Anomaly-Free Tensor-Yang-Mills System and Its Dual Formulation

We consider the (1,0) supersymmetric Yang-Mills multiplet coupled to a self-dual tensor multiplet in six dimensions. It is shown that the counterterm required to cancel the one-loop gauge anomaly modifies the classical equations of motion previously obtained by Bergshoeff, Sezgin and Sokatchev (BSS). We discuss the supermultiplet structure of the anomalies exhibited in the resulting equations of motion. The anomaly corrected field equations agree with the global limit, recently obtained by Duff, Liu, Lu and Pope, of a matter coupled supergravity theory in six dimensions. We also obtain the dual formulation of the BSS model in which the tensor multiplet is free while the field equations of the Yang-Mills multiplet contain the fields of the tensor multiplet at the classical level

OPEs and 3-point correlators of protected operators in N=4 SYM

Two- and three-point correlation functions of arbitrary protected operators are constructed in N=4 SYM using analytic superspace methods. The OPEs of two chiral primary multiplets are given. It is shown that the $n$-point functions of protected operators for $n\leq4$ are invariant under $U(1)_Y$ and it is argued that this implies that the two- and three-point functions are not renormalised. It is shown explicitly how unprotected operators can be accommodated in the analytic superspace formalism in a way which is fully compatible with analyticity. Some new extremal correlators are exhibited

Operator product expansions in four-dimensional superconformal field theories

The operator product expansion in four-dimensional superconformal field theory is discussed. The OPE takes a particularly simple form for chiral operators, in N=1 and N=2, and for analytic operators, in N=2 and N=4. It is argued that the Green's functions of such operators can be determined up to constants.The operator product expansion in four-dimensional superconformal field theory is discussed. The OPE takes a particularly simple form for chiral operators, in $N=1$ and $N=2$, and for analytic operators, in $N=2$ and $N=4$. It is argued that the Green's functions of such operators can be determined up to constants.The operator product expansion in four-dimensional superconformal field theory is discussed. It is demonstrated that the OPE takes a particularly simple form for certain classes of operators. These are chiral operators, principally of interest in theories with N = 1 or N = 2 supersymmetry, and analytic operators, of interest in N = 2 and N = 4. It is argued that the Green's functions of such operators can be determined up to constants

On the symmetries of special holonomy sigma models

In addition to superconformal symmetry, (1,1) supersymmetric two-dimensional sigma models on special holonomy manifolds have extra symmetries that are in one-to-one correspondence with the covariantly constant forms on these manifolds. The superconformal algebras extended by these symmetries close as W-algebras, i.e. they have field-dependent structure functions. It is shown that it is not possible to write down cohomological equations for potential quantum anomalies when the structure functions are field-dependent. In order to do this it is necessary to linearise the algebras by treating composite currents as generators of additional symmetries. It is shown that all cases can be linearised in a finite number of steps, except for G_2 and SU(3). Additional problems in the quantisation procedure are briefly discussed.Comment: 16 pages. Abstract improved and a few typographical errors correcte