arXiv subjects

Stathis Vitouladitis

Publications and source records attributed to Stathis Vitouladitis.

9 recordsLinked to original sources

arXiv2026

Ising the way into de Sitter

We study the two-dimensional Ising model deformed by the relevant thermal operator and placed on de Sitter (dS) spacetime. Despite being strongly interacting in its original formulation, the theory is exactly solvable on account of fermionisation. We compute exact cosmological correlators and compare them with conformal perturbation theory. In the Euclidean formulation of the model, we first compute the renormalised sphere partition function and the exact two-point functions of the thermal operator and descendant-like operators. We analytically continue the two-point functions to Lorentzian dS$_2$. Their late-time behaviour is governed by de Sitter representation theory and includes oscillations associated with principal-series scaling dimensions. We then analyse two-point functions of the spin and disorder operators, which are non-local in the fermionic variables, and derive non-perturbative constraints on their late-time scaling dimensions. In both cases, we compare the exact answers to conformal perturbation theory (CPT) and we show that divergent secular terms generically spoil the perturbative series at late times. The de Sitter Ising model shows explicitly how late-time perturbative pathologies are resummed in non-perturbative cosmological observables and provides a minimal solvable laboratory for quantum field theory dynamics in de Sitter space.

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arXiv2026

Axions on de Sitter space

We study a massless minimally coupled compact scalar, or axion, on global $D$-dimensional de Sitter space (dS$_D$). We quantise the theory canonically, determine the quantum dS charges, and find that the axion zero mode supplies a quantum-mechanical factor beyond the oscillator Fock space, $\mathcal{F}$. The full Hilbert space is $\mathcal{H}=L^2(S^1)\otimes\mathcal{F}$, with the integer quantum-mechanical momentum on $L^2(S^1)$ identified with the conserved $\mathrm{U}(1)$ shift charge. The 1-particle unitary irreducible representation (UIR) of the dS group, $\mathrm{SO}(D,1)$, captures the oscillator sector, but misses the zero mode. We find that the neutral 0-particle state is dS-invariant and normalisable. Charged 0-particle states are normalisable, but only $\mathrm{SO}(D)$ invariant. This implies that geodesic observers related by dS boosts do not agree on the particle number in a charged sector, an effect absent in QFTs equipped only with the standard Bunch-Davies vacuum. We compute field-strength Wightman 2-point functions in charged sectors and find that they are Hadamard. For non-zero charge they are not dS-invariant at finite global times, but they are asymptotically so at early and late times. We complement this analysis with a Euclidean perspective. The ordinary $D$-sphere path integral, $Z_{S^D}$, written in terms of Harish-Chandra characters, has access only to the neutral sector. Charged sectors require vertex-operator insertions, and summing over them gives a decorated sphere path integral, $\widehat{Z}_{S^D}=Z_\text{QM}\,Z_{S^D}$, that captures the entire Hilbert space, with $Z_\text{QM}$ denoting the partition function of a quantum rotor at a dimension-dependent effective temperature. Finally, in dS$_3$, we use the duality between an axion and a photon to translate our results to electromagnetism, where the axion zero mode gives rise to magnetic monopoles.

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arXiv2026

The state/defect correspondence

We formulate a one-to-one correspondence between states and defects for higher-form gauge theories in arbitrary dimensions. The correspondence is not predicated on conformal invariance, as these theories are in general not conformal. Instead, it relies on the existence of infinitely many conserved charges associated with the mixed anomaly of electric and magnetic higher-form symmetries. In $p$-form Maxwell theory, these charges generate an extended Kac-Moody algebra that acts simultaneously on states and on extended operators. We show that this algebra organizes the Hilbert space on $S^p \times S^{d-p-1}$ into highest-weight representations allowing for a direct identification between states and $p$-dimensional defects. In particular, Wilson-'t Hooft defects dressed with local gauge-invariant operators are mapped to squeezed energy eigenstates. We further relate these novel symmetries to higher-spin currents and demonstrate that their construction persists in a class of interacting non-linear electrodynamics theories.

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arXiv2025

Higher-form entanglement asymmetry. Part I. The limits of symmetry breaking

Entanglement asymmetry is a relative entropy that faithfully diagnoses symmetry breaking in quantum states, possibly within a spatial subregion. In this work, we extend such framework to higher-form symmetries and compute entanglement asymmetry in theories with spontaneously-broken continuous zero- and higher-form symmetries. One of our central results is an entropic Coleman-Mermin-Wagner theorem, for 0- and $p$-form symmetries, valid also on subregions, which forbids spontaneous breaking of continuous $p$-form symmetries in spacetime dimensions $d\leq p+2$. Our theorem not only qualifies symmetry breaking, it also quantifies it: spontaneous breaking triggers a nonvanishing entanglement asymmetry that grows monotonically towards the infrared, and counts the number of Goldstone fields. Along the way, we derive standalone results concerning the entanglement entropy and asymmetry of Goldstone bosons and gauge fields. In particular, we find a closed-form expression for the R\'enyi asymmetries of a compact scalar field on spherical subregions in three and four spacetime dimensions, and for higher-form gauge fields in higher dimensions.

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arXiv2025

Higher-form anomalies and state-operator correspondence beyond conformal invariance

We establish a state-operator correspondence for a class of non-conformal quantum field theories with continuous higher-form symmetries and a mixed anomaly. Such systems can always be realised as a relativistic superfluid. The symmetry structure induces an infinite tower of conserved charges, which we construct explicitly. These charges satisfy an abelian current algebra with a central extension, generalising the familiar Kac-Moody algebras to higher dimensions. States and operators are organised into representations of this algebra, enabling a direct correspondence. We demonstrate the correspondence explicitly in free examples by performing the Euclidean path integral on a $d$-dimensional ball, with local operators inserted in the origin, and matching to energy eigenstates on $S^{d-1}$ obtained by canonical quantisation. Interestingly, in the absence of conformal invariance, the empty path integral prepares a squeezed vacuum rather than the true ground state.

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arXiv2024

Generalised symmetries and state-operator correspondence for nonlocal operators

We provide a one-to-one correspondence between line operators and states in four-dimensional CFTs with continuous 1-form symmetries. In analogy with 0-form symmetries in two dimensions, such CFTs have a free photon realisation and enjoy an infinite-dimensional current algebra that generalises the familiar Kac-Moody algebras. We construct the representation theory of this current algebra, which allows for a full description of the space of states on an arbitrary closed spatial slice. On $\mathbb{S}^2\times\mathbb{S}^1$, we rederive the spectrum by performing a path integral on $\mathbb{B}^3\times\mathbb{S}^1$ with insertions of line operators. This leads to a direct and explicit correspondence between the line operators of the theory and the states on $\mathbb{S}^2\times\mathbb{S}^1$. Interestingly, we find that the vacuum state is not prepared by the empty path integral but by a squeezing operator. Additionally, we generalise some of our results in two directions. Firstly, we construct current algebras in $(2p+2)$-dimensional CFTs, that are universal whenever the theory has a $p$-form symmetry, and secondly we provide a non-invertible generalisation of those higher-dimensional current algebras.

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arXiv2023

Entanglement in BF theory II: Edge-modes

We consider the entanglement entropy arising from edge-modes in Abelian $p$-form topological field theories in $d$ dimensions on arbitrary spatial topology and across arbitrary entangling surfaces. We find a series of descending area laws plus universal corrections proportional to the Betti numbers of the entangling surface, which can be taken as a higher-dimensional version of the "topological entanglement entropy." Our calculation comes in two flavors: firstly, through an induced edge-mode theory appearing on the regulated entangling surface in a replica path integral and secondly through a more rigorous definition of the entanglement entropy through an extended Hilbert space. Along the way we establish several key results that are of their own merit. We explain how the edge-mode theory is a novel combination of $(p-1)$-form and $(d-p-2)$-form Maxwell theories linked by a chirality condition, in what we coin a "chiral mixed Maxwell theory." We explicitly evaluate the thermal partition function of this theory. Additionally we show that the extended Hilbert space is completely organized into representations of an infinite-dimensional, centrally extended current algebra which naturally generalizes 2d Kac-Moody algebras to arbitrary dimension and topology. We construct the Verma modules and the representation characters of this algebra. Lastly, we connect the two approaches, showing that the thermal partition function of the chiral mixed Maxwell theory is precisely an extended representation character of our current algebra, establishing an exact correspondence of the edge-mode theory and the entanglement spectrum.

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arXiv2023

Entanglement in BF theory I: Essential topological entanglement

We study the entanglement structure of Abelian topological order described by $p$-form BF theory in arbitrary dimensions. We do so directly in the low-energy topological quantum field theory by considering the algebra of topological surface operators. We define two appropriate notions of subregion operator algebras which are related by a form of electric-magnetic duality. To each subregion algebra we assign an entanglement entropy which we coin essential topological entanglement. This is a refinement to the traditional topological entanglement entropy. It is intrinsic to the theory, inherently finite, positive, and sensitive to more intricate topological features of the state and the entangling region. This paper is the first in a series of papers investigating entanglement and topological order in higher dimensions.

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arXiv2022

One-dimensional Quantum Gravity and the Schwarzian theory

We develop a model of one-dimensional (Conformal) Quantum Gravity. By discussing the connection between Goldstone and Gauge theories, we establish that this model effectively computes the partition function of the Schwarzian theory where the $\textrm{SL}(2,\mathbb{R})$ symmetry is realized on the base space. The computation is straightforward, involves a local quantum measure and does not rely on localization arguments. Non-localities in the model are exclusively related to the value of fixed gauge invariant moduli. Furthermore, we study the properties of these models when all degrees of freedom are allowed to fluctuate. We discuss the UV finiteness properties of these systems and the emergence of a Planck's length.

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