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Register a new userString corrections to AdS amplitudes and the double-trace spectrum of N=4 SYM
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We consider $alpha$ corrections to four-point correlators of half-BPS operators in $mathcal{N}=4$ super Yang-Mills theory in the supergravity limit. By demanding the correct behaviour in the flat space limit, we find that the leading $(alpha)^3$ correction to the Mellin amplitude is fixed for arbitrary charges of the external operators. By considering the mixing of double-trace operators we can find the $(alpha)^3$ corrections to the double-trace spectrum which we give explicitly for $su(4)$-singlet operators. We observe striking patterns in the corrections to the spectra which hint at their common ten-dimensional origin. By extending the observed patterns and imposing them at order $(alpha)^5$ we are able to reproduce the recently found result for the correction to the Mellin amplitude for $langle mathcal{O}_2 mathcal{O}_2 mathcal{O}_p mathcal{O}_p rangle$ correlators. By applying a similar logic to the $[0,1,0]$ channel of $su(4)$ we are able to deduce new results for the correlators of the form $langle mathcal{O}_2 mathcal{O}_3 mathcal{O}_{p-1} mathcal{O}_p rangle$.
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The spectrum of IIB supergravity on AdS${}_5 times S^5$ contains a number of bound states described by long double-trace multiplets in $mathcal{N}=4$ super Yang-Mills theory at large t Hooft coupling. At large $N$ these states are degenerate and to obtain their anomalous dimensions as expansions in $tfrac{1}{N^2}$ one has to solve a mixing problem. We conjecture a formula for the leading anomalous dimensions of all long double-trace operators which exhibits a large residual degeneracy whose structure we describe. Our formula can be related to conformal Casimir operators which arise in the structure of leading discontinuities of supergravity loop corrections to four-point correlators of half-BPS operators.
We consider $alpha$ corrections to the one-loop four-point correlator of the stress-tensor multiplet in $mathcal{N}=4$ super Yang-Mills at order $1/N^4$. Holographically, this is dual to string corrections of the one-loop supergravity amplitude on AdS$_5times$S$^5$. While this correlator has been considered in Mellin space before, we derive the corresponding position space results, gaining new insights into the analytic structure of AdS loop-amplitudes. Most notably, the presence of a transcendental weight three function involving new singularities is required, which has not appeared in the context of AdS amplitudes before. We thereby confirm the structure of string corrected one-loop Mellin amplitudes, and also provide new explicit results at orders in $alpha$ not considered before.
Very recently in arXiv:0705.0303 Alday and Maldacena gave a string theory prescription for computing (all) planar amplitudes in N=4 supersymmetric gauge theory at strong coupling using the AdS/CFT correspondence. These amplitudes are determined by a classical string solution and contain a universal exponential factor involving the action of the classical string. On the gauge theory side, expressions for perturbative amplitudes at strong coupling were previously proposed only for specific helicities of external particles -- the maximally helicity violating or MHV amplitudes. These follow from the exponential ansatz of Bern, Dixon and Smirnov for MHV amplitudes in N=4 SYM. In this paper we examine the amplitudes dependence on helicities and particle-types of external states. We consider the prefactor of string amplitudes and give arguments suggesting that the prefactor at strong coupling should be the same as the Yang-Mills tree-level amplitude for the same process. This implies that scattering amplitudes in N=4 SYM simplify dramatically in the strong coupling limit. It follows from our proposal that in this limit all (MHV and non-MHV) n-point amplitudes are given by the (known) tree-level Yang-Mills result times the helicity-independent (and particle-type-independent) universal exponential.
We consider the description of reggeon amplitudes (Wilson lines form factors) in N=4 SYM within the framework of four dimensional ambitwistor string theory. The latter is used to derive scattering equations representation for reggeon amplitudes with multiple reggeized gluons present. It is shown, that corresponding tree-level string correlation function correctly reproduces previously obtained Grassmannian integral representation of reggeon amplitudes in N=4 SYM.
We give an explicit formula for all tree amplitudes in N=4 SYM, derived by solving the recently presented supersymmetric tree-level recursion relations. The result is given in a compact, manifestly supersymmetric form and we show how to extract from it all possible component amplitudes for an arbitrary number of external particles and any arrangement of external particles and helicities. We focus particularly on extracting gluon amplitudes which are valid for any gauge theory. The formula for all tree-level amplitudes is given in terms of nested sums of dual superconformal invariants and it therefore manifestly respects both conventional and dual superconformal symmetry.
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