On the logarithmic behaviour in N=4 SYM theory

We show that the logarithmic behaviour seen in perturbative and non perturbative contributions to Green functions of gauge-invariant composite operators in N=4 SYM with SU(N) gauge group can be consistently interpreted in terms of anomalous dimensions of unprotected operators in long multiplets of the superconformal group SU(2,2|4). In order to illustrate the point we analyse the short-distance behaviour of a particularly simple four-point Green function of the lowest scalar components of the N=4 supercurrent multiplet. Assuming the validity of the Operator Product Expansion, we are able to reproduce the known value of the one-loop anomalous dimension of the single-trace operators in the Konishi supermultiplet. We also show that it does not receive any non-perturbative contribution from the one-instanton sector. We briefly comment on double- and multi-trace operators and on the bearing of our results on the AdS/SCFT correspondence.Comment: 18 pages, Late

Properties of the Konishi multiplet in N=4 SYM theory

We study perturbative and non-perturbative properties of the Konishi multiplet in N=4 SYM theory in D=4 dimensions. We compute two-, three- and four-point Green functions with single and multiple insertions of the lowest component of the multiplet, and of the lowest component of the supercurrent multiplet. These computations require a proper definition of the renormalized operator and lead to an independent derivation of its anomalous dimension. The O(g^2) value found in this way is in agreement with previous results. We also find that instanton contributions to the above correlators vanish. From our results we are able to identify some of the lowest dimensional gauge-invariant composite operators contributing to the OPE of the correlation functions we have computed. We thus confirm the existence of an operator belonging to the representation 20', which has vanishing anomalous dimension at order g^2 and g^4 in perturbation theory as well as at the non-perturbative level, despite the fact that it does not obey any of the known shortening conditions.Comment: 23 pages, latex, no figure

Correlation Functions of Conserved Currents in Four Dimensional Conformal Field Theory

We derive a generating function for all the 3-point functions of higher spin conserved currents in four dimensional conformal field theory. The resulting expressions have a rather surprising factorized form which suggest that they can all be realized by currents built from free massless fields of arbitrary (half-)integer spin s. This property is however not necessarily true also for the higher-point functions. As an illustration we analyze the general 4-point function of conserved abelian U(1) currents of scale dimension equal to three and find that apart from the two free field realizations there is a unique possible function which may correspond to an interacting theory. Although this function passes several non-trivial consistency tests, it remains an open challenging problem whether it can be actually realized in an interacting CFT.Comment: 20 pages, LaTeX, references adde

SU3SU_3 coherent state operators and invariant correlation functions and their quantum group counterparts

Coherent state operators (CSO) are defined as operator valued functions on G=SL(n,C), homogeneous with respect to right multiplication by lower triangular matrices. They act on a model space containing all holomorphic finite dimensional representations of G with multiplicity 1. CSO provide an analytic tool for studying G invariant 2- and 3-point functions, which are written down in the case of $SU_3$. The quantum group deformation of the construction gives rise to a non-commutative coset space. We introduce a "standard" polynomial basis in this space (related to but not identical with the Lusztig canonical basis) which is appropriate for writing down $U_q(sl_3)$ invariant 2-point functions for representaions of the type $(\lambda,0)$ and $(0,\lambda)$. General invariant 2-point functions are written down in a mixed Poincar\'e-Birkhoff-Witt type basis.Comment: 33 pages, LATEX, preprint IPNO/TH 94-0

Open Strings on the Neveu-Schwarz Pentabrane

We analyze the propagation of open and unoriented strings on the Neveu-Schwarz pentabrane (N5-brane) along the lines of a similar analysis for the SU(2) WZNW models. We discuss the two classes of open descendants of the diagonal models and a series of Z_2 projected models which exist only for even values of the level k and correspond to branes at D-type orbifold singularities. The resulting configurations of branes and planes are T-dual to those relevant to the study of dualities in super Yang-Mills theories. The association of Chan-Paton factors to D-brane multiplicities is possible in the semi-classical limit k -> infinity, but due to strong curvature effects is unclear for finite k. We show that the introduction of a magnetic field implies a twist of the SU(2) current algebra in the open-string sector leading to spacetime supersymmetry breaking.Comment: 22 pages, LaTe

Rationality of the Anomalous Dimensions in N=4 SYM theory

We reconsider the general constraints on the perturbative anomalous dimensions in conformal invariant QFT and in particular in N=4 SYM with gauge group SU(N_c). We show that all the perturbative corrections to the anomalous dimension of a renormalized gauge invariant local operator can be written as polynomials in its one loop anomalous dimension. In the N=4 SYM theory the coefficients of these polynomials are rational functions of the number of colours N_c.Comment: 20 pages, LaTe