arXiv subjects

Alice Bernamonti

Publications and source records attributed to Alice Bernamonti.

17 recordsLinked to original sources

arXiv2026

Temporal Entanglement from Twist Correlators in 2d Conformal Field Theory and Holography

We formulate timelike entanglement entropy and its R\'enyi extension in two-dimensional conformal field theory through the analytic continuation of replica twist correlators to time-ordered, timelike-separated insertions. This field-theoretic construction grounds and generalizes recent developments, and applies to temporal subregions of arbitrary extent. Within three-dimensional holography, the semiclassical boundary correlator identifies boundary-anchored complex geodesics as the relevant bulk saddles and selects the one with the smallest real part of the length. This provides a direct boundary derivation of the proposed complex extremal surface prescription and extends to R\'enyi index $n>1$, for which we explicitly construct the corresponding complex cosmic brane geometry in the vacuum. We develop these ideas in several representative settings, including locally and globally excited states and quantum operator quenches, making manifest the precise agreement between boundary twist correlator and bulk complex geodesic calculations. For AdS-Vaidya, our approach predicts a different result from earlier piecewise geodesic constructions, while reproducing the field theory answer. Across these examples, the operator ordering uniquely determines the imaginary part of the complex-valued entropy, which is quantized in units of $c\pi/6$ and sensitive to the effective causal structure but not to the underlying dynamics.

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arXiv2024

R\'enyi second laws for black holes

Hawking's black hole area theorem provides a geometric realization of the second law of thermodynamics and constrains gravitational processes. In this work we explore a one-parameter extension of this constraint formulated in terms of the monotonicity properties of R\'enyi entropies. We focus on black hole mergers in asymptotically AdS space and determine new restrictions which these R\'enyi second laws impose on the final state. We evaluate the entropic inequalities starting from the thermodynamic ensembles description of black hole geometries, and find that for many situations they set more stringent bounds than those imposed by the area increase theorem.

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arXiv2024

Boundary-induced transitions in Möbius quenches of holographic BCFT

Boundary effects play an interesting role in finite-size physical systems. In this work, we study the boundary-induced properties of 1+1-dimensional critical systems driven by inhomogeneous Möbius-like quenches. We focus on the entanglement entropy in BCFTs with a large central charge and a sparse spectrum of low-dimensional operators. We find that the choice of boundary conditions leads to different scenarios of dynamical phase transitions. We also derive these results in a holographic description in terms of intersecting branes in AdS$_3$, and find a precise match.

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arXiv2021

Holographic and QFT Complexity with angular momentum

We study the influence of angular momentum on quantum complexity for CFT states holographically dual to rotating black holes. Using the holographic complexity=action (CA) and complexity=volume (CV) proposals, we study the full time dependence of complexity and the complexity of formation for two dimensional states dual to rotating BTZ. The obtained results and their dependence on angular momentum turn out to be analogous to those of charged states dual to Reissner-Nordström AdS black holes. For CA, our computation carefully accounts for the counterterm in the gravity action, which was not included in previous analysis in the literature. This affects the complexity early time dependence and its effect becomes negligible close to extremality. In the grand canonical ensemble, the CA and CV complexity of formation are linear in the temperature, and diverge with the same structure in the speed of light angular velocity limit. For CA the inclusion of the counterterm is crucial for both effects. We also address the problem of studying holographic complexity for higher dimensional rotating black holes, focusing on the four dimensional Kerr-AdS case. Carefully taking into account all ingredients, we show that the late time limit of the CA growth rate saturates the expected bound, and find the CV complexity of formation of large black holes diverges in the critical angular velocity limit. Our holographic analysis is complemented by the study of circuit complexity in a two dimensional free scalar model for a thermofield double (TFD) state with angular momentum. We show how this can be given a description in terms of non-rotating TFD states introducing mode-by-mode effective temperatures and times. We comment on the similarities and differences of the holographic and QFT complexity results.

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arXiv2020

Aspects of The First Law of Complexity

We investigate the first law of complexity proposed in arXiv:1903.04511, i.e., the variation of complexity when the target state is perturbed, in more detail. Based on Nielsen's geometric approach to quantum circuit complexity, we find the variation only depends on the end of the optimal circuit. We apply the first law to gain new insights into the quantum circuits and complexity models underlying holographic complexity. In particular, we examine the variation of the holographic complexity for both the complexity=action and complexity=volume conjectures in perturbing the AdS vacuum with coherent state excitations of a free scalar field. We also examine the variations of circuit complexity produced by the same excitations for the free scalar field theory in a fixed AdS background. In this case, our work extends the existing treatment of Gaussian coherent states to properly include the time dependence of the complexity variation. We comment on the similarities and differences of the holographic and QFT results.

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arXiv2020

The First Law of Complexity

We investigate the variation of holographic complexity for two nearby target states. Based on Nielsen's geometric approach, we find the variation only depends on the end point of the optimal trajectory, a result which we designate the first law of complexity. As an example, we examine the complexity=action conjecture when the AdS vacuum is perturbed by a scalar field excitation, which corresponds to a coherent state. Remarkably, the gravitational contributions completely cancel and the final variation reduces to a boundary term coming entirely from the scalar field action. Hence the null boundary of Wheeler-DeWitt patch appears to act like the "end of the quantum circuit".

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arXiv2018

Holographic second laws of black hole thermodynamics

Recently, it has been shown that for out-of-equilibrium systems, there are additional constraints on thermodynamical evolution besides the ordinary second law. These form a new family of second laws of thermodynamics, which are equivalent to the monotonicity of quantum Rényi divergences. In black hole thermodynamics, the usual second law is manifest as the area increase theorem. Hence one may ask if these additional laws imply new restrictions for gravitational dynamics, such as for out-of-equilibrium black holes? Inspired by this question, we study these constraints within the AdS/CFT correspondence. First, we show that the Rényi divergence can be computed via a Euclidean path integral for a certain class of excited CFT states. Applying this construction to the boundary CFT, the Rényi divergence is evaluated as the renormalized action for a particular bulk solution of a minimally coupled gravity-scalar system. Further, within this framework, we show that there exist transitions which are allowed by the traditional second law, but forbidden by the additional thermodynamical constraints. We speculate on the implications of our findings.

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arXiv2017

Heavy-Heavy-Light-Light correlators in Liouville theory

We compute four-point functions of two heavy and two "perturbatively heavy" operators in the semiclassical limit of Liouville theory on the sphere. We obtain these "Heavy-Heavy-Light-Light" (HHLL) correlators to leading order in the conformal weights of the light insertions in two ways: (a) via a path integral approach, combining different methods to evaluate correlation functions from complex solutions for the Liouville field, and (b) via the conformal block expansion. This latter approach identifies an integral over the continuum of normalizable states and a sum over an infinite tower of lighter discrete states, whose contribution we extract by analytically continuing standard results to our HHLL setting. The sum over this tower reproduces the sum over those complex saddlepoints of the path integral that contribute to the correlator. Our path integral computations reveal that when the two light operators are inserted at equal time in radial quantization, the leading-order HHLL correlator is independent of their separation, and more generally that at this order there is no short-distance singularity as the two light operators approach each other. The conformal block expansion likewise shows that in the discrete sum short-distance singularities are indeed absent for all intermediate states that contribute. In particular, the Virasoro vacuum block, which would have been singular at short distances, is not exchanged. The separation-independence of equal-time correlators is due to cancelations between the discrete contributions. These features lead to a Lorentzian singularity that, in conformal theories with anti-de Sitter (AdS) duals, would be associated to locality below the AdS scale.

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arXiv2015

Entanglement Scrambling in 2d Conformal Field Theory

We investigate how entanglement spreads in time-dependent states of a 1+1 dimensional conformal field theory (CFT). The results depend qualitatively on the value of the central charge. In rational CFTs, which have central charge below a critical value, entanglement entropy behaves as if correlations were carried by free quasiparticles. This leads to long-term memory effects, such as spikes in the mutual information of widely separated regions at late times. When the central charge is above the critical value, the quasiparticle picture fails. Assuming no extended symmetry algebra, any theory with $c>1$ has diminished memory effects compared to the rational models. In holographic CFTs, with $c \gg 1$, these memory effects are eliminated altogether at strong coupling, but reappear after the scrambling time $t \gtrsim β\log c$ at weak coupling.

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arXiv2014

Holographic Entanglement Entropy from 2d CFT: Heavy States and Local Quenches

We consider the entanglement entropy in 2d conformal field theory in a class of excited states produced by the insertion of a heavy local operator. These include both high-energy eigenstates of the Hamiltonian and time-dependent local quenches. We compute the universal contribution from the stress tensor to the single interval Renyi entropies and entanglement entropy, and conjecture that this dominates the answer in theories with a large central charge and a sparse spectrum of low-dimension operators. The resulting entanglement entropies agree precisely with holographic calculations in three-dimensional gravity. High-energy eigenstates are dual to microstates of the BTZ black hole, so the corresponding holographic calculation is a geodesic length in the black hole geometry; agreement between these two answers demonstrates that entanglement entropy thermalizes in individual microstates of holographic CFTs. For local quenches, the dual geometry is a highly boosted black hole or conical defect. On the CFT side, the rise in entanglement entropy after a quench is directly related to the monodromy of a Virasoro conformal block.

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arXiv2013

Mutual information after a local quench in conformal field theory

We compute the entanglement entropy and mutual information for two disjoint intervals in two-dimensional conformal field theories as a function of time after a local quench, using the replica trick and boundary conformal field theory. We obtain explicit formulae for the universal contributions, which are leading in the regimes of, for example, close or well-separated intervals of fixed length. The results are largely consistent with the quasiparticle picture, in which entanglement above that present in the ground state is carried by pairs of entangled, freely propagating excitations. We also calculate the mutual information for two disjoint intervals in a proposed holographic local quench, whose holographic energy-momentum tensor matches the conformal field theory one. We find that the holographic mutual information shows qualitative differences from the conformal field theory results and we discuss possible interpretations of this.

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arXiv2013

The spectral function in a strongly coupled, thermalising CFT

In relation to the fluctuation-dissipation theorem, we discuss a time-dependent notion of spectral function and effective temperature. Extending recent results from arXiv:1212.6066, we work out these quantities in a two-dimensional thermalising CFT dual to AdS3-Vaidya spacetime which interpolates between a black brane geometry at early times and a higher temperature black brane at late times. The computation is carried out in the gravitational holographic dual in the geodesic approximation and using a non-standard analytic continuation.

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arXiv2012

Holographic thermalization of mutual and tripartite information in 2d CFTs

We discuss the concepts of mutual and tripartite information by referring to simple intuitive examples, and describe their use as probes of thermalization in holographic models. We then review our computation of these quantities in a simple time dependent model, in which energy injection in a strongly coupled field theory is modeled by a shell of null dust falling into 3d anti-de Sitter space. We complete those results with a discussion of the possible equilibrium phases of the tripartite information.

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arXiv2011

Time-dependent AdS/CFT correspondence and the Quark-Gluon plasma

Experiments on high-energy heavy-ion collisions reveal the formation and some intriguing properties of the Quark-Gluon Plasma (QGP), a new phase of matter predicted by Quantum Chromodynamics (QCD), the quantum field theory of strong interactions. The phenomenological success of relativistic hydrodynamic simulations with remarkably weak shear viscosity, modeling QGP as an almost perfect fluid, are in favor of the occurrence of a strongly-coupled QGP expanding and cooling during the reaction. A derivation of these features in QCD at strong coupling is still lacking and represents a very intricate theoretical challenge. As a quite unique modern tool to relate these dynamical features to a microscopic gauge field theory at strong coupling, time-dependent realizations of the AdS/CFT correspondence provide a fruitful way to study these properties in a realistic kinematic configuration. Relating a 4-dimensional Yang-Mills gauge theory with four supersymmetries (which is a conformal field theory, CFT) with gravity in Anti-de Sitter space in five dimensions (AdS), the AdS/CFT correspondence provides a useful "laboratory" to study yet unknown strong coupling properties of QCD. Besides the interest of revealing new aspects of the AdS/CFT correspondence in a dynamical set-up, the application to plasma formation leads to non trivial theoretical properties, as we will discuss in the lectures. The highlights of the present lectures are: 1. Emergence of an (almost) perfect hydrodynamic fluid at late proper-times after the collision. 2. Duality between an expanding 4-dimensional plasma and a black hole moving radially in the bulk. 3. Intimate link between conformal hydrodynamics and Einstein's equations in the asymptotically AdS space. 4. Possibility of studying the far-from-equilibrium stage of a gauge field theory at early collisional proper-times.

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arXiv2011

Holographic Thermalization

Using the AdS/CFT correspondence, we probe the scale-dependence of thermalization in strongly coupled field theories following a quench, via calculations of two-point functions, Wilson loops and entanglement entropy in d=2,3,4. In the saddlepoint approximation these probes are computed in AdS space in terms of invariant geometric objects - geodesics, minimal surfaces and minimal volumes. Our calculations for two-dimensional field theories are analytical. In our strongly coupled setting, all probes in all dimensions share certain universal features in their thermalization: (1) a slight delay in the onset of thermalization, (2) an apparent non-analyticity at the endpoint of thermalization, (3) top-down thermalization where the UV thermalizes first. For homogeneous initial conditions the entanglement entropy thermalizes slowest, and sets a timescale for equilibration that saturates a causality bound over the range of scales studied. The growth rate of entanglement entropy density is nearly volume-independent for small volumes, but slows for larger volumes.

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arXiv2010

D-Brane Potentials from Multi-Trace Deformations in AdS/CFT

It is known that certain AdS boundary conditions allow smooth initial data to evolve into a big crunch. To study this type of cosmological singularity, one can use the dual quantum field theory, where the non-standard boundary conditions are reflected by the presence of a multi-trace potential unbounded below. For specific AdS_4 and AdS_5 models, we provide a D-brane (or M-brane) interpretation of the unbounded potential. Using probe brane computations, we show that the AdS boundary conditions of interest cause spherical branes to be pushed to the boundary of AdS in finite time, and that the corresponding potential agrees with the multi-trace deformation of the dual field theory. Systems with expanding spherical D3-branes are related to big crunch supergravity solutions by a phenomenon similar to geometric transition.

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arXiv2008

Black strings in AdS_5

We present non-extremal magnetic black string solutions in five-dimensional gauged supergravity. The conformal infinity is the product of time and S^1xS_h, where S_h denotes a compact Riemann surface of genus h. The construction is based on both analytical and numerical techniques. We compute the holographic stress tensor, the Euclidean action and the conserved charges of the solutions and show that the latter satisfy a Smarr-type formula. The phase structure is determined in the canonical ensemble, and it is shown that there is a first order phase transition from small to large black strings, which disappears above a certain critical magnetic charge that is obtained numerically. For another particular value of the magnetic charge, that corresponds to a twisting of the dual super Yang-Mills theory, the conformal anomalies coming from the background curvature and those arising from the coupling to external gauge fields exactly cancel. We also obtain supersymmetric solutions describing waves propagating on extremal BPS magnetic black strings, and show that they possess a Siklos-Virasoro reparametrization invariance.

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