September 7, 2001
In a recent paper hep-th/0109064, quarter-BPS chiral primaries were constructed in the fully interacting four dimensional N=4 Super-Yang-Mills theory with gauge group SU(N). These operators are annihilated by four supercharges, and at order g^2 have protected scaling dimension and normalization. Here, we compute three-point functions involving these quarter-BPS operators along with half-BPS operators. The combinatorics of the problem is rather involved, and we consider the following special cases: (1) correlators < half half BPS > of two half-BPS primaries with an arbitrary chiral primary; (2) certain classes of < half quarter quarter > and < quarter quarter quarter > three-point functions; (3) three-point functions involving the Delta < 8 operators found in hep-th/0109064; (4) < half quarter quarter> correlators with the special quarter-BPS operator made of single and double trace operators only. The analysis in cases (1)-(3) is valid for general N, while (4) is a large N approximation. Order g^2 corrections to all three-point functions considered in this paper are found to vanish. In the AdS/CFT correspondence, quarter-BPS chiral primaries are dual to threshold bound states of elementary supergravity excitations. We present a supergravity discussion of two- and three-point correlators involving these bound states.
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September 7, 2001
Chiral primary operators annihilated by a quarter of the supercharges are constructed in the four dimensional N=4 Super-Yang-Mills theory with gauge group SU(N). These quarter-BPS operators share many non-renormalization properties with the previously studied half-BPS operators. However, they are much more involved, which renders their construction nontrivial in the fully interacting theory. In this paper we calculate order g^2 two-point functions of local, polynomial, scalar...
November 12, 2021
We start a systematic study of quarter-BPS operators in four-dimensional $\mathcal{N}=4$ Super Yang-Mills with gauge group $\mathrm{SU}(N)$ making use of recently developed tools in conformal field theory. We adapt the technology of embedding space tensor structures in four dimensions to the problem of computing R-symmetry tensor structures and we use the underlying chiral algebra to obtain the superconformal Ward identities. This allows us to fix the protected part of the fo...
August 15, 2014
We calculate the four-point correlation function of half-BPS operators with weights 2, 3, 3, 4 in N=4 SYM to two-loop order. The OPE of this correlation function provides a nontrivial check of the integrability conjecture for a class of three-point functions formulated in arXiv:1311.6404. Our perturbative calculation exploits the supergraph formalism in N=2 harmonic superspace.
June 3, 2011
Four point functions of general N=4 1/2-BPS primary fields, satisfying the next-next-to-extremality condition \Delta_{1}+\Delta_{2}+\Delta_{3}-\Delta_{4}=4 are studied at large N and strong coupling. We apply new techniques to evaluate the effective couplings in supergravity, and confirm that the four derivative couplings arising in the five-dimensional supergravity vanish on-shell. We then show that the four point amplitude resulting from supergravity naturally splits into a...
July 18, 2003
In this dissertation we explore various aspects of the AdS/CFT correspondence. As string quantization on general backgrounds with fluxes is very difficult, one often uses the duality at the level of canonical fields of supergravity and the corresponding half-BPS operators in SYM, since they both belong to the shortest multiplets of the superconformal group SU(2,2|4). In addition to half-BPS operators, there are others with non-renormalization properties. One such class of ope...
March 22, 2007
In this note we study half-BPS operators in N=4 super Yang-Mills for gauge group SU(N) at finite N. In particular we elaborate on the results of hep-th/0410236, providing an exact formula for the null basis operators algorithmically constructed there. For gauge groups U(N) and SU(N) we show that this basis is dual to the basis of multi-trace operators with respect to the two point function. We use this to extend the results of hep-th/0611290 concerning factorisation and proba...
September 10, 2007
We calculate four-point correlation functions of two weight-2 and two weight-3 1/2-BPS operators in \mathcal{N}=4 SYM in the large N limit in supergravity approximation. By the AdS/CFT conjecture, these operators are dual to AdS supergravity scalar fields s_2 and s_3 with mass m^2 = -4 and m^2 = -3 respectively. This is the first non-trivial four-point function of mixed-weight operators of lowest conformal dimensions. We show that the supergravity-induced four-point functio...
January 15, 2003
A systematic construction is presented of 1/4 BPS operators in N=4 superconformal Yang-Mills theory, using either analytic superspace methods or components. In the construction, the operators of the classical theory annihilated by 4 out of 16 supercharges are arranged into two types. The first type consists of those operators that contain 1/4 BPS operators in the full quantum theory. The second type consists of descendants of operators in long unprotected multiplets which dev...
March 3, 2000
We discuss recent results on two-point functions of chiral primary operators in {\cal N}=4 SU(N) supersymmetric Yang-Mills theory. Our results give further support to the belief that such correlators are not renormalized to all orders in g and to all orders in N.
November 26, 2002
A new derivation is given of four-point functions of charge $Q$ chiral primary multiplets in N=4 supersymmetric Yang-Mills theory. A compact formula, valid for arbitrary $Q$, is given which is manifestly superconformal and analytic in the internal bosonic coordinates of analytic superspace. This formula allows one to determine the spacetime four-point function of any four component fields in the multiplets in terms of the four-point function of the leading chiral primary fiel...