Conformally coupled supermultiplets in four and five dimensions

We obtain by superfield methods the exceptional representations of the OSp(2N/4,R) and SU(2,2/1) superalgebras which extend to supersingletons of SU(2,2/2N) and F(4), respectively. These representations describe superconformally coupled multiplets and appear in three- and four-dimensional superconformal field theories which are holographic descriptions of certain anti-de Sitter supergravities

Supersymmetric null-surfaces

Single trace operators with the large R-charge in supersymmetric Yang-Mills theory correspond to the null-surfaces in $AdS_5\times S^5$. We argue that the moduli space of the null-surfaces is the space of contours in the super-Grassmanian parametrizing the complex $(2|2)$-dimensional subspaces of the complex $(4|4)$-dimensional space. The odd coordinates on this super-Grassmanian correspond to the fermionic degrees of freedom of the superstring.Comment: v4: added a reference to the earlier work; corrected the formula for the stabilizer of the BMN vacuum; added the discussion of the complex structure of the odd coordinates in Section 3.

Conformal fields in the pp-wave limit

The pp-wave (Penrose limit) in conformal field theory can be viewed as a special contraction of the unitary representations of the conformal group. We study the kinematics of conformal fields in this limit in a geometric approach where the effect of the contraction can be visualized as an expansion of space-time. We discuss the two common models of space-time as carrier spaces for conformal fields: One is the usual Minkowski space and the other is the coset of the conformal group over its maximal compact subgroup. We show that only the latter manifold and the corresponding conformal representation theory admit a non-singular contraction limit. We also address the issue of correlation functions of conformal fields in the pp-wave limit. We show that they have a well-defined contraction limit if their space-time dependence merges with the dependence on the coordinates of the R symmetry group. This is a manifestation of the fact that in the limit the space-time and R symmetries become indistinguishable. Our results might find applications in actual calculations of correlation functions of composite operators in N=4 super Yang-Mills theory.Comment: LaTex, 32 pages, 1 figure, discussion of correlation functions extended; some corrections made; references adde

The ultra-violet question in maximally supersymmetric field theories

We discuss various approaches to the problem of determining which supersymmetric invariants are permitted as counterterms in maximally supersymmetric super Yang--Mills and supergravity theories in various dimensions. We review the superspace non-renormalisation theorems based on conventional, light-cone, harmonic and certain non-Lorentz covariant superspaces, and we write down explicitly the relevant invariants. While the first two types of superspace admit the possibility of one-half BPS counterterms, of the form $F^4$ and $R^4$ respectively, the last two do not. This suggests that UV divergences begin with one-quarter BPS counterterms, i.e. $d^2 F^4$ and $d^4 R^4$, and this is supported by an entirely different approach based on algebraic renormalisation. The algebraic formalism is discussed for non-renormalisable theories and it is shown how the allowable supersymmetric counterterms can be determined via cohomological methods. These results are in agreement with all the explicit computations that have been carried out to date. In particular, they suggest that maximal supergravity is likely to diverge at four loops in D=5 and at five loops in D=4, unless other infinity suppression mechanisms not involving supersymmetry or gauge invariance are at work.Comment: 56 pages, 1 figure, uses youngtab.sty. Contribution to the proceedings of the W.E. Heraeus Workhop "Quantum Gravity: Challenges and Perspectives", Bad Honnef, 14-16 April 2008. References and clarifying comments adde

(N,p,q) - harmonic superspaces and their applications

SIGLEAvailable from British Library Document Supply Centre-DSC:DXN005142 / BLDSC - British Library Document Supply CentreGBUnited Kingdo