7 research outputs found
The black hole behind the cut
We study the analytic structure of the heavy-heavy-light-light holographic
correlators in the supergravity approximation of the AdS/CFT
duality. As an explicit example, we derive the correlator where the heavy
operator is a classical microstate of the 5D supersymmetric black hole and its
dual geometry interpolates as a function of a continuous parameter between
global AdS and the extremal BTZ black hole. The simplest perturbation of
this interpolating geometry by a light field is described by the Heun equation
and we exploit the relation of its connection coefficients to the Liouville CFT
to analytically compute the correlator in the two limits, focusing in
particular on the black hole regime. In this limit we find that the real poles
of the correlator become dense and can be approximated by a cut. We show that,
when the charges of the heavy state are in the black hole regime, the
discontinuity across the cut has complex poles corresponding to the
quasi-normal modes of BTZ. This behaviour is qualitatively similar to what is
expected for the large central charge limit of a typical black hole microstateComment: 59 pages, 1 figur
Black hole bulk-cone singularities
Lorentzian correlators of local operators exhibit surprising singularities in
theories with gravity duals. These are associated with null geodesics in an
emergent bulk geometry. We analyze singularities of the thermal response
function dual to propagation of waves on the AdS Schwarzschild black hole
background. We derive the analytic form of the leading singularity dual to a
bulk geodesic that winds around the black hole. Remarkably, it exhibits a
boundary group velocity larger than the speed of light, whose dual is the
angular velocity of null geodesics at the photon sphere. The strength of this
singularity is controlled by the classical Lyapunov exponent associated with
the instability of nearly bound photon orbits. In this sense, the bulk-cone
singularity can be identified as the universal feature that encodes the
ubiquitous black hole photon sphere in a dual holographic CFT. To perform the
computation analytically, we express the two-point correlator as an infinite
sum over Regge poles, and then evaluate this sum using WKB methods. We also
compute the smeared correlator numerically, which in particular allows us to
check and support our analytic predictions. We comment on the resolution of
black hole bulk-cone singularities by stringy and gravitational effects into
black hole bulk-cone "bumps". We conclude that these bumps are robust, and
could serve as a target for simulations of black hole-like geometries in
table-top experiments.Comment: 63 pages, 17 figure
Holographic thermal correlators from supersymmetric instantons
We present an exact formula for the thermal scalar two-point function in
four-dimensional holographic conformal field theories. The problem of finding
it reduces to the analysis of the wave equation on the AdS-Schwarzschild
background. The two-point function is computed from the connection coefficients
of the Heun equation, which can be expressed in terms of the
Nekrasov-Shatashvili partition function of an SU(2) supersymmetric gauge theory
with four fundamental hypermultiplets. The result is amenable to numerical
evaluation upon truncating the number of instantons in the convergent expansion
of the partition function. We also examine it analytically in various limits.
At large spin the instanton expansion of the thermal two-point function
directly maps to the light-cone bootstrap analysis of the heavy-light
four-point function. Using this connection, we compute the OPE data of
heavy-light double-twist operators. We compare our prediction to the
perturbative results available in the literature and find perfect agreement.Comment: 9 pages + appendices, 2 figures. v2: typos corrected, references
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A thermal product formula
We show that holographic thermal two-sided two-point correlators take the form of a product over quasi-normal modes (QNMs). Due to this fact, the two-point function admits a natural dispersive representation with a positive discontinuity at the location of QNMs. We explore the general constraints on the structure of QNMs that follow from the operator product expansion, the presence of the singularity inside the black hole, and the hydrodynamic expansion of the correlator. We illustrate these constraints through concrete examples. We suggest that the product formula for thermal correlators may hold for more general large N chaotic systems, and we check this hypothesis in several models.We show that holographic thermal two-sided two-point correlators take the form of a product over quasi-normal modes (QNMs). Due to this fact, the two-point function admits a natural dispersive representation with a positive discontinuity at the location of QNMs. We explore the general constraints on the structure of QNMs that follow from the operator product expansion, the presence of the singularity inside the black hole, and the hydrodynamic expansion of the correlator. We illustrate these constraints through concrete examples. We suggest that the product formula for thermal correlators may hold for more general large N chaotic systems, and we check this hypothesis in several models
Irregular Liouville correlators and connection formulae for Heun functions
We perform a detailed study of a class of irregular correlators in Liouville
Conformal Field Theory, of the related Virasoro conformal blocks with irregular
singularities and of their connection formulae. Upon considering their
semi-classical limit, we provide explicit expressions of the connection
matrices for the Heun function and a class of its confluences. Their
calculation is reduced to concrete combinatorial formulae from conformal block
expansions.Comment: 61 pages, many diagrams, 2 figures, huge list of symbols, comments
welcom
Black Hole Perturbation Theory Meets CFT: Kerr Compton Amplitudes from Nekrasov-Shatashvili Functions
International audienceWe present a novel study of Kerr Compton amplitudes in a partial wave basis in terms of the Nekrasov-Shatashvili (NS) function of the \textit{confluent Heun equation} (CHE). Remarkably, NS-functions enjoy analytic properties and symmetries that are naturally inherited by the Compton amplitudes. Based on this, we characterize the analytic dependence of the Compton phase-shift in the Kerr spin parameter and provide a direct comparison to the standard post-Minkowskian (PM) perturbative approach within General Relativity (GR). We also analyze the universal large frequency behavior of the relevant characteristic exponent of the CHE -- also known as the renormalized angular momentum -- and find agreement with numerical computations. Moreover, we discuss the analytic continuation in the harmonics quantum number of the partial wave, and show that the limit to the physical integer values commutes with the PM expansion of the observables. Finally, we obtain the contributions to the tree level, point-particle, gravitational Compton amplitude in a covariant basis through , without the need to take the super-extremal limit for Kerr spin
Holographic thermal correlators from supersymmetric instantons
We present an exact formula for the thermal scalar two-point function in four-dimensional holographic conformal field theories. The problem of finding it reduces to the analysis of the wave equation on the AdS-Schwarzschild background. The two-point function is computed from the connection coefficients of the Heun equation, which can be expressed in terms of the Nekrasov-Shatashvili partition function of an supersymmetric gauge theory with four fundamental hypermultiplets. The result is amenable to numerical evaluation upon truncating the number of instantons in the convergent expansion of the partition function. We also examine it analytically in various limits. At large spin the instanton expansion of the thermal two-point function directly maps to the light-cone bootstrap analysis of the heavy-light four-point function. Using this connection, we compute the OPE data of heavy-light double-twist operators. We compare our prediction to the perturbative results available in the literature and find perfect agreement