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- Francis Dolan
- 2000

Various aspects of the four point function for scalar fields in conformally invariant theories are analysed. This depends on an arbitrary function of two conformal invariants u, v. A recurrence relation for the function corresponding to the contribution of an arbitrary spin field in the operator product expansion to the four point function is derived. This… (More)

Possible short and semi-short representations for N = 2 and N = 4 superconformal symmetry in four dimensions are discussed. For N = 4 the well known short supermultiplets whose lowest dimension conformal primary operators correspond to 1 2 -BPS or 1 4 -BPS states and are scalar fields belonging to the SU(4)r symmetry representations [0, p, 0] and [q, p, q]… (More)

By solving the two variable differential equations which arise from finding the eigenfunctions for the Casimir operator for O(d, 2) succinct expressions are found for the functions, conformal partial waves, representing the contribution of an operator of arbitrary scale dimension ∆ and spin l together with its descendants to conformal four point functions… (More)

We study four-point correlation functions of 12 -BPS operators in N = 4 SYM which are dual to massive KK modes in AdS5 supergravity. On the field theory side, the procedure of inserting the SYM action yields partial non-renormalisation of the four-point amplitude for such operators. In particular, if the BPS operators have dimensions equal to three or four,… (More)

The results of Römelsberger for a N = 1 superconformal index counting protected operators, satisfying a BPS condition and which cannot be combined to form long multiplets, are analysed further. The index is expressible in terms of single particle superconformal characters for N = 1 scalar and vector multiplets. For SQCD, involving SU(Nc) gauge groups and… (More)

We study the N = 2 four-dimensional superconformal index in various interesting limits, such that only states annihilated by more than one supercharge contribute. Extrapolating from the SU(2) generalized quivers, which have a Lagrangian description, we conjecture explicit formulae for all A-type quivers of class S, which in general do not have one. We test… (More)

Superconformal transformations are derived for the N = 2, 4 supermultiplets corresponding to the simplest chiral primary operators. These are applied to two, three and four point correlation functions. When N = 4, results are obtained for the three point function of various descendant operators, including the energy momentum tensor and SU(4) current. For… (More)

- Francis Dolan, Yang Mills
- 2008

The free field partition function for a generic U(N) gauge theory, where the fundamental fields transform in the adjoint representation, is analysed in terms of symmetric polynomial techniques. It is shown by these means how this is related to the cycle polynomial for the symmetric group and how the large N result may be easily recovered. Higher order… (More)

- Francis Dolan
- 2005

A discussion of character formulae for positive energy unitary irreducible representations of the the conformal group is given, employing Verma modules and Weyl group reflections. Product formulae for various conformal group representations are found. These include generalisations of those found by Flato and Fronsdal for SO(3, 2). In even dimensions the… (More)

qi = 3 where qi is the scale dimension for the i’th superfield and is related to the U(1) R-charge. In the latter case the relevant Ward identities reduce to eight differential equations for four functions of u, v which are invariants when the superconformal symmetry is reduced to the usual conformal group. The differential equations have a general solution… (More)