Effective conformal theory and the flat-space limit of AdS

The Goldstone equivalence theorem allows one to relate scattering amplitudes of massive gauge fields to those of scalar fields in the limit of large scattering energies. We generalize this theorem under the framework of the AdS/CFT correspondence. First, we obtain an expression of the equivalence theorem in terms of correlation functions of creation and annihilation operators by using an AdS wave function approach to the AdS/CFT dictionary. It is shown that the divergence of the non-conserved conformal current dual to the bulk gauge field is approximately primary when computing correlators for theories in which the masses of all the exchanged particles are sufficiently large. The results are then generalized to higher spin fields.We then go on to generalize the theorem using conformal blocks in two and fourdimensional CFTs. We show that when the scaling dimensions of the exchanged operators are large compared to both their spins and the dimension of the current, the conformal blocks satisfy an equivalence theorem.

Section: Jhep08(2015)002supporting

confidence: 70%

“…In AdS, the initial and final states which are related by the S-matrix are prepared by acting on the vacuum state with CFT operators ( [29][30][31]). Moreover, the LSZ formula becomes a generalization of the AdS/CFT dictionary that relates correlators of boundary creation and annihilation operators to integrals of bulk fields.…”

Section: Et In Adsmentioning

confidence: 99%

The Goldstone equivalence theorem and AdS/CFT

Anand

Cantrell

2015

“…• It will be very interesting to verify our claims for the n 1 limit using an effective field theory approach as in [33]. In that paper it was shown how for the zero spin but large twist form of the anomalous dimension changes due to a massive mode.…”

Section: Jhep11(2015)083mentioning

confidence: 75%

Analytic bootstrap at large spin

Kaviraj

Sen

Sinha

2015

106

137

We use analytic conformal bootstrap methods to determine the anomalous dimensions and OPE coefficients for large spin operators in general conformal field theories in four dimensions containing a scalar operator of conformal dimension ∆ φ . It is known that such theories will contain an infinite sequence of large spin operators with twists approaching 2∆ φ + 2n for each integer n. By considering the case where such operators are separated by a twist gap from other operators at large spin, we analytically determine the n, ∆ φ dependence of the anomalous dimensions. We find that for all n, the anomalous dimensions are negative for ∆ φ satisfying the unitarity bound. We further compute the first subleading correction at large spin and show that it becomes universal for large twist. In the limit when n is large, we find exact agreement with the AdS/CFT prediction corresponding to the Eikonal limit of a 2-2 scattering with dominant graviton exchange.

“…Our argument is somewhat indirect. It is believed that if we take a consistent interacting CFT with various conditions on its operator spectrum (such as the presence of only a small number of operators at low dimensions) then we should be able to write down a bulk interaction in anti-de Sitter space that reproduces any set of boundary correlators [38,[81][82][83][84]. Of course, implementing this procedure in practice is quite difficult but schematically let us say that we have constructed the bulk Lagrangian that reproduces the boundary correlators.…”

Section: Uniqueness Of Our Construction and Interactionsmentioning

confidence: 99%

An infalling observer in AdS/CFT

Papadodimas

Raju

2013

346

593

We describe the experience of an observer falling into a black hole using the AdS/CFT correspondence. In order to do this, we reconstruct the local bulk operators measured by the observer along his trajectory outside the black hole. We then extend our construction beyond the black hole horizon. We show that this is possible because of an effective doubling of the observables in the boundary theory, when it is in a pure state that is close to the thermal state. Our construction allows us to rephrase questions about information-loss and the structure of the metric at the horizon in terms of more familiar CFT correlators. It suggests that to precisely identify black-hole microstates, the observer would need to conduct measurements to an accuracy of e −S BH . This appears to be inconsistent with the "fuzzball" proposal, and other recent proposals in which pure states in the ensemble of the black hole are represented by macroscopically distinct geometries. Furthermore, our description of the black hole interior in terms of CFT operators provides a natural realization of black hole complementarity and a method of preserving unitarity without "firewalls."