Three-Point Functions of Quarter BPS Operators in N=4 SYM

We study the large N degeneracy in the structure of the four-point amplitudes of 1/2-BPS operators of arbitrary weight k in perturbative N=4 SYM theory. At one loop (order g^2) this degeneracy manifests itself in a smaller number of independent conformal invariant functions describing the amplitude, compared to AdS_5 supergravity results. To study this phenomenon at the two-loop level (order g^4) we consider a particular N=2 hypermultiplet projection of the general N=4 amplit...

We study all three-point functions of normalized chiral operators in D=4, $\mathcal{N}=4$, U(N) supersymmetric Yang-Mills theory in the large $N$ limit. We compute them for small 't Hooft coupling $\lambda=g_{YM}^2N<<1$ using free field theory and at strong coupling $\lambda=g_{YM}^2>>1$ using the $AdS$/CFT correspondence. Surprisingly, we find the same answers in the two limits. We conjecture that at least for large $N$ the exact answers are independent of $\lambda $ .

Half BPS correlators in N=4 super Yang-Mills theory are key quantities both in the AdS/CFT correspondence as well as in scattering amplitudes research. They are dual at strong coupling to quantum gravity amplitudes. At weak coupling on the other hand they contain all N=4 SYM amplitudes. They have been found to possess a number of hidden symmetries, for example non-trivial permutation symmetry of perturbative four-point integrands and a higher dimensional conformal symmetry. T...

We present the computation of all the correlators of 1/2-BPS operators in $\mathcal{N} = 4$ SYM with weights up to 8 as well as some very high-weight correlation functions from the effective supergravity action. The computation is done by implementing the recently developed simplified algorithm in combination with the harmonic polynomial formalism. We provide a database of these results attached to this publication and additionally check for almost all of the functions in thi...

An expression for the four point function for half-BPS operators belonging to the [0,p,0] SU(4) representation in N=4 superconformal theories at strong coupling in the large N limit is suggested for any p. It is expressed in terms of the four point integrals defined by integration over AdS_5 and agrees with, and was motivated by, results for p=2,3,4 obtained via the AdS/CFT correspondence. Using crossing symmetry and unitarity, the detailed form is dictated by the requirement...

We compute four-point functions in the Heavy-Heavy-Light-Light limit involving all possible $\frac{1}{8}$-BPS heavy states whose dual supergravity solutions are explicitly known, avoiding the use of Witten diagrams. This is achieved by using the AdS/CFT dictionary of type IIB supergravity on AdS$_3 \times S^3 \times {\cal M}_4$ that maps supersymmetric heavy operators whose conformal dimension is the order of the central charge to explicit asymptotically AdS supergravity solu...

We consider a set of half-BPS operators in $\mathcal{N}=4$ super Yang-Mills theory which are appropriate for describing single-particle states of superstring theory on AdS${}_5 \times S^5$. These single-particle operators are defined to have vanishing two-point functions with all multi-trace operators and therefore correspond to admixtures of single- and multi-traces. We find explicit formulae for all single-particle operators and for their two-point function normalisation. W...

We present a complete basis of multi-trace multi-matrix operators that has a diagonal two point function for the free matrix field theory at finite N. This generalises to multiple matrices the single matrix diagonalisation by Schur polynomials. Crucially, it involves intertwining the gauge group U(N) and the global symmetry group U(M) with Clebsch-Gordan coefficients of symmetric groups S_n. When applied to N=4 super Yang-Mills we consider the U(3) subgroup of the full symmet...

Recently a Mellin-space formula was conjectured for the form of correlation functions of $1/2$ BPS operators in planar $\mathcal{N}=4$ SYM in the strong 't Hooft coupling limit. In this work we report on the computation of two previously unknown four-point functions of operators with weights $\langle 2345 \rangle$ and $\langle 3456\rangle$, from the effective type-IIB supergravity action using AdS/CFT. These correlators are novel: they are the first correlators with all-diffe...

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 corrections for finite N are also discussed in terms of symmetric group characters. For finite N, the partition function invol...