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Register a new userThe CFT$_6$ origin of all tree-level 4-point correlators in AdS$_3 times S^3$
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We provide strong evidence that all tree-level 4-point holographic correlators in AdS$_3 times S^3$ are constrained by a hidden 6D conformal symmetry. This property has been discovered in the AdS$_5 times S^5$ context and noticed in the tensor multiplet subsector of the AdS$_3 times S^3$ theory. Here we extend it to general AdS$_3 times S^3$ correlators which contain also the chiral primary operators of spin zero and one that sit in the gravity multiplet. The key observation is that the 6D conformal primary field associated with these operators is not a scalar but a self-dual $3$-form primary. As an example, we focus on the correlators involving two fields in the tensor multiplets and two in the gravity multiplet and show that all such correlators are encoded in a conformal 6D correlator between two scalars and two self-dual $3$-forms, which is determined by three functions of the cross ratios. We fix these three functions by comparing with the results of the simplest correlators derived from an explicit supergravity calculation.
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We present a constructive derivation of all four-point tree-level holographic correlators for eleven dimensional supergravity on $AdS_7 times S^4$. These correlators correspond to four-point functions of arbitrary one-half BPS operators in the six-dimensional $(2,0)$ theory at large central charge. The crucial observation is that the polar part of the correlators in Mellin space is fully captured by a drastically simpler Maximally R-symmetry Violating (MRV) amplitude, while the contact part is fully fixed by superconformal Ward identities and the flat space limit.
We consider string theory on AdS$_3$ $times$ (S$^3$ $times$ S$^3$ $times$ S$^1)/mathbb Z_2$, a background supporting $mathcal N=(3,3)$ spacetime supersymmetry. We propose that string theory on this background is dual to the symmetric product orbifold of $mathcal S_0/mathbb Z_2$ where $mathcal S_0$ is a theory of four free fermions and one free boson. We show that the BPS spectra of the two sides of the duality match precisely. Furthermore, we compute the elliptic genus of the dual CFT and that of the supergravity limit of string theory and demonstrate that they match, hence providing non-trivial support for the holographic proposal.
The non-renormalization of the 3-point functions $tr X^{k_1} tr X^{k_2} tr X^{k_3}$ of chiral primary operators in N=4 super-Yang-Mills theory is one of the most striking facts to emerge from the AdS/CFT correspondence. A two-fold puzzle appears in the extremal case, e.g. k_1 = k_2 + k_3. First, the supergravity calculation involves analytic continuation in the k_i variables to define the product of a vanishing bulk coupling and an infinite integral over AdS. Second, extremal correlators are uniquely sensitive to mixing of the single-trace operators $tr X^k$ with protected multi-trace operators in the same representation of SU(4). We show that the calculation of extremal correlators from supergravity is subject to the same subtlety of regularization known for the 2-point functions, and we present a careful method which justifies the analytic continuation and shows that supergravity fields couple to single traces without admixture. We also study extremal n-point functions of chiral primary operators, and argue that Type IIB supergravity requires that their space-time form is a product of n-1 two-point functions (as in the free field approximation) multiplied by a non-renormalized coefficient. This non-renormalization property of extremal n-point functions is a new prediction of the AdS/CFT correspondence. As a byproduct of this work we obtain the cubic couplings $t phi phi$ and $s phi phi$ of fields in the dilaton and 5-sphere graviton towers of Type IIB supergravity on $AdS_5 times S^5$.
Surface operators in the 6d (2,0) theory at large $N$ have a holographic description in terms of M2 branes probing the AdS$_7 times S^4$ M-theory background. The most symmetric, 1/2-BPS, operator is defined over a planar or spherical surface, and it preserves a 2d superconformal group. This includes, in particular, an $SO(2,2)$ subgroup of 2d conformal transformations, so that the surface operator may be viewed as a conformal defect in the 6d theory. The dual M2 brane has an AdS$_3$ induced geometry, reflecting the 2d conformal symmetry. Here we use the holographic description to extract the defect CFT data associated to the surface operator. The spectrum of transverse fluctuations of the M2 brane is found to be in one-to-one correspondence with a protected multiplet of operator insertions on the surface, which includes the displacement operator. We compute the one-loop determinants of fluctuations of the M2 brane, and extract the conformal anomaly coefficient of the spherical surface to order $N^0$. We also briefly discuss the RG flow from the non-supersymmetric to the 1/2-BPS defect operator, and its consistency with a $b$-theorem for the defect CFT. Starting with the M2 brane action, we then use AdS$_3$ Witten diagrams to compute the 4-point functions of the elementary bosonic insertions on the surface operator, and extract some of the defect CFT data from the OPE. The 4-point function is shown to satisfy superconformal Ward identities, and we discuss a related subsector of twisted scalar insertions, whose correlation functions are constrained by the residual superconformal symmetry.
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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