arXiv subjects

Rodolfo Russo

Publications and source records attributed to Rodolfo Russo.

At least 37 records · Page 2Linked to original sources

arXiv2021

Holographic correlators with multi-particle states

We derive the connected tree-level part of 4-point holographic correlators in AdS$_3\times S^3\times \mathcal{M}$ (where ${\cal M}$ is $T^4$ or $K3$) involving two multi-trace and two single-trace operators. These connected correlators are obtained by studying a heavy-heavy-light-light correlation function in the formal limit where the heavy operators become light. These results provide a window into higher-point holographic correlators of single-particle operators. We find that the correlators involving multi-trace operators are compactly written in terms of Bloch-Wigner-Ramakrishnan functions -- particular linear combinations of higher-order polylogarithm functions. Several consistency checks of the derived expressions are performed in various OPE channels. We also extract the anomalous dimensions and 3-point couplings of the non-BPS double-trace operators of lowest twist at order $1/c$ and find some positive anomalous dimensions at spin zero and two in the K3 case.

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arXiv2021

Radiation Reaction from Soft Theorems

Radiation reaction (RR) terms at the third post-Minkowskian (3PM) order have recently been found to be instrumental in restoring smooth continuity between the non-relativistic, relativistic, and ultra-relativistic (including the massless) regimes. Here we propose a new and intriguing connection between RR and soft (bremsstrahlung) theorems which short-circuits the more involved conventional loop computations. Although first noticed in the context of the maximally supersymmetric theory, unitarity and analyticity arguments support the general validity of this 3PM-order connection that we apply, in particular, to Einstein's gravity and to its Jordan-Brans-Dicke extension. In the former case we find full agreement with a recent result by Damour obtained through a very different reasoning.

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arXiv2020

The Regge limit of AdS$_3$ holographic correlators

We study the Regge limit of 4-point AdS$_3 \times S^3$ correlators in the tree-level supergravity approximation and provide various explicit checks of the relation between the eikonal phase derived in the bulk picture and the anomalous dimensions of certain double-trace operators. We consider both correlators involving all light operators and HHLL correlators with two light and two heavy multi-particle states. These heavy operators have a conformal dimension proportional to the central charge and are pure states of the theory, dual to asymptotically AdS$_3 \times S^3$ regular geometries. Deviation from AdS$_3 \times S^3$ is parametrised by a scale $μ$ and is related to the conformal dimension of the dual heavy operator. In the HHLL case, we work at leading order in $μ$ and derive the CFT data relevant to the bootstrap relations in the Regge limit. Specifically, we show that the minimal solution to these equations relevant for the conical defect geometries is different to the solution implied by the microstate geometries dual to pure states.

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arXiv2020

Universality of ultra-relativistic gravitational scattering

We discuss the ultra-relativistic gravitational scattering of two massive particles at two-loop (3PM) level. We find that in this limit the real part of the eikonal, determining the deflection angle, is universal for gravitational theories in the two derivative approximation. This means that, regardless of the number of supersymmetries or the nature of the probes, the result connects smoothly with the massless case discussed since the late eighties by Amati, Ciafaloni and Veneziano. We analyse the problem both by using the analyticity and crossing properties of the scattering amplitudes and, in the case of the maximally supersymmetric theory, by explicit evaluation of the 4-point 2-loop amplitude using the results for the integrals in the full soft region. The first approach shows that the observable we are interested in is determined by the inelastic tree-level amplitude describing the emission of a graviton in the high-energy double-Regge limit, which is the origin of the universality property mentioned above. The second approach strongly suggests that the inclusion of the whole soft region is a necessary (and possibly sufficient) ingredient for recovering ultra relativistic finiteness and universality at the 3PM level. We conjecture that this universality persists at all orders in the PM expansion.

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arXiv2020

The CFT$_6$ origin of all tree-level 4-point correlators in AdS$_3 \times S^3$

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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arXiv2020

A tale of two exponentiations in ${\cal N}=8$ supergravity at subleading level

High-energy massless gravitational scattering in ${\cal N}=8$ supergravity was recently analyzed at leading level in the deflection angle, uncovering an interesting connection between exponentiation of infrared divergences in momentum space and the eikonal exponentiation in impact parameter space. Here we extend that analysis to the first non trivial sub-leading level in the deflection angle which, for massless external particles, implies going to two loops, i.e. to third post-Minkowskian (3PM) order. As in the case of the leading eikonal, we see that the factorisation of the momentum space amplitude into the exponential of the one-loop result times a finite remainder hides some basic simplicity of the impact parameter formulation. For the conservative part of the process, the explicit outcome is infrared (IR) finite, shows no logarithmic enhancement, and agrees with an old claim in pure Einstein gravity, while the dissipative part is IR divergent and should be regularized, as usual, by including soft gravitational bremsstrahlung. Finally, using recent three-loop results, we test the expectation that eikonal formulation accounts for the exponentiation of the lower-loop results in the momentum space amplitude. This passes a number of highly non-trivial tests, but appears to fail for the dissipative part of the process at all loop orders and sufficiently subleading order in $ε$, hinting at some lack of commutativity of the relevant infrared limits for each exponentiation.

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arXiv2019

Holographic correlators in AdS$_3$ without Witten diagrams

We present a formula for the holographic 4-point correlators in AdS$_3 \times S^3$ involving four single-trace operators of dimension $k, k, l, l$. As an input we use the supergravity results for the Heavy-Heavy-Light-Light correlators that can be derived by studying the linear fluctuations around known asymptotically AdS$_3 \times S^3$ geometries. When the operators of dimension $k$ and $l$ are in the same multiplet there are contributions due to the exchange of single-trace operators in the $t$ and $u$ channels, which are not captured by the approach mentioned above. However by rewriting the $s$-channel results in Mellin space we obtain a compact expression for the $s$-channel contribution that makes it possible to conjecture a formula for the complete result. We discuss some consistency checks that our proposal meets.

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arXiv2019

A tale of two exponentiations in ${\cal N}=8$ supergravity

The structure of scattering amplitudes in supergravity theories continues to be of interest. Recently, the amplitude for $2\rightarrow 2$ scattering in ${\cal N}=8$ supergravity was presented at three-loop order for the first time. The result can be written in terms of an exponentiated one-loop contribution, modulo a remainder function which is free of infrared singularities, but contains leading terms in the high energy Regge limit. We explain the origin of these terms from a well-known, unitarity-restoring exponentiation of the high-energy gravitational $S$-matrix in impact-parameter space. Furthermore, we predict the existence of similar terms in the remainder function at all higher loop orders. Our results provide a non-trivial cross-check of the recent three-loop calculation, and a necessary consistency constraint for any future calculation at higher loops.

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arXiv2019

Revisiting the 2PM eikonal and the dynamics of binary black holes

In this paper we study the two-body gravitational scattering of massive scalars with different masses in general spacetime dimensions. We focus on the Regge limit (eikonal regime) of the resulting scattering amplitudes and discuss how to extract the classical information representing the scattering of two black holes. We derive the leading eikonal and explicitly show the resummation of the first leading energy contribution up to second order in Newton's gravitational constant. We also calculate the subleading eikonal showing that in general spacetime dimensions it receives a non-trivial contribution from the box integral. From the eikonal we extract the two-body classical scattering angle between the two black holes up to the second post-Minkowskian order (2PM). Taking various probe-limits of the two-body scattering angles we are able to show agreement between our results and various results in the literature. We highlight that the box integral also has a log-divergent (in energy) contribution at subsubleading order which violates perturbative unitarity in the ultra-relativistic limit. We expect this term to play a role in the calculation of the eikonal at the 3PM order.

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arXiv2019

Holographic correlators in AdS$_3$

We derive the four-point correlators of scalar operators of dimension one in the supergravity limit of the D1D5 CFT holographically dual to string theory on AdS$_3\times S^3\times \mathcal{M}$, with $\mathcal{M}$ either $T^4$ or $K3$. We avoid the use of Witten diagrams but deduce our result from a limit of the heavy-heavy-light-light correlators computed in arXiv:1705.09250, together with several consistency requirements of the OPE in the various channels. This result represents the first holographic correlators of single-trace operators computed in AdS$_3$.

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arXiv2019

Supercharging Superstrata

We construct a new class of smooth horizonless microstate geometries of the supersymmetric D1-D5-P black hole in type IIB supergravity. We first work in the AdS$_3 \times S^3$ decoupling limit and use the fermionic symmetries of the theory to generate new momentum carrying perturbations in the bulk that have an explicit CFT dual description. We then use the supergravity equations to calculate the backreaction of these perturbations and find the full non-linear solutions both in the asymptotically AdS and asymptotically flat case. These new geometries have a simpler structure than the previously known superstrata solutions.

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arXiv2018

The Subleading Eikonal in Supergravity Theories

In this paper we study the subleading contributions to eikonal scattering in (super)gravity theories with particular emphasis on the role of both elastic and inelastic scattering processes. For concreteness we focus on the scattering of various massless particles off a stack of D$p$-branes in type II supergravity in the limit of large impact parameter $b$. We analyse the relevant field theory Feynman diagrams which naturally give rise to both elastic and inelastic processes. We show that in the case analysed the leading and subleading eikonal only depend on elastic processes, while inelastic processes are captured by a pre-factor multiplying the exponentiated leading and subleading eikonal phase. In addition to the traditional Feynman diagram computations mentioned above, we also present a novel method for computing the amplitudes contributing to the leading and subleading eikonal phases, which, in the large $b$ limit, only involves knowledge of the onshell three and four-point vertices. The two methods are shown to give the same results. Furthermore we derive these results in yet another way, by computing various one-point amplitudes which allow us to extract the classical solution of the gravitational back reaction of the target D$p$-branes. Finally we show how our expressions for the leading and subleading eikonal agree with the calculation of the metric and corresponding deflection angle for massless states moving along geodesics in the relevant curved geometry.

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arXiv2018

A note on the Virasoro blocks at order $1/c$

We derive an explicit expression for the $1/c$ contribution to the Virasoro blocks in 2D CFT in the limit of large $c$ with fixed values of the operators' dimensions. We follow the direct approach of orthonormalising, at order $1/c$, the space of the Virasoro descendants to obtain the blocks as a series expansion around $z=0$. For generic conformal weights this expansion can be summed in terms of hypergeometric functions and their first derivatives with respect to one parameter. For integer conformal weights we provide an equivalent expression written in terms of a finite sum of undifferentiated hypergeometric functions. These results make the monodromies of the blocks around $z=1$ manifest.

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arXiv2017

Asymptotically-flat supergravity solutions deep inside the black-hole regime

We construct an infinite family of smooth asymptotically-flat supergravity solutions that have the same charges and angular momenta as general supersymmetric D1-D5-P black holes, but have no horizon. These solutions resemble the corresponding black hole to arbitrary accuracy outside of the horizon: they have asymptotically flat regions, AdS_3 x S^3 throats and very-near-horizon AdS_2 throats, which however end in a smooth cap rather than an event horizon. The angular momenta of the solutions are general, and in particular can take arbitrarily small values. Upon taking the AdS_3 x S^3 decoupling limit, we identify the holographically-dual CFT states.

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arXiv2017

Unitary 4-point correlators from classical geometries

We compute correlators of two heavy and two light operators in the strong coupling and large $c$ limit of the D1D5 CFT which is dual to weakly coupled AdS$_3$ gravity. The light operators have dimension two and are scalar descendants of the chiral primaries considered in arXiv:1705.09250, while the heavy operators belong to an ensemble of Ramond-Ramond ground states. We derive a general expression for these correlators when the heavy states in the ensemble are close to the maximally spinning ground state. For a particular family of heavy states we also provide a result valid for any value of the spin. In all cases we find that the correlators depend non-trivially on the CFT moduli and are not determined by the symmetries of the theory, however they have the properties expected for correlators among pure states in a unitary theory, in particular they do not decay at large Lorentzian times.

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arXiv2017

Holographic 4-point correlators with heavy states

The AdS/CFT duality maps supersymmetric heavy operators with conformal dimension of the order of the central charge to asymptotically AdS supergravity solutions. We show that by studying the quadratic fluctuations around such backgrounds it is possible to derive the 4-point correlators of two light and two heavy states in the supergravity approximation. We provide an explicit example in the AdS$_3$ setup relevant for the duality with the D1-D5 CFT. Contrary to previously studied examples, the supergravity correlator derived in this work differs from the result obtained at the CFT orbifold point. Our method bypasses the difficulties of applying the standard Witten's diagrams approach to correlators with operators of large conformal dimension and also avoids some technical steps that have made the computation of dynamical 4-point correlators in the AdS$_3$/CFT$_2$ context unfeasible until now.

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arXiv2016

Correlators at large c without information loss

We study a simple class of correlators with two heavy and two light operators both in the D1D5 CFT and in the dual AdS$_3 \times S^3 \times T^4$ description. On the CFT side we focus on the free orbifold point and discuss how these correlators decompose in terms of conformal blocks, showing that they are determined by protected quantities. On the gravity side, the heavy states are described by regular, asymptotically AdS$_3 \times S^3 \times T^4$ solutions and the correlators are obtained by studying the wave equation in these backgrounds. We find that the CFT and the gravity results agree and that, even in the large central charge limit, these correlators do not have (Euclidean) spurious singularities. We suggest that this is indeed a general feature of the heavy-light correlators in unitary CFTs, which can be relevant for understanding how information is encoded in black hole microstates.

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arXiv2016

Smooth horizonless geometries deep inside the black-hole regime

We construct the first family of horizonless supergravity solutions that have the same mass, charges and angular momenta as general supersymmetric rotating D1-D5-P black holes in five dimensions. This family includes solutions with arbitrarily small angular momenta, deep within the regime of quantum numbers and couplings for which a large classical black hole exists. These geometries are well-approximated by the black-hole solution, and in particular exhibit the same near-horizon throat. Deep in this throat, the black-hole singularity is resolved into a smooth cap. We also identify the holographically-dual states in the N=(4,4) D1-D5 orbifold CFT. Our solutions are among the states counted by the CFT elliptic genus, and provide examples of smooth microstate geometries within the ensemble of supersymmetric black-hole microstates.

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