS Wilson loop operators recently introduced in arXiv:1506.07614. We perform a two-loop evaluation and find the same result for the two kinds of operators, so moving to higher loops a possible quantum uplift of the classical degeneracy. We also compute the 1/4 BPS bosonic Wilson loop and discuss the quantum version of the cohomological equivalence between fermionic and bosonic Wilson loops. We compare the perturbative result with the Matrix Model prediction and find perfect matching, after identification and remotion of a suitable framing factor. Finally, we discuss the potential appearance of three-loop contributions that might break the classical degeneracy and briefly analyze possible implications on the BPS nature of these operators.

We study a family of circular BPS Wilson loops in N = 6 super Chern-Simons-matter theories, generalizing the usual 1/2-BPS circle. The scalar and fermionic couplings depend on two deformation parameters and these operators can be considered as the ABJ(M) counterpart of the DGRT latitudes defined in N = 4 SYM. We perform a complete two-loop analysis of their vacuum expectation value, discuss the appearance of framing-like phases and propose a general relation with cohomologically equivalent bosonic operators. We make an all-loop proposal for computing the Bremsstrahlung function associated to the 1/2-BPS cusp in terms of these generalized Wilson loops. When applied to our two-loop result it reproduces the known expression. Finally, we comment on the generalization of this proposal to the bosonic 1/6-BPS case. © 2014 The Author(s)

We compute the expectation value of the 1/2 BPS circular Wilson loop operator in ABJ(M) theory at two loops in perturbation theory. Our result turns out to be in exact agreement with the weak coupling limit of the prediction coming from localization, including finite N contributions associated to non-planar diagrams. It also confirms the identification of the correct framing factor that connects framing-zero and framing-one expressions, previously proposed. The evaluation of the 1/2 BPS operator is made technically difficult in comparison with other observables of ABJ(M) theory by the appearance of integrals involving the coupling between fermions and gauge fields, which are absent for instance in the 1/6 BPS case. We describe in detail how to analytically solve these integrals in dimensional regularization with dimensional reduction (DRED). By suitably performing the physical limit to three dimensions we clarify the role played by short distance divergences on the final result and the mechanism of their cancellation

We evaluate ABJM observables at two loops, for any value of the rank N of the gauge group. We compute the color subleading contributions to the four-point scattering amplitude in ABJM at two loops. Contrary to the four dimensional case, IR divergent N-subleading contributions are proportional to leading poles in the regularization parameter. We then exploit the non-planar calculation for the amplitude to derive an expression for the two-loop Sudakov form factor at any N. In the planar limit the result coincides with the one recently obtained in literature by using Feynman diagrams and unitarity. Finally, we analyze the subleading contributions to the light-like four-cusps Wilson loop and interpret the result in terms of the non-abelian exponentiation theorem. All these perturbative results satisfy the uniform transcendentality principle, hinting at its validity in ABJM beyond the planar limit. © SISSA 2013.

We compute the expectation value of the 1/2 BPS circular Wilson loop in N=6 superconformal Chern-Simons (ABJM) theory at two loops in perturbation theory. The result shows perfect agreement with the prediction from localization and the proposed framing factor. © 2013 American Physical Society.

We revisit the computation of the two-loop light-like tetragonal Wilson loop for three dimensional pure Chern-Simons and N = 6 Chern-Simons-matter theory, within dimensional regularization with dimensional reduction scheme. Our examination shows that, contrary to prior belief, the result respects maximal transcendentality as is the case of the four-point scattering amplitude of the theory. Interestingly, the corrected result matches exactly the scattering amplitude both in the divergent and in the finite parts, constants included

In planar N = 4 SYM we study a particular class of helicity preserving amplitudes. These are scalar amplitudes whose flavor configuration is chosen in such a way that only a limited number of diagrams is allowed, which exhibit an iterative structure. For such amplitudes we evaluate the tree level and one-loop contributions, providing a general formula valid for any number of particles. The ratio between the one-loop and tree level results is a simple combination of dual conformally invariant box functions with at most two massive legs. Along with the MHV and NMHV series, this constitutes the third known infinite sequence of one-loop amplitudes in N = 4 SYM

We derive an exact algebraic identity between the two–loop four–point amplitude in ABJM theory and the corresponding one–loop amplitude in N = 4 SYM theory. This identity generalizes previous partial results to an exact relation valid at all orders in the IR regulator. Moreover, it allows to conjecture an exact iterative expression for the complete three dimensional amplitude in terms of the BDS ansatz for the four dimensional one, indicating that the strict relation between the two amplitudes experimented at two loops might propagate to all orders. In particular, an almost complete expression for the ABJM amplitude at four loops is derived

For N = 6 superconformal Chern–Simons–matter theories in three dimen- sions, by a direct superspace Feynman diagram approach, we compute the two–loop four–point scattering amplitude with external chiral matter fields. We find that the result is in perfect agreement with the two–loop result for a light–like four–polygon Wilson loop. This is a nontrivial evidence of the scattering amplitudes/Wilson loop duality in three dimensions. Moreover, both the IR divergent and the finite parts of our two–loop result agree with a BDS–like ansatz for all–loop amplitudes where the scaling function is given in terms of the N = 4 SYM one, according to the conjectured Bethe equations for ABJM. Consequently, we are able to make a prediction for the four–loop correction to the amplitude. We also discuss the dual conformal invariance of the two–loop result

For three dimensional N = 6 superconformal field theories we compute one–loop scattering amplitudes for any number of external particles. We focus on a particular subsector of N = 2 invariant superamplitudes for which the ordinary pertur- bative evaluation becomes very easy. The result we obtain is in general non–vanishing. For six external particles our findings are sufficient for determining the complete ex- pression of the N = 6 superamplitude at this order. We discuss the symmetries of the result and its anomalous variation under superconformal generators

We study the correspondence between scattering amplitudes and Wilson loops in three–dimensional Chern–Simons matter theories. In particular, using N = 2 superspace formalism, we compute at one loop the whole spectrum of four–point superamplitudes for generic N ≥ 2 supersymmetric theories and find a vanishing result for N = 6 ABJ(M) and N = 8 BLG models. This restricts the possible range of theories for which Wilson loops/scattering amplitudes duality might work. At two loops, we present the computation of the four-point ABJ scattering amplitude for external chiral superfields. Extending the known result for the ABJM Wilson loop to the ABJ case we find perfect agreement. We also discuss the dual conformal invariance of our results and the relationship between the Feynman diagram computation and unitarity methods. While for the ABJM theory dual conformally invariant integrals exactly reproduce the amplitude, for the ABJ case this happens only up to a residual constant depending on the parity–violating parameter. Finally we propose a BDS–like exponentiation for the amplitude based on an analogy with the four dimensional N = 4 SYM case, and discuss its strong coupling dual counterpart.

We study n–point correlation functions for chiral primary operators in three dimensional supersymmetric Chern–Simons matter theories. Our analysis is car- ried on in N = 2 superspace and covers N = 2, 3 supersymmetric CFT’s, the N = 6 ABJM and the N = 8 BLG models. In the limit where the positions of adjacent opera- tors become light–like, we find that the one–loop n–point correlator divided by its tree level expression coincides with a light–like n–polygon Wilson loop. Remarkably, the result can be simply expressed as a linear combination of five dimensional two–mass easy boxes. We manage to evaluate the integrals analytically and find a vanishing result, in agreement with previous findings for Wilson loops

We determine perturbatively the conformal manifold of N = 2 Chern-Simons matter theories with the aim of checking in the three dimensional case the general prescription based on global symmetry breaking, recently introduced in [1-3]. We discuss in details few remarkable cases like the N = 6 ABJM theory and its less supersymmetric generalizations with/without flavors. In all cases we find perfect agreement with the predictions of global symmetry breaking prescription. For unflavored theories the conformal manifold is a three dimensional compact surface. This feature is peculiar of three dimensions, as it has no direct analogue in four dimensional supersymmetric models. © SISSA 2011.

According to the AdS4/CFT3 correspondence, N=2 supersymmetric Chern-Simons matter theories should have a stable fixed point in the infrared. In order to support this prediction we study RG flows of two-level Chern-Simons matter theories with/without flavors induced by the most general marginal superpotential compatible with N=2 supersymmetry. At two loops we determine the complete spectrum of fixed points and study their IR stability. Our analysis covers a large class of models including perturbations of the ABJM/ABJ theories with and without flavors, N=2,3 theories with different CS levels corresponding to turning on a Romans mass and beta-deformations. In all cases we find curves (or surfaces) of fixed points which are globally IR stable but locally unstable in the following sense: The system has only one direction of stability which in the ABJM case coincides with the maximal global symmetry preserving perturbation, whereas along any other direction it flows to a different fixed point on the surface. The question of conformal invariance vs. finiteness is also addressed: While in general vanishing beta-functions imply two-loop finiteness, we find a particular set of flavored theories where this is no longer true.

We consider marginal deformations of the superconformal ABJM/ABJ models which preserve N=2 supersymmetry. We determine perturbatively the spectrum of fixed points and study their infrared stability. We find a closed line of fixed points which is IR stable. The fixed point corresponding to the ABJM/ABJ models is stable under marginal deformations which respect the original SU(2)xSU(2) invariance, while deformations which break this group destabilize the theory which then flows to a less symmetric fixed point. We discuss the addition of flavor degrees of freedom. We prove that in general a flavor marginal superpotential does not destabilize the system in the IR. An exception is represented by a marginal coupling which mixes matter charged under different gauge sectors. Finally, we consider the case of relevant deformations which should drive the system to a strongly coupled IR fixed point recently investigated in arXiv:0909.2036 [hep-th].Chern–Simons theories, N = 2 Supersymmetry, Infrared stability

We consider nonanticommutative SYM theories with chiral matter in the adjoint representation of the SU(N) x U(1) gauge group. In a superspace setup and manifest background covariant approach we investigate the one-loop renormalization of the theory when a cubic superpotential is present. The structure of the divergent terms reveals that the theory simply obtained from the ordinary one by trading products for star products is not renormalizable. Moreover, because of the different renormalization undergone by the abelian field compared to the non-abelian ones, the superpotential seems to be incompatible with the requests of renormalizability, gauge and N=1/2 invariance. However, by a suitable modification of the quadratic action for the U(1) (anti)chiral superfields and the addition of extra couplings, we find an action which is one-loop renormalizable and manifestly N=1/2 supersymmetric and supergauge invariant. We conclude that interacting matter can be safely introduced in NAC gauge theories, in contrast with previous results.

Renormalizable nonanticommutative SYM theories with chiral matter in the adjoint representation of the gauge group have been recently constructed in [arXiv:0901.3094]. In the present paper we focus on the U*(1) case with matter interacting through a cubic superpotential. For a single flavor, in a superspace setup and manifest background covariant approach we perform the complete one-loop renormalization and compute the beta-functions for all couplings appearing in the action. We then generalize the calculation to the case of SU(3) flavor matter with a cubic superpotential viewed as a nontrivial NAC generalization of the ordinary abelian N=4 SYM and its marginal deformations. We find that, as in the ordinary commutative case, the NAC N=4 theory is one-loop finite. We provide general arguments in support of all-loop finiteness. Instead, deforming the superpotential by marginal operators gives rise to beta-functions which are in general non-vanishing. We study the spectrum of fixed points and the RG flows. We find that nonanticommutativity always makes the fixed points unstable.

We study the embedding of spacetime filling D7-branes in beta-deformed backgrounds which, according to the AdS/CFT dictionary, corresponds to flavoring beta-deformed N=4 super Yang-Mills. We consider supersymmetric and more general non-supersymmetric three parameter deformations. The equations of motion for quadratic fluctuations of a probe D7-brane wrapped on a deformed three-sphere exhibit a non-trivial coupling between scalar and vector modes induced by the deformation. Nevertheless, we manage to solve them analytically and find that the mesonic mass spectrum is discrete, with a mass gap and a Zeeman-like splitting occurs. Finally we propose the action for the dual field theory as obtained by star-product deformation of super Yang-Mills with fundamental matter.

We study the cal{N}=1 SU(N) SYM theory which is a marginal deformation of the cal{N}=4 theory, with a complex deformation parameter eta. We consider the large N limit and study perturbatively the conformal invariance condition. We find that finiteness requires reality of the deformation parameter eta.

This is a sequel of our paper hep-th/0606125 in which we have studied the {cal N}=1 SU(N) SYM theory obtained as a marginal deformation of the {cal N}=4 theory, with a complex deformation parameter eta and in the planar limit. There we have addressed the issue of conformal invariance imposing the theory to be finite and we have found that finiteness requires reality of the deformation parameter eta. In this paper we relax the finiteness request and look for a theory that in the planar limit has vanishing beta functions. We perform explicit calculations up to five loop order: we find that the conditions of beta function vanishing can be achieved with a complex deformation parameter, but the theory is not finite and the result depends on the arbitrary choice of the subtraction procedure. Therefore, while the finiteness condition leads to a scheme independent result, so that the conformal invariant theory with a real deformation is physically well defined, the condition of vanishing beta function leads to a result which is scheme dependent and therefore of unclear significance. In order to show that these findings are not an artefact of dimensional regularization, we confirm our results within the differential renormalization approach.

We study exact string backgrounds (WZW models) generated by nonsemisimple algebras which are obtained as double extensions of generic D-dimensional semisimple algebras. Even if a suitable change of coordinates always exists which reduces these backgrounds to be the product of the non-trivial background associated to the original algebra and two-dimensional Minkowski. under Inonu-Wigner contraction the algebra reduces to a Nappi-Witten algebra and the corresponding plane wave spacetime, no more factorized, is the Penrose limit of the original background. We construct the spectrum of D-branes for the double-extended background and study their behavior under the Penrose limit. While in general D-branes become singular in this limit, we prove that a class of solutions with a well-defined limit exists and it gives rise to the spectrum of configurations of the contracted model. Therefore. all D-branes of the plane wave background can be obtained as suitable contractions of original ones. We also discuss the Penrose limit at the quantum level and argue that the procedures of contraction and quantization commute. (c) 2007 Elsevier B.V. All rights reserved.

In this note, we establish the formulation of 6D, N=1 hypermultiplets in terms of 4D chiral-nonminimal (CNM) scalar multiplets. The coupling of these to 6D, N=1 Yang-Mills multiplets is described. A 6D, N=1 projective superspace formulation is given in which the above multiplets naturally emerge. The covariant superspace quantization of these multiplets is studied in details.

For cal{N}=1 SU(N) SYM theories obtained as marginal deformations of the cal{N}=4 parent theory we study perturbatively some sectors of the chiral ring in the weak coupling regime and for finite N. By exploiting the relation between the definition of chiral ring and the effective superpotential we develop a procedure which allows us to easily determine protected chiral operators up to n loops once the superpotential has been computed up to (n-1) order. In particular, for the Lunin-Maldacena beta-deformed theory we determine the quantum structure of a large class of operators up to three loops. We extend our procedure to more general Leigh-Strassler deformations whose chiral ring is not fully understood yet and determine the weight-two and weight-three sectors up to two loops. We use our results to infer general properties of the chiral ring.

Using 4D, N; = 1 superfield techniques, a discussion of the 6D sigma-model possessing simple supersymmetry is given. Two such approaches are described. Foremost it is shown that the simplest and most transparent description arises by use of a doublet of chiral scalar superfields for each 6D hypermultiplet. A second description that is most directly related to projective superspace is also presented. The latter necessarily implies the use of one chiral superfield and one nonminimal scalar superfield for each 6D hypermultiplet. A separate study of models of this class, outside the context of projective superspace, is also undertaken.

We present a systematic investigation of one-loop renormalizability for nonanticommutative N = 1/2, U(N) SYM theory in superspace. We first discuss classical gauge invariance of the pure gauge theory and show that in contradistinction to the ordinary anti-commutative case, different representations of supercovariant derivatives and field strengths do not lead to equivalent descriptions of the theory. Subsequently we develop background field methods which allow us to compute a manifestly covariant gauge effective action. One-loop evaluation of divergent contributions reveals that the theory simply obtained from the ordinary one by trading products for star products is not renormalizable. In the case of SYM with no matter we present a N = 1/2 improved action which we show to be one-loop renormalizable and which is perfectly compatible with the algebraic structure of the star product. For this action we compute the beta functions. A brief discussion on the inclusion of chiral matter is also presented.

We compute two-point functions of lowest weight operators at the next-to-leading order in the couplings for the beta-deformed N=4 SYM. In particular we focus on the CPO Tr(Phi_1^2) and the operator Tr(Phi_1 Phi_2) 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 in hep-th/0506128. However, in both cases a finite correction to the two-point function appears.

So far, quantum properties of N = 1/2 nonanticommutative (NAC) super Yang-Mills theories have been investigated in the WZ gauge. The gauge independence of the results requires assuming that at the quantum level supergauge invariance is not broken by nonanticommutative geometry. In this paper we use an alternative approach which allows studying these theories in a manifestly gauge independent superspace setup. This is accomplished by generalizing the background field method to the NAC case, by moving to a momentum superspace where star products are treated as exponential factors and by developing momentum supergraph techniques. We compute the one-loop gauge effective action for NAC U(N) gauge theories with matter in the adjoint representation. Despite the appearance of divergent contributions which break (super)gauge invariance, we prove that the effective action at this order is indeed invariant.

Requiring an infinite number of conserved local charges or the existence of an underlying linear system does not uniquely determine the Moyal deformation of (1 + 1)-dimensional integrable field theories. As an example, the sine-Gordon model may be obtained by dimensional and algebraic reduction from (2 + 2)-dimensional self-dual U(2) Yang-Mills through a (2 + 1)-dimensional integrable U(2) sigma model, with some freedom in the noncommutative extension of this algebraic reduction. Relaxing the latter from U(2) --> U(1) to U(2) --> U(1) x U(1), we arrive at novel noncommutative sine-Gordon equations for a pair of scalar fields. The dressing method is employed to construct its multi-soliton solutions. Finally, we evaluate various tree-level amplitudes to demonstrate that our model possesses a factorizable and causal S-matrix in spite of its time-space noncommutativity. (C) 2004 Elsevier B.V. All rights reserved.

In the beta-deformed N = 4 supersymmetric SU(N) Yang-Mills theory we study the class of operators O-J = Tr(Phi(i)(J)Phi(k)), i not equal k and compute their exact anomalous dimensions for N,J -> infinity. 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 g(2) = h (h) over bar 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 OJ sector of this theory shares many similarities with the BMN sector of the N = 4 theory in the large R-charge limit.

In this paper we continue the program, initiated in ref. [1], to investigate an integrable noncommutative version of the sine-Gordon model. We discuss the origin of the extra constraint which the field function has to satisfy in order to guarantee classical integrability. We show that the system of constraint plus dynamical equation of motion can be obtained by a suitable reduction of a noncommutative version of 4d self-dual Yang-Mills theory. The field equations can be derived from an action which is the sum of two WZNW actions with cosine potentials corresponding to a complexified noncommutative U(1) gauge group. A brief discussion of the relation with the bosonized noncommutative Thirring model is given. In spite of integrability we show that the S-matrix is acausal and particle production takes place

In these proceedings, we review the main results concerning superspace geometries with nonanticommutative spinorial variables and field theories formulated on them. In particular, we report on the quantum properties of the WZ model formulated in the N = 1/2 nonanticommutative superspace

We investigate the most general non(anti)commutative geometry in N=1 four-dimensional superspace, invariant under the classical (i.e., undeformed) supertranslation group. We find that a nontrivial non(anti)commutative superspace geometry compatible with supertranslations exists with non(anti)commutation parameters which may depend on the spinorial coordinates. The algebra is in general nonassociative. Imposing associativity introduces additional constraints which however allow for nontrivial commutation relations involving fermionic coordinates. We obtain explicitly the first three terms of a series expansion in the deformation parameter for a possible associative *-product. We also consider the case of N=2 euclidean superspace where the different conjugation relations among spinorial coordinates allow for a more general supergeometry

Using the bicomplex approach we discuss an integrable noncommutative system in two-dimensional Euclidean space. It is described by an equation of motion which reduces to the ordinary sine-Gordon equation when the noncommutation parameter is removed, plus a constraint equation which is nontrivial only in the noncommutative case. The implications of this constraint, which is required by integrability but seems to reduce the space of classical solutions, remain to be understood. We show that the system has an infinite number of conserved currents and we give the general recursive relation for constructing them. For the particular cases of lower spin nontrivial currents we work out the explicit expressions and perform a direct check of their conservation. These currents reduce to the usual sine-Gordon currents in the commutative limit. We find classical "localized" solutions to first order in the noncommutativity parameter and describe the Backlund transformations for our system. Finally, we comment on the relation of our noncommutative system to the commutative sine-Gordon system. © 2003 Elsevier Science B.V. All rights reserved.

We study systematically, through two loops, the divergence structure of the supersymmetric WZ model defined on the N = 1/2 nonanticommutative superspace. By introducing a spurion field to represent the supersymmetry breaking term F-3 we are able to perform our calculations using conventional supergraph techniques. Divergent terms proportional to F, F-2 and F-3 are produced (the first two are to be expected on general grounds) but no higher-point divergences are found. By adding ab initio F and F-2 terms to the original lagrangian we render the model renormalizable. We determine the renormalization constants and beta functions through two loops, thus making it possible to study the renormalization group flow of the nonanticommutation parameter

We study a class of non-protected local composite operators which occur in the R-symmetry singlet channel of the OPE of two stress-tensor multiplets in N = 4 SYM. At tree level these are quadrilinear scalar dimension four operators, two single-traces and two double-traces. In the presence of interaction, due to a non-trivial mixing under renormalization, they split into linear combinations of conformally covariant operators. We resolve the mixing by computing the one-loop two-point functions of all the operators in an N = I setup, then diagonalizing the anomalous dimension matrix and identifying the quasiprimary operators. We find one operator whose anomalous dimension is negative and suppressed by a factor of 1/N-2 with respect to the anomalous dimensions of the Konishi-like operators. We reveal the mechanism responsible for this suppression and argue that it works at every order in perturbation theory. In the context of the AdS/CFT correspondence such an operator should be dual to a multiparticle supergravity state whose energy is less than the sum of the corresponding individual single-particle states. (C) 2002 Elsevier Science B.V. All rights reserved.

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 extend the general method of S.J. Gates Jr. et al. [hep-th/0009192] to compute the consistent gauge anomaly for noncommutative 4d SSYM coupled to chiral matter. The choice of the minimal homotopy path allows us to obtain a simple and compact result. We perform the reduction to components in the WZ gauge proving that our result contains, as lowest component, the busonic chiral anomaly for noncommutative YM theories recently obtained in literature. (C) 2001 Elsevier Science B.V. All rights reserved.

We use the method of Banerjee, Banerjee and Mitra and minimal homotopy paths to compute the consistent gauge anomaly for several superspace models of SSYM coupled to matter, We review the derivation of the anomaly for N = 1 in four dimensions and then discuss the anomaly For two-dimensional models with (2, 0) supersymmetry

In a N = 1 superspace setup and using dimensional regularization, we give a general and simple prescription to compute anomalous dimensions of composite operators in N = 4, SU(N) supersymmetric Yang-Mills theory, perturbatively in the coupling constant g. We show in general that anomalous dimensions are responsible for the appearance of higher order poles in the perturbative expansion of the two-point function and that their lowest contribution can be read directly from the coefficient of the 1/epsilon (2) pole. As a check of our procedure we rederive the anomalous dimension of the Konishi superfield at order g(2). We then apply this procedure to the case of the double trace, dimension 4, superfield in the 20 of SU(4) recently considered in the literature. We find that its anomalous dimension vanishes for all N in agreement with previous results. (C) 2001 Elsevier Science B.V. All rights reserved

We discuss features of the 4D, N = 1 WZNW term expressed as a function of chiral superfields and defined in a manner appropriate to calculate phenomenological matrix elements. (C) 2001 Published by Elsevier Science B.V.