arXiv subjects

Anastasios C. Petkou

Publications and source records attributed to Anastasios C. Petkou.

At least 19 recordsLinked to original sources

arXiv2026

A thermal representation for conformal ladder integrals

I discuss the recently discovered representation of conformal four-point ladder integrals in terms of the thermal free energy of free massive scalar fields. These integrals satisfy a novel second-order differential equation in even dimensions $D$ at arbitrary loop order $L$. I also present a simple derivation of the all-loop resummation of conformal ladder integrals for arbitrary $D$. Possible connections to the thermal bootstrap, multiloop calculations, integrability, AdS/CFT and string theory are briefly discussed. This is a proceedings contribution to the Athens Workshop in Theoretical Physics: 10th Anniversary, held at the National and Kapodistrian University of Athens on December 17--19 2025.

hep-th↗

arXiv2025

The thermal representation of conformal ladder integrals

We present the details of a recently discovered representation of conformal four-point ladder integrals as thermal one-point functions in scalar field theories. We show that the conformal ladder integrals can be constructed from the partition function of two harmonic oscillators twisted by an imaginary chemical potential and that for any even dimension $D$ and any loop order $L$ they satisfy a familiar second order differential equation. In our representation, thermal one-point functions of higher-spin operators correspond to linear combinations of multi-loop ladder graphs in $D=2$ and $D=4$ dimensions. Moreover, we give a simple derivation for the all-loop resummation of conformal ladder integrals for arbitrary $D$. We conclude by highlighting possible connections between our work and recent developments in the thermal bootstrap, multiloop calculations, integrability, AdS/CFT and string theory.

hep-th↗

arXiv2025

Remarks on the quasinormal modes of Taub-NUT-AdS$_4$

We present results for the numerical evaluation of scalar quasinormal modes in Taub-NUT-AdS$_4$ spacetimes. To achieve this we consider angular modes that correspond to non-unitary highest weight $SU(2)$ representations since global regularity is not consistent with the presence of complex quasinormal modes. We show that for any non-zero value of the NUT charge $n$ there exists a region in the complex plane that contains only stable quasinormal modes. The radius of this region increases with the horizon distance and decreases with $n$ towards a constant value for infinite $n$. We also find analytic and numerical evidence for the existence of a critical NUT charge $n_{cr}$ beyond which the lowest lying stable quasinormal modes become overdamped. Our results draw an intricate picture for the holographic fluid of Taub-NUT-AdS$_4$.

gr-qc↗

arXiv2024

Conformal graphs as twisted partition functions

We show that a class of $L$-loop conformal ladder graphs correspond to twisted partition functions of free massive complex scalars in $d=2L+1$ dimensions. The graphs arise as four-point functions in certain two- and four-dimensional conformal fishnet models. The twisted thermal two-point function of the scalars is a generator of such conformal graphs for all loops. We argue that this correspondence is seeded by a system of two decoupled harmonic oscillators twisted by an imaginary chemical potential. We find a number of algebraic and differential relations among the conformal graphs which mirror the underlying free dynamics.

hep-th↗

arXiv2022

Relativistic Fluids, Hydrodynamic Frames and their Galilean versus Carrollian Avatars

We comprehensively study Galilean and Carrollian hydrodynamics on arbitrary backgrounds, in the presence of a matter/charge conserved current. For this purpose, we follow two distinct and complementary paths. The first is based on local invariance, be it Galilean or Carrollian diffeomorphism invariance, possibly accompanied by Weyl invariance. The second consists in analyzing the relativistic fluid equations at large or small speed of light, after choosing an adapted gauge, ADM-Zermelo for the former and Papapetrou-Randers for the latter. Unsurprisingly, the results agree, but the second approach is superior as it effortlessly captures more elaborate situations with multiple degrees of freedom. It furthermore allows to investigate the fate of hydrodynamic-frame invariance in the two limits at hand, and conclude that its breaking (in the Galilean) or its preservation (in the Carrollian) are fragile consequences of the behaviour of transport attributes at large or small $c$. Both methods do also agree on the doom of Noetherian currents generated in the relativistic theory by isometries: non-trivial currents are not always guaranteed in Newton-Cartan or Carroll spacetimes as a consequence of Galilean or Carrollian isometries. Comparison of Galilean and Carrollian fluid equations exhibits a striking but often superficial resemblance, which we comment in relation to black-hole horizon dynamics, awkwardly akin to Navier-Stokes equations. This congruity is authentic in one instance though and turns out then to describe Aristotelian dynamics, which is the last item in our agenda.

hep-th↗

arXiv2021

Thermal one-point functions and single-valued polylogarithms

I point out that the thermal one-point functions of a pair of relevant operators in massive free QFTs, in odd dimensions and in the presence of an imaginary chemical potential for a U(1) global charge, are given by certain classes of single-valued polylogarithms. This result is verified by a direct calculation using the thermal OPE. The complex argument of the polylogarithms parametrize a two-dimensional subspace of relevant deformations of generalised free CFTs, while the rank of the polylogarithms is related to the dimension d. This may be compared with the well-known representation of single-valued polylogarithms as multiloop Feynman amplitudes. As an example, the thermal one-point function of the U(1) charge in d-dimensions generalises the thermal average of the twist operator in a pair of harmonic oscillators and is given by the well-known conformal ladder graphs in four dimensions.

hep-th↗

arXiv2020

Aspects of Holography of Taub-NUT-AdS4

In this paper we consider aspects of the holographic interpretation of Taub-NUT-AdS$_4$. We review our earlier results which show that TNAdS$_4$ gives rise to a holographic three-dimensional conformal fluid having constant vorticity. We then study the holographic relevance of the Misner string by considering bulk scalar fluctuations. The scalar fluctuations organize naturally into representations of the $SU(2)\times \mathbb{R}$ isometry algebra. If we require the string's invisibility we obtain a Dirac-like quantization relating the frequency of the scalar field modes to the NUT charge. As the latter quantity determines the total vorticity flux of the boundary fluid, we argue that such an assumption allows for a holographic interpretation of TNAdS$_4$ as a {\it non-dissipative} superfluid whose excitations are quantized vortices. Alternatively, if we regard the Misner string as a physical object, as has recently been advocated for thermodynamically, the aforementioned quantization conditions are removed, and we find that TNAdS$_4$ corresponds to a holographic fluid whose dissipative properties are probed as usual by the complex quasinormal modes of the bulk fluctuations. We show that such quasinormal modes are, perhaps surprisingly, organized into infinite-dimensional non-unitary representations of the isometry algebra.

hep-th↗

arXiv2018

Flat holography and Carrollian fluids

We show that a holographic description of four-dimensional asymptotically locally flat spacetimes is reached smoothly from the zero-cosmological-constant limit of anti-de Sitter holography. To this end, we use the derivative expansion of fluid/gravity correspondence. From the boundary perspective, the vanishing of the bulk cosmological constant appears as the zero velocity of light limit. This sets how Carrollian geometry emerges in flat holography. The new boundary data are a two-dimensional spatial surface, identified with the null infinity of the bulk Ricci-flat spacetime, accompanied with a Carrollian time and equipped with a Carrollian structure, plus the dynamical observables of a conformal Carrollian fluid. These are the energy, the viscous stress tensors and the heat currents, whereas the Carrollian geometry is gathered by a two-dimensional spatial metric, a frame connection and a scale factor. The reconstruction of Ricci-flat spacetimes from Carrollian boundary data is conducted with a flat derivative expansion, resummed in a closed form in Eddington-Finkelstein gauge under further integrability conditions inherited from the ancestor anti-de Sitter set-up. These conditions are hinged on a duality relationship among fluid friction tensors and Cotton-like geometric data. We illustrate these results in the case of conformal Carrollian perfect fluids and Robinson-Trautman viscous hydrodynamics. The former are dual to the asymptotically flat Kerr-Taub-NUT family, while the latter leads to the homonymous class of algebraically special Ricci-flat spacetimes.

hep-th↗

arXiv2018

The Raychaudhuri equation in spacetimes with torsion and non-metricity

We introduce and develop the 1+3 covariant approach to relativity and cosmology to spacetimes of arbitrary dimensions that have nonzero torsion and do not satisfy the metricity condition. Focusing on timelike observers, we identify and discuss the main differences between their kinematics and those of their counterparts living in standard Riemannian spacetimes. At the centre of our analysis lies the Raychaudhuri equation, which is the fundamental formula monitoring the convergence/divergence, namely the collapse/expansion, of timelike worldline congruences. To the best of our knowledge, we provide the most general expression so far of the Raychaudhuri equation, with applications to an extensive range of non-standard astrophysical and cosmological studies. Assuming that metricity holds, but allowing for nonzero torsion, we recover the results of analogous previous treatments. Focusing on non-metricity alone, we identify a host of effects that depend on the nature of the timelike congruence and on the type of the adopted non-metricity. We also demonstrate that in spaces of high symmetry one can recover the pure-torsion results from their pure non-metricity analogues, and vice-versa, via a simple ansatz between torsion and non-metricity.

gr-qc↗

arXiv2018

Torsion/non-metricity duality in f(R) gravity

Torsion and nonmetricity are inherent ingredients in modifications of Eintein's gravity that are based on affine spacetime geometries. In the context of pure f(R) gravity we discuss here, in some detail, the relatively unnoticed duality between torsion and nonmetricity. In particular we show that for R2 gravity torsion and nonmetricity are related by projective transformations. Since the latter correspond simply to redefining the affine parameters of autoparallels, we conclude that torsion and nonmetricity are physically equivalent properties of spacetime. As a simple example we show that both torsion and nonmetricity can act as geometric sources of accelerated expansion in a spatially homogenous cosmological model within R2 gravity and we brie y discuss possible implications of our results.

gr-qc↗

arXiv2018

Covariant Galilean versus Carrollian hydrodynamics from relativistic fluids

We provide the set of equations for non-relativistic fluid dynamics on arbitrary, possibly time-dependent spaces, in general coordinates. These equations are fully covariant under either local Galilean or local Carrollian transformations, and are obtained from standard relativistic hydrodynamics in the limit of infinite or vanishing velocity of light. All dissipative phenomena such as friction and heat conduction are included in our description. Part of our work consists in designing the appropriate coordinate frames for relativistic spacetimes, invariant under Galilean or Carrollian diffeomorphisms. The guide for the former is the dynamics of relativistic point particles, and leads to the Zermelo frame. For the latter, the relevant objects are relativistic instantonic space-filling branes in Randers-Papapetrou backgrounds. We apply our results for obtaining the general first-derivative-order Galilean fluid equations, in particular for incompressible fluids (Navier-Stokes equations) and further illustrate our findings with two applications: Galilean fluids in rotating frames or inflating surfaces and Carrollian conformal fluids on two-dimensional time-dependent geometries. The first is useful in atmospheric physics, while the dynamics emerging in the second is governed by the Robinson-Trautman equation, describing a Calabi flow on the surface, and known to appear when solving Einstein's equations for algebraically special Ricci-flat or Einstein spacetimes.

hep-th↗

arXiv2018

Dynamics of Finite-Temperature CFTs from OPE Inversion Formulas

We apply the OPE inversion formula to thermal two-point functions of bosonic and fermionic CFTs in general odd dimensions. This allows us to analyze in detail the operator spectrum of these theories. We find that nontrivial thermal CFTs arise when the thermal mass satisfies an algebraic transcendental equation that ensures the absence of an infinite set of operators from the spectrum. The solutions of these gap equations for general odd dimensions are in general complex numbers and follow a particular pattern. We argue that this pattern unveils the large-$N$ vacuum structure of the corresponding theories at zero temperature.

hep-th↗

arXiv2018

Petrov Classification and holographic reconstruction of spacetime

Using the asymptotic form of the bulk Weyl tensor, we present an explicit approach that allows us to reconstruct exact four-dimensional Einstein spacetimes which are algebraically special with respect to Petrov's classification. If the boundary metric supports a traceless, symmetric and conserved complex rank-two tensor, which is related to the boundary Cotton and energy-momentum tensors, and if the hydrodynamic congruence is shearless, then the bulk metric is exactly resummed and captures modes that stand beyond the hydrodynamic derivative expansion. We illustrate the method when the congruence has zero vorticity, leading to the Robinson-Trautman spacetimes of arbitrary Petrov class, and quote the case of non-vanishing vorticity, which captures the Plebanski-Demianski Petrov D family.

hep-th↗

arXiv2018

The Robinson-Trautman spacetime and its holographic fluid

We discuss the holographic reconstruction of four-dimensional asymptotically anti-de Sitter Robinson-Trautman spacetime from boundary data. We use for that a resummed version of the derivative expansion. The latter involves a vector field, which is interpreted as the dual-holographic-fluid velocity field and is naturally defined in the Eckart frame. In this frame the analysis of the non-perfect holographic energy-momentum tensor is considerably simplified. The Robinson-Trautman fluid is at rest and its time evolution is a heat-diffusion kind of phenomenon: the Robinson-Trautman equation plays the rôle of heat equation, and the heat current is identified with the gradient of the extrinsic curvature of the two-dimensional boundary spatial section hosting the conformal fluid, interpreted as an out-of-equilibrium kinematical temperature. The hydrodynamic-frame-independent entropy current is conserved for vanishing chemical potential, and the evolution of the fluid resembles a Moutier thermodynamic path. We finally comment on the general transformation rules for moving to the Landau-Lifshitz frame, and on possible drawbacks of this option.

hep-th↗

arXiv2018

The fermion-boson map for large d

We show that the three-dimensional map between fermions and bosons at finite temperature generalises for all odd dimensions $d>3$. We further argue that such a map has a nontrivial large $d$ limit. Evidence comes from studying the gap equations, the free energies and the partition functions of the $U(N)$ Gross-Neveu and CP$^{N-1}$ models for odd $d\geq 3$ in the presence of imaginary chemical potential. We find that the gap equations and the free energies can be written in terms of the Bloch-Wigner-Ramakrishnan $D_d(z)$ functions analysed by Zagier. Since $D_2(z)$ gives the volume of ideal tetrahedra in 3$d$ hyperbolic space our three-dimensional results are related to resent studies of complex Chern-Simons theories, while for $d>3$ they yield corresponding higher dimensional generalizations. As a spinoff, we observe that particular complex saddles of the partition functions correspond to the zeros and the extrema of the Clausen functions $Cl_d(θ)$ with odd and even index $d$ respectively. These saddles lie on the unit circle at positions remarkably well approximated by a sequence of rational multiples of $π$.

hep-th↗

arXiv2017

The analytic structure of conformal blocks and the generalized Wilson-Fisher fixed points

We describe in detail the method used in our previous work arXiv:1611.10344 to study the Wilson-Fisher critical points nearby generalized free CFTs, exploiting the analytic structure of conformal blocks as functions of the conformal dimension of the exchanged operator. Our method is equivalent to the mechanism of conformal multiplet recombination set up by null states. We compute, to the first non-trivial order in the $ε$-expansion, the anomalous dimensions and the OPE coefficients of infinite classes of scalar local operators using just CFT data. We study single-scalar and $O(N)$-invariant theories, as well as theories with multiple deformations. When available we agree with older results, but we also produce a wealth of new ones. Unitarity and crossing symmetry are not used in our approach and we are able to apply our method to non-unitary theories as well. Some implications of our results for the study of the non-unitary theories containing partially conserved higher-spin currents are briefly mentioned.

hep-th↗

arXiv2017

Generalized Wilson-Fisher critical points from the conformal OPE

We study possible smooth deformations of Generalized Free Conformal Field Theories in arbitrary dimensions by exploiting the singularity structure of the conformal blocks dictated by the null states. We derive in this way, at the first non trivial order in the $ε$-expansion, the anomalous dimensions of an infinite class of scalar local operators, without using the equations of motion. In the cases where other computational methods apply, the results agree.

hep-th↗

arXiv2016

The free $σ$CFTs

We introduce the conformal field theories that describe the shadows of the lowest dimension composites made out of massless free scalars and fermions in $d$ dimensions. We argue that these theories can be consistently defined as free CFTs for even $d\geq 4$. We use OPE techniques to study their spectrum and show that for $d\rightarrow\infty$ it matches that of free bosonic CFTs in $d=6$ and $d=4$ dimensions. For these $σ$CFTs we calculate $c_T$ in $d=6,8,10$ and $12$ dimensions using the OPE and also a direct construction of their higher-derivative energy momentum tensors. Our results agree with the general proposal of arXiv:1601.07198.

hep-th↗