arXiv subjects

Joao Penedones

Publications and source records attributed to Joao Penedones.

53 records · Page 3Linked to original sources

arXiv2014

Spinning AdS Propagators

We develop the embedding formalism to describe symmetric traceless tensors in Anti-de Sitter space. We use this formalism to construct the bulk-to-bulk propagator of massive spin J fields and check that it has the expected short distance and massless limits. We also and a split representation for the bulk-to-bulk propagator, by writing it as an integral over the boundary of the product of two bulk-to-boundary propagators. We exemplify the use of this representation with the computation of the conformal partial wave decomposition of Witten diagrams. In particular, we determine the Mellin amplitude associated to AdS graviton exchange between minimally coupled scalars of general dimension, including the regular part of the amplitude.

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arXiv2013

The role of leading twist operators in the Regge and Lorentzian OPE limits

We study two kinematical limits, the Regge limit and the Lorentzian OPE limit, of the four-point function of the stress-tensor multiplet in Super Yang-Mills at weak coupling. We explain how both kinematical limits are controlled by the leading twist operators. We use the known expression of the four-point function up to three loops, to extract the pomeron residue at next-to-leading order. Using this data and the known form of pomeron spin up to next-to-leading order, we predict the behaviour of the four-point function in the Regge limit at higher loops. Specifically, we determine the leading log behaviour at any loop order and the next-to-leading log at four loops. Finally, we check the consistency of our results with conformal Regge theory. This leads us to predict the behaviour around $J=1$ of the OPE coefficient of the spin $J$ leading twist operator in the OPE of two chiral primary operators.

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arXiv2011

Spinning Conformal Blocks

For conformal field theories in arbitrary dimensions, we introduce a method to derive the conformal blocks corresponding to the exchange of a traceless symmetric tensor appearing in four point functions of operators with spin. Using the embedding space formalism, we show that one can express all such conformal blocks in terms of simple differential operators acting on the basic scalar conformal blocks. This method gives all conformal blocks for conformal field theories in three dimensions. We demonstrate how this formalism can be applied in a few simple examples.

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arXiv2011

A Natural Language for AdS/CFT Correlators

We provide dramatic evidence that `Mellin space' is the natural home for correlation functions in CFTs with weakly coupled bulk duals. In Mellin space, CFT correlators have poles corresponding to an OPE decomposition into `left' and `right' sub-correlators, in direct analogy with the factorization channels of scattering amplitudes. In the regime where these correlators can be computed by tree level Witten diagrams in AdS, we derive an explicit formula for the residues of Mellin amplitudes at the corresponding factorization poles, and we use the conformal Casimir to show that these amplitudes obey algebraic finite difference equations. By analyzing the recursive structure of our factorization formula we obtain simple diagrammatic rules for the construction of Mellin amplitudes corresponding to tree-level Witten diagrams in any bulk scalar theory. We prove the diagrammatic rules using our finite difference equations. Finally, we show that our factorization formula and our diagrammatic rules morph into the flat space S-Matrix of the bulk theory, reproducing the usual Feynman rules, when we take the flat space limit of AdS/CFT. Throughout we emphasize a deep analogy with the properties of flat space scattering amplitudes in momentum space, which suggests that the Mellin amplitude may provide a holographic definition of the flat space S-Matrix.

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arXiv2011

AdS black disk model for small-x DIS

Using the approximate conformal invariance of QCD at high energies we consider a simple AdS black disk model to describe saturation in DIS. Deep inside saturation the structure functions have the same power law scaling, F_T ~ F_L ~ 1/x^w, where w is related to the expansion rate of the black disk with energy. Furthermore, the ratio F_L /F_T is given by the universal value (1+w)/(3+w), independently of the target. For virtual photon-photon scattering at high energies we obtain explicit expressions and ratios for the total cross sections of transverse and longitudinal photons in terms of the single parameter w.

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arXiv2010

Writing CFT correlation functions as AdS scattering amplitudes

We explore the Mellin representation of conformal correlation functions recently proposed by Mack. Examples in the AdS/CFT context reinforce the analogy between Mellin amplitudes and scattering amplitudes. We conjecture a simple formula relating the bulk scattering amplitudes to the asymptotic behavior of Mellin amplitudes and show that previous results on the flat space limit of AdS follow from our new formula. We find that the Mellin amplitudes are particularly useful in the case of conformal gauge theories in the planar limit. In this case, the four point Mellin amplitudes are meromorphic functions whose poles and their residues are entirely determined by two and three point functions of single-trace operators. This makes the Mellin amplitudes the ideal objects to attempt the conformal bootstrap program in higher dimensions.

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arXiv2010

String scattering in flat space and a scaling limit of Yang-Mills correlators

We use the flat space limit of the AdS/CFT correspondence to derive a simple relation between the 2 to 2 scattering amplitude of massless string states in type IIB superstring theory on ten-dimensional Minkowski space and a scaling limit of the N=4 super Yang-Mills four point functions. We conjecture that this relation holds non-perturbatively and at arbitrarily high energy.

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arXiv2010

Deep Inelastic Scattering in Conformal QCD

We consider the Regge limit of a CFT correlation function of two vector and two scalar operators, as appropriate to study small-x deep inelastic scattering in N=4 SYM or in QCD assuming approximate conformal symmetry. After clarifying the nature of the Regge limit for a CFT correlator, we use its conformal partial wave expansion to obtain an impact parameter representation encoding the exchange of a spin j Reggeon for any value of the coupling constant. The CFT impact parameter space is the three-dimensional hyperbolic space H3, which is the impact parameter space for high energy scattering in the dual AdS space. We determine the small-x structure functions associated to the exchange of a Reggeon. We discuss unitarization from the point of view of scattering in AdS and comment on the validity of the eikonal approximation. We then focus on the weak coupling limit of the theory where the amplitude is dominated by the exchange of the BFKL pomeron. Conformal invariance fixes the form of the vector impact factor and its decomposition in transverse spin 0 and spin 2 components. Our formalism reproduces exactly the general results predict by the Regge theory, both for a scalar target and for gamma*-gamma* scattering. We compute current impact factors for the specific examples of N=4 SYM and QCD, obtaining very simple results. In the case of the R-current of N=4 SYM, we show that the transverse spin 2 component vanishes. We conjecture that the impact factors of all chiral primary operators of N=4 SYM only have components with 0 transverse spin.

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arXiv2009

Holography from Conformal Field Theory

The locality of bulk physics at distances below the AdS length is one of the remarkable aspects of AdS/CFT duality, and one of the least tested. It requires that the AdS radius be large compared to the Planck length and the string length. In the CFT this implies a large-N expansion and a gap in the spectum of anomalous dimensions. We conjecture that the implication also runs in the other direction, so that any CFT with a planar expansion and a large gap has a local bulk dual. For an abstract CFT we formulate the consistency conditions, most notably crossing symmetry, and show that the conjecture is true in a broad range of CFT's, to first nontrivial order in 1/N^2: any CFT with a gap and a planar expansion is generated via the AdS/CFT dictionary from a local bulk interaction. We establish this result by a counting argument on each side, and also investigate various properties of some explicit solutions.

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arXiv2009

Local bulk S-matrix elements and CFT singularities

We give a procedure for deriving certain bulk S-matrix elements from corresponding boundary correlators. These are computed in the plane wave limit, via an explicit construction of certain boundary sources that give bulk wavepackets. A critical role is played by a specific singular behavior of the lorentzian boundary correlators. It is shown in examples how correlators derived from the bulk supergravity exhibit the appropriate singular structure, and reproduce the corresponding S-matrix elements. This construction thus provides a nontrivial test for whether a given boundary conformal field theory can reproduce bulk physics, and where it does, supplies a prescription to extract bulk S-matrix elements in the plane wave limit.

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arXiv2008

Eikonal Methods in AdS/CFT: BFKL Pomeron at Weak Coupling

We consider correlators of N=4 super Yang Mills of the form A ~ < O_1 O_2 O*_1 O*_2 >, where the operators O_1 and O_2 are scalar primaries. In particular, we analyze this correlator in the planar limit and in a Lorentzian regime corresponding to high energy interactions in AdS. The planar amplitude is dominated by a Regge pole whose nature varies as a function of the 't Hooft coupling g^2. At large g, the pole corresponds to graviton exchange in AdS, whereas at weak g, the pole is that of the hard perturbative BFKL pomeron. We concentrate on the weak coupling regime and analyze pomeron exchange directly in position space. The analysis relies heavily on the conformal symmetry of the transverse space E^2 and of its holographic dual hyperbolic space H_3, describing with an unified language, both the weak and strong 't Hooft coupling regimes. In particular, the form of the impact factors is highly constrained in position space by conformal invariance. Finally, the analysis suggests a possible AdS eikonal resummation of multi-pomeron exchanges implementing AdS unitarity, which differs from the usual 4-dimensional eikonal exponentiation. Relations to violations of 4-dimensional unitarity at high energy and to the onset of nonlinear effects and gluon saturation become immediate questions for future research.

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arXiv2008

Toy models for wrapping effects

The anomalous dimensions of local single trace gauge invariant operators in N=4 supersymmetric Yang-Mills theory can be computed by diagonalizing a long range integrable Hamiltonian by means of perturbative asymptotic Bethe ansatz. This formalism breaks down when the number of fields of the composite operator is smaller than the range of the Hamiltonian which coincides with the order in perturbation theory at study. We analyze two spin chain toy models which might shed some light on the physics behind these wrapping effects. One of them, the Hubbard model, is known to be closely related to N=4 SYM. In this example, we find that the knowledge of the effective spin chain description is insufficient to reconstruct the finite size effects of the underlying electron theory. We compute the wrapping corrections for generic states and relate them to a Luscher like approach. The second toy models are long range integrable Hamiltonians built from the standard algebraic Bethe anstatz formalism. This construction is valid for any symmetry group. In particular, for non-compact groups it exhibits an interesting relation between wrapping interactions and transcendentality.

hep-th↗

arXiv2008

High Energy Scattering in the AdS/CFT Correspondence

This work explores the celebrated AdS/CFT correspondence in the regime of high energy scattering in Anti--de Sitter (AdS) spacetime. In particular, we develop the eikonal approximation to high energy scattering in AdS and explore its consequences for the dual Conformal Field Theory (CFT). Using position space Feynman rules, we rederive the eikonal approximation for high energy scattering in flat space. Following this intuitive position space perspective, we then generalize the eikonal approximation for high energy scattering in AdS and other spacetimes. Remarkably, we are able to resum, in terms of a generalized phase shift, ladder and cross ladder Witten diagrams associated to the exchange of an AdS spin j field, to all orders in the coupling constant. By the AdS/CFT correspondence, the eikonal amplitude in AdS is related to the four point function of CFT primary operators in the regime of large 't Hooft coupling, including all terms of the 1/N expansion. We then show that the eikonal amplitude determines the behavior of the CFT four point function for small values of the cross ratios in a Lorentzian regime and that this controls its high spin and dimension conformal partial wave decomposition. These results allow us to determine the anomalous dimension of high spin and dimension double trace primary operators, by relating it to the AdS eikonal phase shift. Finally we find that, at large energies and large impact parameters in AdS, the gravitational interaction dominates all other interactions, as in flat space. Therefore, the anomalous dimension of double trace operators, associated to graviton exchange in AdS, yields a universal prediction for CFT's with AdS gravitational duals.

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arXiv2007

Eikonal Approximation in AdS/CFT: Resumming the Gravitational Loop Expansion

We derive an eikonal approximation to high energy interactions in Anti-de Sitter spacetime, by generalizing a position space derivation of the eikonal amplitude in flat space. We are able to resum, in terms of a generalized phase shift, ladder and cross ladder graphs associated to the exchange of a spin j field, to all orders in the coupling constant. Using the AdS/CFT correspondence, the resulting amplitude determines the behavior of the dual conformal field theory four point function < O_1 O_2 O_1 O_2 > for small values of the cross ratios, in a Lorentzian regime. Finally we show that the phase shift is dominated by graviton exchange and computes, in the dual CFT, the anomalous dimension of the double trace primary operators O_1 \partial ... \partial O_2 of large dimension and spin, corresponding to the relative motion of the two interacting particles. The results are valid at strong t'Hooft coupling and are exact in the 1/N expansion.

hep-th↗

arXiv2006

From Fundamental Strings to Small Black Holes

We give evidence in favour of a string/black hole transition in the case of BPS fundamental string states of the Heterotic string. Our analysis goes beyond the counting of degrees of freedom and considers the evolution of dynamical quantities in the process. As the coupling increases, the string states decrease their size up to the string scale when a small black hole is formed. We compute the absorption cross section for several fields in both the black hole and the perturbative string phases. At zero frequency, these cross sections can be seen as order parameters for the transition. In particular, for the scalars fixed at the horizon the cross section evolves to zero when the black hole is formed.

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arXiv2006

Eikonal Approximation in AdS/CFT: Conformal Partial Waves and Finite N Four-Point Functions

We introduce the impact-parameter representation for conformal field theory correlators of the form A ~ < O_1 O_2 O_1 O_2 >. This representation is appropriate in the eikonal kinematical regime, and approximates the conformal partial-wave decomposition in the limit of large spin and dimension of the exchanged primary. Using recent results on the two-point function < O_1 O_1 >_{shock} in the presence of a shock wave in Anti-de Sitter, and its relation to the discontinuity of the four-point amplitude A across a kinematical branch-cut, we find the high spin and dimension conformal partial- wave decomposition of all tree-level Anti-de Sitter Witten diagrams. We show that, as in flat space, the eikonal kinematical regime is dominated by the T-channel exchange of the massless particle with highest spin (graviton dominance). We also compute the anomalous dimensions of the high-spin O_1 O_2 composites. Finally, we conjecture a formula re-summing crossed-ladder Witten diagrams to all orders in the gravitational coupling.

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arXiv2005

Coleman meets Schwinger

It is well known that spherical D-branes are nucleated in the presence of an external RR electric field. Using the description of D-branes as solitons of the tachyon field on non-BPS D-branes, we show that the brane nucleation process can be seen as the decay of the tachyon false vacuum. This process can describe the decay of flux-branes in string theory or the decay of quintessence potentials arising in flux compactifications.

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