arXiv subjects

Joris Raeymaekers

Publications and source records attributed to Joris Raeymaekers.

At least 19 recordsLinked to original sources

arXiv2026

On conformal symmetry in large-$N$ quiver mechanics

The microscopic description of extremal supersymmetric black holes in AdS$_2$/CFT$_1$ holography has remained elusive despite recent progress in the statistical description of near-extremal black hole physics. In this work we revisit Denef's quiver mechanics description of D-brane bound states in the Coulomb branch, which displays an emergent conformal symmetry in the AdS$_2$ scaling limit. This conformal symmetry is however broken by superpotential corrections near the locus where the Coulomb and Higgs branches meet, and its significance has so far remained unclear. In order to to clarify this issue, we derive and interpret a fixed-point formula for the superconformal quiver index using localization techniques. Focusing on cyclic abelian quivers, we show that, in a certain large-$N$ limit (with the rank $N$ of the quiver gauge group), the fixed points are located in the regime where the conformal description is reliable. In this limit, our expression for the superconformal index precisely captures a contribution to the microscopic scaling BPS index derived by Beaujard, Mondal and Pioline, which was hitherto not visible on the Coulomb branch. Our results are hoped to provide a step towards a stringy realization of AdS$_2$/CFT$_1$ duality.

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arXiv2025

Index and localization for type B superconformal mechanics on singular spaces

Type B superconformal quantum mechanical sigma models are of physical interest as they arise in the description of D-brane bound states forming an AdS$_2$ throat. In this work we discuss the applicability of localization methods to compute the superconformal index in these theories, despite the fact that their target spaces are generically singular. Similar in spirit to recent works on type A models, we propose to work on a suitably resolved target space to compute a regularized index. While this regularized index correctly captures the actual index unambiguously in models of physical interest, we do uncover a subtlety in more pathological examples. This occurs in situations where the supercharge is not essentially-selfadjoint, in which case the index becomes ambiguous and depends on the chosen selfadjoint extension. We also discuss the special class of models with Kähler target spaces, which can accommodate both type A and type B models, and show that the type B index is a particular limit of the type A index. For Calabi-Yau cones, the type B index coincides with the Hilbert series of the unresolved space.

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arXiv2025

Color-kinematics and double-copy relations for selfdual solutions

We clarify the relation between the classical double copy and the double copy for amplitudes in the setting of selfdual gauge and gravity theories. To this end we construct explicit all-order perturbative solutions in these theories and show that they are related by a version of color-kinematics duality. This relation can be expressed in a double-copy form and embodies the most general manifestation of the selfdual classical double copy. Our classical double copy relations directly lead to known amplitude double-copy relations, both for Berends-Giele currents and on-shell amplitudes, through the perturbiner expansion.

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arXiv2024

Superconformal indices and localization in $N=2B$ quantum mechanics

Superconformal `type B' quantum mechanical sigma models arise in a variety of interesting contexts, such as the description of D-brane bound states in an AdS$_2$ decoupling limit. Focusing on $N=2B$ models, we study superconformal indices which count short multiplets and provide an alternative to the standard Witten index, as the latter suffers from infrared issues. We show that the basic index receives contributions from lowest Landau level states in an effective magnetic field and that, due to the noncompactness of the target space, it is typically divergent. Fortunately, the models of interest possess an additional target space isometry which allows for the definition of a well-behaved refined index. We compute this index using localization of the functional integral and find that the result agrees with a naive application of the Atiyah-Bott fixed point formula outside of it's starting assumptions. In the simplest examples, this formula can also be directly verified by explicitly computing the short multiplet spectrum.

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arXiv2024

Superconformal Symmetry and Index Theory

Formulation and supersymmetry localization of superconformal indices for $\mathcal{N}=2B$ superconformal quantum mechanics are reviewed by providing a generalization to fixed point submanifolds of resolved target space geometries, and future applications to gauged scaling quivers are discussed.

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arXiv2024

Wormholes and surface defects in rational ensemble holography

We study wormhole contributions to the bulk path integral in holographic models which are dual to ensembles of rational free boson conformal field theories. We focus on the path integral on a geometry connecting two toroidal boundaries, which should capture the variance of the ensemble distribution. We show that this requirement leads to a nontrivial set of constraints which generically picks out the uniform, maximum entropy, ensemble distribution. Furthermore, we show that the two-boundary path integral should receive contributions from `exotic' wormholes, which arise from the inclusion of topological surface defects.

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arXiv2023

A note on the admissibility of complex BTZ metrics

We perform a nontrivial check of Witten's recently proposed admissibility criterion for complex metrics. We consider the `quasi-Euclidean' metrics obtained from continuing the BTZ class of metrics to imaginary time. Of special interest are the overspinning metrics, which are smooth in this three-dimensional context. Their inclusion as saddle points in the gravitational path integral would lead to puzzling results in conflict with those obtained using other methods. It is therefore encouraging that the admissibility criterion discards them. For completeness, we perform an analysis of smoothness and admissibility for the family of quasi-Euclidean BTZ metrics at all values of the mass and angular momentum.

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arXiv2022

Holography for bulk states in 3D quantum gravity

In this work we discuss the holographic description of states in the Hilbert space of (2+1)-dimensional quantum gravity, living on a time slice in the bulk. We focus on pure gravity coupled to pointlike sources for heavy spinning particles. We develop a formulation where the equations for the backreacted metric reduce to two decoupled Liouville equations with delta-function sources under pseudosphere boundary conditions. We show that both the semiclassical wavefunction and the gravity solution are determined by a universal object, namely a classical Virasoro vacuum block on the sphere. In doing so we derive a version of Polyakov's conjecture, as well as an existence criterion, for classical Liouville theory on the pseudosphere. We also discuss how some of these results are modified when considering closed universes with compact spatial slices.

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arXiv2022

The geometry of gauged (super)conformal mechanics

Motivated by recently explored examples, we undertake a systematic study of conformal invariance in one-dimensional sigma models where an isometry group has been gauged. Perhaps surprisingly, we uncover classes of sigma models which are only scale invariant in their ungauged form and become fully conformally invariant only after gauging. In these cases the target space of the gauged sigma model satisfies a deformation of the well-known conformal geometry constraints. We consider bosonic models as well as their $\mathcal{N} = 1,2,4$ supersymmetric extensions. We solve the quantum ordering ambiguities in implementing (super-) conformal symmetry on the physical Hilbert space. Examples of our general results are furnished by the $D(2,1;0)$-invariant Coulomb branch quiver models relevant for black hole physics.

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arXiv2022

A note on ensemble holography for rational tori

We study simple examples of ensemble-averaged holography in free compact boson CFTs with rational values of the radius squared. These well-known rational CFTs have an extended chiral algebra generated by three currents. We consider the modular average of the vacuum character in these theories, which results in a weighted average over all modular invariants. In the simplest case, when the chiral algebra is primitive (in a sense we explain), the weights in this ensemble average are all equal. In the non-primitive case the ensemble weights are governed by a semigroup structure on the space of modular invariants. These observations can be viewed as evidence for a holographic duality between the ensemble of CFTs and an exotic gravity theory based on a compact $U(1) \times U(1)$ Chern-Simons action. In the bulk description, the extended chiral algebra arises from soliton sectors, and including these in the path integral on thermal AdS$_3$ leads to the vacuum character of the chiral algebra. We also comment on wormhole-like contributions to the multi-boundary path integral.

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arXiv2020

Conical spaces, modular invariance and $c_{p,1}$ holography

We propose a non-unitary example of holography for the family of two-dimensional logarithmic conformal field theories with negative central charge $c= c_{p,1} = - 6p +13 - 6 p^{-1}$. We argue that at large $p$, these models have a semiclassical gravity-like description which contains, besides the global AdS$_3$ spacetime, a tower of solitonic solutions describing conical excess angles. Evidence comes from the fact that the central charge and the natural modular invariant partition function of such a theory coincide with those of the $c_{p,1}$ model. These theories have an extended chiral W-algebra whose currents have large spin of order $|c|$, and which in the bulk are realized as spinning conical solutions. As a by-product we also find a direct link between geometric actions for exceptional Virasoro coadjoint orbits, which describe fluctuations around the conical spaces, and Felder's free field construction of degenerate representations.

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arXiv2020

Superconformal mechanics of AdS$_2$ D-brane boundstates

We explicitly construct a family of ${\cal N}=4$ superconformal mechanics of dyonic particles, generalizing the work of Anninos et al.\,\cite{Anninos:2013nra} to an arbitrary number of particles. These mechanics are obtained from a scaling limit of the effective Coulomb branch description of ${\mathcal N}=4$ quiver quantum mechanics describing D-branes in type II Calabi-Yau compactifications. In the supergravity description of these D-branes this limit changes the asymptotics to AdS$_2\times $S$^2\times$CY$_3$. We exhibit the $D(1,2;0)$ superconformal symmetry and conserved charges of the mechanics in detail. In addition we present an alternative formulation as a sigma model on a hyperkähler manifold with torsion.

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arXiv2020

Information recovery from pure state geometries in 3D

It is a well-studied phenomenon in AdS$_3$/CFT$_2$ that pure states often appear 'too thermal' in the classical gravity limit, leading to a version of the information puzzle. One example is the case of a heavy scalar primary state, whose associated classical geometry is the BTZ black hole. Another example is provided by a heavy left-moving primary, which displays late time decay in chiral correlators. In this paper we study a special class of pure state geometries which do not display such information loss. They describe heavy CFT states created by a collection of chiral operators at various positions on the complex plane. In the bulk, these take the form of multi-centered solutions from the backreaction of a collection of spinning particles, which we construct for circular distributions of particles. We compute the two-point function of probe operators in these backgrounds and show that information is retrieved. We observe that the states for which our geometric picture is reliable are highly extended star-like objects in the bulk description. This may point to limitations of the semiclassical fuzzball picture of black hole microstates.

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arXiv2019

On tensionless string field theory in AdS$_3$

We report on progress in formulating a field theory of tensionless strings in $AdS_3$, starting from the dual large-$N$ symmetric orbifold CFT. We propose a set of field equations which are gauge invariant under the higher spin algebra of the theory, the `Higher Spin Square'. The massless higher spin sector is captured by a Chern-Simons gauge field, while the matter sector is described by unfolded equations similar to those appearing in Vasiliev theory. Our equations incorporate the full perturbative spectrum of the theory, including states coming from the twisted sectors, and capture some of the interactions fixed by gauge invariance. We also discuss the spectrum of the bulk theory and explain how linearization around $AdS_3$ gives rise to the expected set of decoupled wave equations. Our results can be generalized to describe bulk duals of other large-$N$ symmetric orbifolds.

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arXiv2018

Multi-centered higher spin solutions from $W_N$ conformal blocks

Motivated by the question of bulk localization in holography, we study the problem of constructing multi-centered solutions in higher spin gravity which describe point particles in the interior of AdS$_3$. In the Chern-Simons formulation these take into account the backreaction after adding Wilson line sources. We focus on chiral solutions where only the left-moving sector is excited. In that case it is possible to choose a gauge where the dynamical variables are a set of Toda fields living in the bulk. The problem then reduces to solving the $\mathcal{A}_{N-1}$ Toda equations with delta function sources, which in turn requires solving an associated monodromy problem. We show that this monodromy problem is equivalent to the monodromy problem for a particular $\mathcal{W}_N$ vacuum conformal block at large central charge. Therefore, knowledge of the $\mathcal{W}_N$ vacuum block determines the multi-centered solution. Our calculations go beyond the heavy-light approximation by including the backreaction of all higher spin particles.

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arXiv2018

Simple Unfolded Equations for Massive Higher Spins in AdS$_3$

We propose a simple unfolded description of free massive higher spin particles in anti-de-Sitter spacetime. While our unfolded equation of motion has the standard form of a covariant constancy condition, our formulation differs from the standard one in that our field takes values in a different internal space, which for us is simply a unitary irreducible representation of the symmetry group. Our main result is the explicit construction, for the case of AdS$_3$, of a map from our formulation to the standard wave equations for massive higher spin particles, as well as to the unfolded description prevalent in the literature. It is hoped that our formulation may be used to clarify the group-theoretic content of interactions in higher spin theories.

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arXiv2018

Quantizing higher-spin gravity in free-field variables

We study the formulation of massless higher-spin gravity on AdS$_3$ in a gauge in which the fundamental variables satisfy free field Poisson brackets. This gauge choice leaves a small portion of the gauge freedom unfixed, which should be further quotiented out. We show that doing so leads to a bulk version of the Coulomb gas formalism for $W_N$ CFT's: the generators of the residual gauge symmetries are the classical limits of screening charges, while the gauge-invariant observables are classical $W_N$ charges. Quantization in these variables can be carried out using standard techniques and makes manifest a remnant of the triality symmetry of $W_\infty[λ]$. This symmetry can be used to argue that the theory should be supplemented with additional matter content which is precisely that of the Prokushkin-Vasiliev theory. As a further application, we use our formulation to quantize a class of conical surplus solutions and confirm the conjecture that these are dual to specific degenerate $W_N$ primaries, to all orders in the large central charge expansion.

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arXiv2017

Chiral boundary conditions for singletons and W-branes

We revisit the holographic dictionary for a free massless scalar in AdS$_3$, focusing on the `singleton' solutions for which the boundary profile is an arbitrary chiral function. We look for consistent boundary conditions which include this class of solutions. On one hand, we give a no-go argument that they cannot be interpreted within any boundary condition which preserves full conformal invariance. On the other hand, we show that such solutions fit naturally in a generalization of the Compère-Song-Strominger boundary conditions, which preserve a chiral Virasoro and current algebra. These observations have implications for the black hole deconstruction proposal, which proposes singleton solutions as candidate black hole microstate geometries. Our results suggest that the chiral boundary condition, which also contains the extremal BTZ black hole, is the natural setting for holographically interpreting the black hole deconstruction proposal.

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