arXiv subjects

Nele Callebaut

Publications and source records attributed to Nele Callebaut.

18 recordsLinked to original sources

arXiv2026

Brane effective actions and their island rule from $T\overline T$ flows

We derive a $2d$ effective action for semi-classical AdS$_3$ gravity with an EOW brane of arbitrary tension by solving the radial Hamiltonian flow in a derivative expansion. Interpreting the radial flow as an RG flow, the effective theory is identified with a $T\bar T$-like deformed CFT. This leads us to propose that the holographic dual for semi-classical AdS$_3$ gravity with Neumann or conformal boundary conditions is obtained by setting the $T\bar T$-like deformed CFT free. We verify our proposal explicitly for saddles corresponding to $(A)dS_2$ branes in empty AdS$_3$. We discuss three useful ways to decompose the effective brane theory into a matter sector ($T\bar T$-deformed, $T\bar T$-like deformed, and undeformed CFT, respectively) and a corresponding braneworld gravity sector. In particular, the split into $T\bar T$-deformed CFT coupled to $T\bar T$-like deformed Liouville gravity directly extends the Liouville description of the integrated Weyl anomaly into the bulk. The effective action is then used to perform an island-rule calculation for a non-asymptotic brane in an AdS/bCFT set-up, finding exact agreement with the Ryu-Takayanagi result. This extends previous holographic checks on the island rule to non-asymptotic regimes of application, as well as provides a Wald entropy interpretation for $T\bar T$ entanglement. Finally, we relate our effective theory and its higher derivative corrections to AdS$_3$ gravity with a fluctuating radial cutoff by explicit calculation of the on-shell action.

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arXiv2026

Introduction to holography

These are course notes for the 'Introduction to holography' Master level course at University of Cologne. The goal of the course is to give a pedogogical introduction to holography. Holography is a popular approach to quantum gravity, in which a theory of gravity can be described by a lower-dimensional boundary theory that itself has no gravity. The most concrete known example of a holographic model is the AdS/CFT correspondence, where the gravitational theory has a negative cosmological constant (the universe is asymptotically Anti-de Sitter) and the boundary theory is a conformal field theory. Symmetry plays a very important role in this duality. We therefore start the course with a review of Poincaré symmetry in quantum field theory, before moving on in the second chapter to conformal symmetry in conformally invariant quantum field theories or CFT's. Then we move to the basics of AdS physics in chapters 3 and 4, which will already reveal hints to the existence of a duality with CFT. After gathering the basic ingredients (CFT and AdS), in the second half of the course we are ready to formulate the AdS/CFT correspondence (chapter 5), including finite temperature AdS/CFT (chapter 6), which involves black holes and their thermodynamics in the gravitational theory (chapter 7). We end the course with an introduction to entanglement in AdS/CFT and the origin of statements that 'gravity emerges from entanglement' in holography.

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arXiv2025

Deforming and dissecting AdS$_3$ with matter

We study deformations of the model by Henneaux, Martínez, Troncoso and Zanelli [arXiv:hep-th/0201170] which features asymptotically AdS$_3$ black hole solutions that incorporate the exact backreaction of a scalar field. The presence of bulk matter causes the $T \overline T$ deformation of the (putative) dual CFT$_2$ to differ from the deformation defined in the bulk by imposing Dirichlet boundary conditions at finite radius. We work out both of these deformations explicitly and verify that $T \overline T$-deforming the boundary theory corresponds to imposing mixed boundary conditions on the metric at the conformal boundary, whereas the bulk "Dirichlet deformation" gives rise to a field theory deforming operator that includes $T \overline T$ as well as other irrelevant terms. We check our results by calculating the deformed energy spectrum for either case using both the bulk and boundary prescriptions, finding agreement after taking into account additional terms coming from the flow of the scalar source. We interpret our explicit results and compare them with the predictions of similar proposals in the literature.

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arXiv2025

Setting $T^2$ free for braneworld holography

We identify what has been referred to as 'cut-off CFT' in holographic braneworld with $T^2$ or $T\bar T$ theory (depending on the dimension of the bulk), so that the holographic dual of AdS-gravity with Neumann boundary conditions is a $T^2$-deformed CFT that is set free. After making statements that apply for general dimensions higher than three, we focus on the case of a three-dimensional bulk. We find from bulk arguments that the effective theory on the brane is governed by a $T\bar T$-like flow equation, such that under certain assumptions the effective gravity theory on the brane is given by a $T\bar T$-like deformed timelike Liouville theory, which limits to the description of the holographic Weyl anomaly for branes that approach the asymptotic boundary.

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arXiv2025

Radial canonical AdS$_3$ gravity and $T\bar{T}$

We employ an ADM deparametrization strategy to discuss the radial canonical formalism of asymptotically AdS$_3$ gravity. It leads to the identification of a radial 'time' before quantization, which is the volume time, canonically conjugate to York time. Holographically, this allows to interpret the semi-classical path integral of $T\bar T$ theory as a Schrödinger wavefunctional satisfying a Schrödinger evolution equation in volume time, and the $T\bar T$ operator expectation value in terms of the Hamiltonian that generates volume time translations -- both consistent with cut-off holography. We make use of the canonical perspective to construct the rotating BTZ solution from the Hamilton-Jacobi equation, with a finite cut-off energy spectrum that has a known holographic $T\bar T$ interpretation, as well as semi-classical Wheeler-DeWitt states for that solution.

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arXiv2025

Radial canonical $Λ<0$ gravity

We apply an ADM deparametrization strategy to radial canonical $Λ< 0$ gravity in three dimensions. It gives rise to a concise notation for previous holographic interpretations in terms of an identified radial 'volume time' and 'true' ADM degrees of freedom. We further discuss York time and conformal boundary conditions in this context, and construct a BTZ wavepacket solution to the radial WdW equation.

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arXiv2025

The chiral SYK model in three-dimensional holography

A celebrated realization of the holographic principle posits an approximate duality between the $(0+1)$-dimensional quantum mechanical SYK model and two-dimensional Jackiw-Teitelboim gravity, mediated by the Schwarzian action as an effective low energy theory common to both systems. We here propose a generalization of this correspondence to one dimension higher. Starting from different microscopic realizations of effectively chiral $(1+1)$-dimensional generalizations of the SYK model, we derive a reduction to the Alekseev-Shatashvilli (AS)-action, a minimal extension of the Schwarzian action which has been proposed as the effective boundary action of three-dimensional gravity. In the bulk, we show how the same action describes fluctuations around the Euclidean BTZ black hole configuration, the dominant stationary solution of three-dimensional gravity. These two constructions allow us to match bulk and boundary coupling constants, and to compute observables. Specifically, we apply semiclassical techniques inspired by condensed matter physics to the computation of out-of-time-order correlation functions (OTOCs), demonstrating maximal chaos in the chiral SYK chain and its gravity dual.

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arXiv2023

Entanglement in conformal field theory and holography

In these notes we give a pedagogical account of the replica trick derivation of CFT entanglement and its holographic counterpart, i.e. the Lewkowycz Maldacena derivation of the Ryu-Takayanagi formula. The application to an 'island set-up' for the calculation of black hole radiation entropy is briefly discussed. Further topics focused on are the relation to thermal entropy, thermofield double constructions and statements about the emergence of gravity from entanglement through reinterpretations of gravitational first laws.

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arXiv2022

Reconstructing bulk equation of motion using CFT modular Hamiltonians

In the framework of bulk reconstruction, we elucidate the relationship between the action of CFT modular Hamiltonians on bulk operators, the possible equation of motion for the bulk operators, and the charge distribution at infinity corresponding to such bulk fields. In particular for scalar fields interacting with gravity or with gauge fields, we show how CFT considerations of the action of the modular Hamiltonian constrain the possible bulk equation of motion to be consistent with bulk gauge invariance and diffeomorphism invariance. In fact we show that requiring that the action of the modular Hamiltonian on a dressed bulk scalar operator be compatible with some unknown simple equation of motion, fixes, under reasonable assumptions, both the equation of motion and the action of the modular Hamiltonian once the first order $\frac{1}{N}$ terms are known.

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arXiv2020

Electro-Magnetic Energy Extraction from Rotating Black Holes in AdS

Force-Free Electrodynamics for black holes in Anti de Sitter is considered. We present new, energy extracting solutions of Force-Free Electrodynamics in Anti de Sitter - Near Horizon Extremal Kerr and Super-Entropic Near Horizon Extremal Kerr geometries. The relevant equations of motion are derived from an action for force-free plasma surrounding spinning black holes with generic asymptotics. We consider the energy flux of electrodynamic fields in rotating frames to argue that the correct measure for energy extraction is the energy flux measured by a rotating observer in the near horizon region. We illustrate this procedure by application to near horizon solutions in Kerr, AdS-Kerr and BTZ.

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arXiv2019

The gravitational dynamics of kinematic space

We show that the dynamics of the kinematic space of a 2-dimensional CFT is gravitational and described by Jackiw-Teitelboim theory. We discuss the first law of this 2-dimensional dilaton gravity theory to support the relation between modular Hamiltonian and dilaton that underlies the kinematic space construction. It is further argued that Jackiw-Teitelboim gravity can be derived from a 2-dimensional version of Jacobson's maximal vacuum entanglement hypothesis. Applied to the kinematic space context, this leads us to the statement that the kinematic space of a 2-dimensional boundary CFT can be obtained from coupling the boundary CFT to JT gravity through a maximal vacuum entanglement principle.

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arXiv2019

$T\bar{T}$ deformed CFT as a non-critical string

We present a new exact treatment of $T\bar{T}$ deformed 2D CFT in terms of the worldsheet theory of a non-critical string. The transverse dimensions of the non-critical string are represented by the undeformed CFT, while the two longitudinal light-cone directions are described by two scalar fields $X^+$ and $X^-$ with free field OPE's but with a modified stress tensor, arranged so that the total central charge adds up to 26. The relation between our $X^\pm$ field variables and 2D dilaton gravity is indicated. We compute the physical spectrum and the partition function and find a match with known results. We describe how to compute general correlation functions and present an integral expression for the three point function, which can be viewed as an exact formula for the OPE coefficients of the $T\bar{T}$ deformed theory. We comment on the relationship with other proposed definitions of local operators.

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arXiv2018

Entanglement Dynamics in 2D CFT with Boundary: Entropic origin of JT gravity and Schwarzian QM

We study the dynamics of the geometric entanglement entropy of a 2D CFT in the presence of a boundary. We show that this dynamics is governed by local equations of motion, that take the same form as 2D Jackiw-Teitelboim gravity coupled to the CFT. If we assume that the boundary has a small thickness $ε$ and constant boundary entropy, we derive that its location satisfies the equations of motion of Schwarzian quantum mechanics with coupling constant $C = {c ε}/{12π}$. We rederive this result via energy-momentum conservation.

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arXiv2016

Equivalence of Emergent de Sitter Spaces from Conformal Field Theory

Recently, two groups have made distinct proposals for a de Sitter space that is emergent from conformal field theory (CFT). The first proposal is that, for two-dimensional holographic CFTs, the kinematic space of geodesics on a spacelike slice of the asymptotically anti-de Sitter bulk is two-dimensional de Sitter space (dS$_2$), with a metric that can be derived from the entanglement entropy of intervals in the CFT. In the second proposal, de Sitter dynamics emerges naturally from the first law of entanglement entropy for perturbations around the vacuum state of CFTs. We provide support for the equivalence of these two emergent spacetimes in the vacuum case and beyond. In particular, we study the kinematic spaces of nontrivial solutions of $3$d gravity, including the BTZ black string, BTZ black hole, and conical singularities. We argue that the resulting spaces are generically globally hyperbolic spacetimes that support dynamics given boundary conditions at future infinity. For the BTZ black string, corresponding to a thermal state of the CFT, we show that both prescriptions lead to an emergent hyperbolic patch of dS$_2$. We offer a general method for relating kinematic space and the auxiliary de Sitter space that is valid in the vacuum and thermal cases.

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arXiv2015

Segmented Strings in $AdS_3$

We study segmented strings in flat space and in $AdS_3$. In flat space, these well known classical motions describe strings which at any instant of time are piecewise linear. In $AdS_3$, the worldsheet is composed of faces each of which is a region bounded by null geodesics in an $AdS_2$ subspace of $AdS_3$. The time evolution can be described by specifying the null geodesic motion of kinks in the string at which two segments are joined. The outcome of collisions of kinks on the worldsheet can be worked out essentially using considerations of causality. We study several examples of closed segmented strings in $AdS_3$ and find an unexpected quasi-periodic behavior. We also work out a WKB analysis of quantum states of yo-yo strings in $AdS_3$ and find a logarithmic term reminiscent of the logarithmic twist of string states on the leading Regge trajectory.

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arXiv2014

Background field and time dependence effects in holographic models

This thesis deals with applications of holographic dualities to the study of background field and time dependence effects in strongly coupled field theories. The first chapters (2-5) aim to provide a self-contained review of the Sakai-Sugimoto model (SSM) as a top-down approach to holographic QCD, introducing first the necessary background on QCD, string theory and AdS/CFT. Chapter 7 reviews finite temperature holography, to be used in the subsequent chapters. We use the non-Abelian ($N_f = 2$) SSM to study a possible magnetically induced instability of the QCD vacuum towards a superconducting phase, as previously discussed in phenomenological QCD models and there referred to as "rho meson condensation". We find that this instability can indeed be holographically described by the SSM, and obtain increasingly higher predictions for the necessary critical magnetic field in increasingly complicated (i.e. less simplified) set-ups. The obtained results are presented in chapter 6 and are based on arXiv:1105.2217 and arXiv:1309.5042. In chapter 8 we discuss the splitting of chiral transition temperatures per flavour in the finite temperature regime of the $N_f = 2$ SSM, indicating an intermediate phase where chiral symmetry is only partially restored. This was previously presented in arXiv:1303.5674. In chapter 9, instead of a top-down approach, bottom-up models known as "AdS-Vaidya" models are used in the context of condensed matter applications to study far-from-equilibrium behaviour of strongly coupled electron systems. A notion of a time-dependent spectral function is defined and calculated in Reissner-Nordström-AdS$_4$-Vaidya as a very first step towards extracting in principle measurable quantities in time-resolved ARPES experiments [arXiv:1407.5975]. Focus is put on explaining the used numerical method (pseudospectral method).

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arXiv2013

A magnetic instability of the non-Abelian Sakai-Sugimoto model

In this follow-up paper of 1105.2217 we further discuss the occurrence of a magnetically induced tachyonic instability of the rho meson in the two-flavour Sakai-Sugimoto model, uplifting two remaining approximations in the previous paper. That is, firstly, the magnetically induced splitting of the branes is now taken into account, evaluating without approximations the symmetrized trace which enters in the non-Abelian Dirac-Born-Infeld (DBI) action. This leads to an extra mass generating effect for the charged heavy-light rho meson through a holographic Higgs mechanism. Secondly, we compare the results in the approximation to second order in the field strength to the results using the full DBI-action. Both improvements cause an increase of the critical magnetic field for the onset of rho meson condensation. In addition, the stability in the scalar sector in the presence of the magnetic field is discussed.

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arXiv2011

Holographic study of rho meson mass in an external magnetic field: paving the road towards a magnetically induced superconducting QCD vacuum?

We study the rho meson mass in a uniform background magnetic field eB at zero temperature, in search of indications for the magnetically induced rho meson condensation, as predicted recently by Chernodub. The holographic model used is the Sakai-Sugimoto model with two flavours and a non-zero constituent quark mass. We fix the free holographic parameters by matching them to the phenomenological value for the constituent quark mass and the experimental values for the pion decay constant and the rho meson mass, this in absence of a magnetic field. In a first approximation, the Landau levels are recovered, indeed indicating an instability of the QCD vacuum at a critical magnetic field, eB_c ~ m_ρ^2, to a phase where rho mesons are condensed. We improve on this result by also taking into account the holographic analogue of chiral magnetic catalysis, numerically solving the mass eigenvalue equation for the rho meson, which depends on eB both explicitly and implicitly through the changed embedding of the flavour probe branes. This turns out to raise eB_c with a few percents. As a byproduct of our analysis we find that the separation between the chiral symmetry restoration temperature T_χ(eB) and the deconfinement temperature T_c is 3.2 percent at eB = 30 m_π^2 ~ 0.57 GeV^2.

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