arXiv subjects

Dionysios Anninos

Publications and source records attributed to Dionysios Anninos.

At least 19 recordsLinked to original sources

arXiv2026

Aspects of Closed Matricial Worlds

We investigate the Hilbert space structure for simple theories of gravity with $Λ>0$ on closed spatial sections. Our motivation ties to the presence of gravitational saddles in four-dimensional $Λ>0$ Einstein-Maxwell theory with $S^2\times Σ_h$ topology, where $Σ_h$ is a genus-$h$ Riemann surface. Here, as a concrete starting point, the problem is explored for two-dimensional $Λ>0$ quantum gravity. We revisit and elaborate on exact results in the matrix model literature. We study gravitational wavefunctions from both the perspective of the Wheeler-DeWitt equation and the gravitational path integral. Though simple, the setting displays many features of general interest such as large volume effects that disrupt the perturbative expansion, topological corrections to the path-integral wavefunction that offend the exact Wheeler-DeWitt equation, and a sphere path integral ${Z}^{(0)}_{\text{grav}}$ with non-trivial structure in $Λ$. We discuss candidate inner products for the infinite-dimensional canonical gravitational Hilbert space uncovered by Lian and Zuckerman. By establishing explicit results up to genus-six, we argue that the dominant contribution to the genus-$h$ gravitational disk path integral at large spatial size mimics the behavior of two-dimensional topological gravity. In passing, we show that for ${Z}^{(0)}_{\text{grav}}$ to give rise to a positive counting problem for discretised Riemann surfaces, it must have a negative pre-factor. We contrast our analysis to the more realistic case of timelike Liouville theory.

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arXiv2026

de Sitter Vacua & pUniverses

We analyze a simple extension of the Schwinger model, which we refer to as the $p$-Schwinger model, on a de Sitter background. In this theory, the charged massless fermions carry non-unit integer charge $p$. In Minkowski space, the $p$-Schwinger model has discrete zero- and one-form global symmetries that are spontaneously broken, yielding $p$ degenerate ground states. We demonstrate that these features persist upon placing the $p$-Schwinger model on a global de Sitter background, establishing that such discrete global symmetries can be spontaneously broken for quantum field theories in de Sitter space. In particular, the theory is endowed with $p$ distinct, but locally-indistinguishable, de Sitter invariant states, the de Sitter vacua, satisfying the Hadamard property. We couple a variant of the $p$-Schwinger model with ${\rm N}_{\rm f}$ flavors to quantum gravity with $Λ>0$, and demonstrate the existence of a semiclassical de Sitter saddle at large ${\rm N}_{\rm f}$. In the gravitational theory, the $p$ de Sitter invariant vacua are speculatively interpreted as microstates of the de Sitter horizon in the low-energy effective field theory.

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arXiv2026

Quantum Liouville Cosmology

We provide a detailed analysis of the disk path integral of timelike Liouville theory, conceived as a tractable and precise toy-model quantum cosmology in two dimensions. Disk path integrals with the insertion of matter field operators, taken along a judiciously chosen complex contour, yield states akin to the Hartle-Hawking wavefunction. Working in the fixed $K$-representation, where $K$ is the trace of the extrinsic curvature, we compute the one-loop wavefunctions and put forward a conjecture for the all-loop expressions. A suitable pairing of Liouville disk path integrals yields a $K$-independent quantity that may form the basis for a well-defined inner product on the space of Euclidean histories. We also consider other ensembles, including one with fixed area, and provide a static patch perspective with a timelike feature.

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arXiv2026

dS$^4$ Metamorphosis

We study the Euclidean path integral of higher spin gravity on $S^4$. Based on a one-loop analysis, we are led to a gluing formula expressing the $S^4$ path integral in terms of an underlying $S^3$ path integral. We view the three-sphere as a boundary hypersurface splitting the four-sphere into two halves. For a higher spin spectrum containing even spins only, the resulting boundary theory living on the $S^3$ cut is the $\mathrm{Sp}(N)$ invariant sector of $N\in \mathbb{Z}^+$ anti-commuting, conformally coupled free scalars, with conformal higher spin sources mediating the gluing. This boundary $\mathrm{Sp}(N)$ theory was previously shown to compute the Hartle-Hawking wavefunction at $\mathcal{I}^+$ in the higher spin dS$_4$/CFT$_3$ correspondence. In contrast to the infinite spatial volume of $\mathcal{I}^+$, here the conformal fields populate a finite size $S^3$ hypersurface of $S^4$. For theories with both bosonic and fermionic higher spin fields, the gluing formula is instead built from an $\mathcal{N}=2$ superconformal boundary field theory coupled to $U(N)$ invariant superconformal sources. Under this assumption, the leading contribution to the four-sphere partition function is $2^N$, and we observe exact cancellations at one-loop.

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arXiv2026

Fermionic fields of higher spin in de Sitter space

We consider fermionic fields of higher spin on a four-dimensional de Sitter background. A particular emphasis is placed on the Rarita-Schwinger spin-$\tfrac{3}{2}$ case. Both massive fields and gauge fields are considered, and their relation to the representation theory of $SO(4,1)$ is discussed. In Lorentzian signature, we study properties of the Bunch-Davies mode functions, and the late time structure of their two-point functions. For the Rarita-Schwinger gauge field, we consider a quantisation procedure based on the Minkowskian limit of the field operator. In Euclidean signature, the fields are placed on a four-sphere and the Euclidean path integral is computed at one-loop. The resulting Euclidean partition function is expressed in terms of unitary Lorentzian group characters with edge corrections. The unitary nature of the characters contrasts the lack of a conventional real action for the Rarita-Schwinger gauge field in de Sitter space. We speculate on the microscopic properties of a theory comprised of an infinite tower of interacting integer and half-integer gauge fields in de Sitter space. Along the way, we discuss a potentially interesting expression for the higher-spin path integral on the four-sphere.

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arXiv2026

The Stretched Horizon Limit

We consider four-dimensional general relativity with a positive cosmological constant, $Λ$, in the presence of a boundary, $Γ$, of finite spatial size. The boundary is located near a cosmological event horizon, and is subject to boundary conditions that fix the conformal class of the induced metric, and, $K$, the trace of the extrinsic curvature along $Γ$. The proximity of $Γ$ to the horizon is controlled by the dimensionless parameter ${K}{Λ^{-\frac{1}{2}}}$. We provide an exhaustive analysis of linearised gravitational perturbations for the setup. This is performed both for a $Γ$ encasing a portion of the static patch that ends just before the cosmological horizon (pole patch), as well as a $Γ$ containing only the region near the cosmological horizon (cosmic patch). In the pole patch, we uncover a layered hierarchy of modes: ordinary normal modes, a novel type of boundary gapless mode, and boundary soft modes of frequency $ω\approx \pm 2πi T_{\text{dS}}$, with $T_{\text{dS}}$ the horizon temperature. Minkowskian behaviour is recovered only for angular momenta $l \gtrsim {K}{Λ^{-\frac{1}{2}}}$ which can be made parametrically large, thus attenuating previously found growing modes. In the cosmic patch, we uncover sound and shear fluid-dynamical modes that we interpret in terms of a conformal fluid with shear viscosity over entropy density ratio $\tfracη{s} = \tfrac{1}{4π}$ and vanishing bulk viscosity $ζ=0$. The fluid dynamical sector is shown to admit a non-linear treatment. We describe a scaling regime in which the stretched horizon gravitational dynamics is dictated by a universal Rindler geometry, independent to the details of the infilling horizon. We briefly discuss quantitative features that distinguish cosmological and black hole horizons away from the Rindler regime.

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arXiv2025

Features of the Partition Function of a $Λ>0$ Universe

We consider properties of the gravitational path integral, ${Z}_{\text{grav}}$, of a four-dimensional gravitational effective field theory with $Λ>0$ at the quantum level. To leading order, ${Z}_{\text{grav}}$ is dominated by a four-sphere saddle subject to small fluctuations. Beyond this, ${Z}_{\text{grav}}$ receives contributions from additional geometries that may include Einstein metrics of positive curvature. We discuss how a general positive curvature Einstein metric contributes to ${Z}_{\text{grav}}$ at one-loop level. Along the way, we discuss Einstein-Maxwell theory with $Λ>0$, and identify an interesting class of closed non-Einstein gravitational instantons. We provide a detailed study for the specific case of $\mathbb{C}P^2$ which is distinguished as the saddle with second largest volume and positive definite tensor eigenspectrum. We present exact one-loop results for scalar particles, Maxwell theory, and Einstein gravity about the Fubini-Study metric on $\mathbb{C}P^2$.

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arXiv2025

Gravitational Observatories

We consider four-dimensional general relativity with vanishing cosmological constant defined on a manifold with a boundary. In Lorentzian signature, the timelike boundary is of the form $\boldsymbolσ \times \mathbb{R}$, with $\boldsymbolσ$ a spatial two-manifold that we take to be either flat or $S^2$. In Euclidean signature, we take the boundary to be $S^2\times S^1$. We consider conformal boundary conditions, whereby the conformal class of the induced metric and trace $K$ of the extrinsic curvature are fixed at the timelike boundary. The problem of linearised gravity is analysed using the Kodama-Ishibashi formalism. It is shown that for a round metric on $S^2$ with constant $K$, there are modes that grow exponentially in time. We discuss a method to control the growing modes by varying $K$. The growing modes are absent for a conformally flat induced metric on the timelike boundary. We provide evidence that the Dirichlet problem for a spherical boundary does not suffer from non-uniqueness issues at the linearised level. We consider the extension of black hole thermodynamics to the case of conformal boundary conditions, and show that the form of the Bekenstein-Hawking entropy is retained.

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arXiv2025

Gravitational Observatories in AdS$_4$

We consider four-dimensional general relativity with a negative cosmological constant in the presence of a finite size boundary, $Γ$, for both Euclidean and Lorentzian signature. As our boundary condition, we consider the `conformal' boundary condition that fixes the conformal class of the induced metric at $Γ$ and the trace of the extrinsic curvature, $K(x^m)$. In Lorentzian signature, we must supplement these with appropriate initial data comprising the standard Cauchy data along a spatial slice and, in addition, initial data for a boundary mode that appears due to the presence of the finite size boundary. We perform a linearised analysis of the gravitational field equations for both an $S^2\times \mathbb{R}$ as well as a Minkowskian, $\mathbb{R}^{1,2}$, boundary. In the $S^2\times \mathbb{R}$ case, in addition to the usual AdS$_4$ normal modes, we uncover a novel linearised perturbation, $\boldsymbolω(x^m)$, which can exhibit complex frequencies at sufficiently large angular momentum. Upon moving $Γ$ toward the infinite asymptotic AdS$_4$ boundary, the complex frequencies appear at increasingly large angular momentum and vanish altogether in the strict limit. In the $\mathbb{R}^{2,1}$ case, although we uncover an analogous novel perturbation, we show it does not exhibit complex frequencies. In Euclidean signature, we show that $K(x^m)$ plays the role of a source for $\boldsymbolω(x^m)$. When close to the AdS$_4$ asymptotic boundary, we speculate on the holographic interpretation of $\boldsymbolω(x^m)$.

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arXiv2025

The two-sphere partition function in two-dimensional quantum gravity

We study the Euclidean path integral of two-dimensional quantum gravity with positive cosmological constant coupled to conformal matter with large and positive central charge. The problem is considered in a semiclassical expansion about a round two-sphere saddle. We work in the Weyl gauge whereby the computation reduces to that for a (timelike) Liouville theory. We present results up to two-loops, including a discussion of contributions stemming from the gauge fixing procedure. We exhibit cancelations of ultraviolet divergences and provide a path integral computation of the central charge for timelike Liouville theory. Combining our analysis with insights from the DOZZ formula we are led to a proposal for an all orders result for the two-dimensional gravitational partition function on the two-sphere.

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arXiv2025

dS$_2$ Supergravity

We construct two-dimensional supergravity theories endowed with a positive cosmological constant, that admit de Sitter vacua. We consider the cases of $\mathcal{N}=1$ as well as $\mathcal{N}=2$ supersymmetry, and couple the supergravity to a superconformal field theory with the same amount of supersymmetry. Upon fixing a supersymmetric extension of the Weyl gauge, the theories are captured, at the quantum level, by supersymmetric extensions of timelike Liouville theory with $\mathcal{N}=1$ and $\mathcal{N}=2$ supersymmetry respectively. The theories exhibit good ultraviolet properties and are amenable to a variety of techniques such as systematic loop expansions and, in the $\mathcal{N}=2$ case, supersymmetric localization. Our constructions offer a novel path toward a precise treatment of the Euclidean gravitational path integral for de Sitter, and in turn, the Gibbons-Hawking entropy of the de Sitter horizon. We argue that the supersymmetric localization method applied to the $\mathcal{N}=2$ theory must receive contributions from boundary terms in configuration space. We also discuss how these theories overcome several obstructions that appear upon combining de Sitter space with supersymmetry.

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arXiv2025

De Sitter Musings

We discuss some of the issues that arise when considering the physics of asymptotically de Sitter spacetimes, and attempts to address them. Our development begins at the classical level, where several initial value problems are discussed, and ends with several proposals for holography in asymptotically de Sitter spacetimes. Throughout the paper we give a review of some basic notions such as the geometry of the Schwarzschild-de Sitter black hole, the Nariai limit, and quantum field theory in a fixed de Sitter background. We also briefly discuss some semiclassical aspects such as the nucleation of giant black holes and the Hartle-Hawking wavefunctional. We end by giving an overview of some open questions. An emphasis is placed on the differences between a static patch observer confined to live in a thermal cavity and the metaobserver who has access to a finite region of the future boundary.

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arXiv2025

Remarks on 2D quantum cosmology

We consider two-dimensional quantum gravity endowed with a positive cosmological constant and coupled to a conformal field theory of large and positive central charge. We study cosmological properties at the classical and quantum level. We provide a complete ADM analysis of the classical phase space, revealing a family of either bouncing or big bang/crunch type cosmologies. At the quantum level, we solve the Wheeler-DeWitt equation exactly. In the semiclassical limit, we link the Wheeler-DeWitt state space to the classical phase space. Wavefunctionals of the Hartle-Hawking and Vilenkin type are identified, and we uncover a quantum version of the bouncing spacetime. We retrieve the Hartle-Hawking wavefunction from the disk path integral of timelike Liouville theory. To do so, we must select a particular contour in the space of complexified fields. The quantum information content of the big bang cosmology is discussed, and contrasted with the de Sitter horizon entropy as computed by a gravitational path integral over the two-sphere.

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arXiv2025

Cosmological Observatories

We study the static patch of de Sitter space in the presence of a timelike boundary. We impose that the conformal class of the induced metric and the trace of the extrinsic curvature, $K$, are fixed at the boundary. We present the thermodynamic structure of de Sitter space subject to these boundary conditions, for static and spherically symmetric configurations to leading order in the semiclassical approximation. In three spacetime dimensions, and taking $K$ constant on a toroidal Euclidean boundary, we find that the spacetime is thermally stable for all $K$. In four spacetime dimensions, the thermal stability depends on the value of $K$. It is established that for sufficiently large $K$, the de Sitter static patch subject to conformal boundary conditions is thermally stable. This contrasts the Dirichlet problem for which the region encompassing the cosmological horizon has negative specific heat. We present an analysis of the linearised Einstein equations subject to conformal boundary conditions. In the worldline limit of the timelike boundary, the underlying modes are linked to the quasinormal modes of the static patch. In the limit where the timelike boundary approaches the cosmological event horizon, the linearised modes are interpreted in terms of the shear and sound modes of a fluid dynamical system. Additionally, we find modes with a frequency of positive imaginary part. Measured in a local inertial reference frame, and taking the stretched cosmological horizon limit, these modes grow at most polynomially.

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arXiv2024

de Sitter at all loops: the story of the Schwinger model

We consider the two-dimensional Schwinger model of a massless charged fermion coupled to an Abelian gauge field on a fixed de Sitter background. The theory admits an exact solution, first examined by Jayewardena, and can be analyzed efficiently using Euclidean methods. We calculate fully non-perturbative, gauge-invariant correlation functions of the electric field as well as the fermion and analyze these correlators in the late-time limit. We compare these results with the perturbative picture, for example by verifying that the one-loop contribution to the fermion two-point function, as predicted from the exact solution, matches the direct computation of the one-loop Feynman diagram. We demonstrate many features endemic of quantum field theory in de Sitter space, including the appearance of late-time logarithms, their resummation to de Sitter invariant expressions, and Boltzmann suppressed non-perturbative phenomena, with surprising late-time features.

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arXiv2023

Renormalisation Group Flows of Deformed SYK Models

We explore computationally tractable deformations of the SYK model. The deformed theories are described by the sum of two SYK Hamiltonians with differing numbers, $q$ and $\tilde{q}$, of interacting fermions. In the large $N$ limit, employing analytic and numerical tools, we compute finite temperature correlation functions and thermodynamic quantities. We identify a novel analytically solvable model in the large $q$ limit. We find that, under certain circumstances, the thermal RG flow in the strongly coupled infrared phase exhibits two regions of linear-in-temperature entropy, which we interpret in terms of Schwarzian actions. Using conformal perturbation theory we compute the leading relevant correction away from the intermediate near-conformal fixed point. Holographic spacetimes in two spacetime dimensions that reproduce the thermodynamics of the microphysical theory are discussed. These are flow geometries that interpolate between two Euclidean near-AdS$_2$ spacetimes with different radii. The Schwarzian soft mode corresponding to the AdS$_2$ region in the deep interior resides entirely within the geometric regime.

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arXiv2023

The Discreet Charm of the Discrete Series in DS$_2$

We study quantum field theories placed on a two-dimensional de Sitter spacetime (dS$_2$) with an eye on the group-theoretic organisation of single and multi-particle states. We explore the distinguished role of the discrete series unitary irreducible representation (UIR) in the Hilbert space. By employing previous attempts to realise these states in free tachyonic scalar field theories, we propose how the discrete series may contribute to the Källén-Lehmann decomposition of an interacting scalar two-point function. We also study BF gauge theories with $SL(N,\mathbb{R})$ gauge group in dS$_2$ and establish a relation between the discrete series UIRs and the operator content of these theories. Although present at the level of the operators, states carrying discrete series quantum numbers are projected out of the gauge-invariant Hilbert space. This projection is reminiscent of what happens for quantum field theories coupled to semiclassical de Sitter gravity, where we must project onto the subspace of de Sitter invariant states. We discuss how to impose the diffeomorphism constraints on local field-theory operators coupled to two-dimensional gravity in de Sitter, with particular emphasis on the role of contact terms. Finally, we discuss an SYK-type model with a random two-body interaction that encodes an infinite tower of discrete series operators. We speculate on its potential microscopic connection to the $SL(N,\mathbb{R})$ BF theory in the large-$N$ limit.

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arXiv2023

Finite Features of Quantum De Sitter Space

We consider degrees of freedom for a quantum de Sitter spacetime. The problem is studied from both a Lorentzian and a Euclidean perspective. From a Lorentzian perspective, we compute dynamical properties of the static patch de Sitter horizon. These are compared to dynamical features of black holes. We point out differences suggestive of non-standard thermal behaviour for the de Sitter horizon. We establish that geometries interpolating between an asymptotically AdS$_2 \times S^2$ space and a dS$_4$ interior are compatible with the null energy condition, albeit with a non-standard decreasing radial size of $S^2$. The putative holographic dual of an asymptotic AdS$_2$ spacetime is comprised of a finite number of degrees of freedom. From a Euclidean perspective we consider the gravitational path integral for fields over compact manifolds. In two-dimensions, we review Polchinski's BRST localisation of Liouville theory and propose a supersymmetric extension of timelike Liouville theory which exhibits supersymmetric localisation. We speculate that localisation of the Euclidean gravitational path integral is a reflection of a finite number of degrees of freedom in a quantum de Sitter universe.

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