arXiv subjects

Kostas Skenderis

Publications and source records attributed to Kostas Skenderis.

At least 19 recordsLinked to original sources

arXiv2026

Brane flows

Based on effective D-brane actions, we present a generalisation of the Ricci flow that includes the flow of a theory with a $n$-form field strength for $n\geq 0$. This is a generalisation of both the Ricci flows and the generalised Ricci flows. Following Perelman, we show that flows that keep a suitable field-dependent volume fixed are monotonic. We also show that all steady brane flow solitons are gradient solitons and use this to demonstrate that on some occasions this implies the existence of a Killing vector field that leaves all the other fields invariant. Particular cases of gradient solitons are NS5 and D5 branes, and the volume which is kept fixed in these cases is the T-duality invariant volume (NS5 brane) or its S-dual (D5 brane). We also generalise the above analysis to gravitational actions coupled to form gauge potentials that also exhibit a Chern-Simons type term. We find an alteration is required in the adaptation of Perelman's modification to this case, which yields a new functional that also exhibits a Chern-Simons term. Under suitable assumptions, we proceed to prove the monotonicity of the flow and that all steady flow solitons are gradient solitons. We also explore the consequences of the last statement on the geometry of solitons.

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arXiv2026

Bulk-to-bulk photon propagator in AdS

We study the photon bulk-to-bulk propagator in AdS in various gauges, including axial, Coulomb, and the standard covariant gauge. We compute the propagator using both momentum and position space techniques. We ensure the propagators obtained obey the right subsidiary conditions arising from gauge invariance. In particular, BRST invariance implies a relation between the longitudinal components of the gauge field propagator and the ghost bulk-to-bulk propagator. Our method relies on decomposing the components of the propagator in terms of independent tensor structures and solving for the form factors. We recover some previously existing results and obtain new expressions for the propagator in other gauges. The propagator in axial and Coulomb gauge is simpler in momentum space, as momentum space makes manisfest the translational invariance in the boundary directions, while the position space expression is the simplest in the covariant Fried-Yennie gauge. In this gauge the propagator has an improved IR behavior, somewhat analogous to the UV improved behavior associated with the Landau gauge in flat space. The results readily extend to Yang-Mills fields.

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arXiv2026

A remarkably simple covariant graviton propagator in Anti-de Sitter spacetime

We present remarkably simple covariant expressions for the graviton and ghost propagators in Anti-de Sitter (AdS) spacetime valid in any spacetime dimension. In gravity there is a $2$-parameter family of covariant gauge-fixing conditions and the simplification occurs for a special choice of these parameters. In this gauge the graviton propagator satisfies $\nabla^μμ\nabla^νμ\, G_{μν,α'β'}(μ)=0$, where $μ$ is the geodesic distance between two points, and this condition implies an improved infrared behavior. This gauge choice is not possible in flat spacetime.

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arXiv2026

Renormalised 3-point functions of stress tensors and conserved currents in CFT

We present a complete momentum-space prescription for the renormalisation of tensorial correlators in conformal field theories. Our discussion covers all 3-point functions of stress tensors and conserved currents in arbitrary spacetime dimensions. In dimensions three and four, we give explicit results for the renormalised correlators, the anomalous Ward identities they obey, and the conformal anomalies. For the stress tensor 3-point function in four dimensions, we identify the specific evanescent tensorial structure responsible for the type A Euler anomaly, and show this anomaly has the form of a double copy of the chiral anomaly.

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arXiv2025

Gravitational charges and radiation in asymptotically locally de Sitter spacetimes

We present a comprehensive discussion of gravitational charges and radiation in four-dimensional asymptotically locally de Sitter (AldS) spacetimes. Such spacetimes have compact spatial sections and possess spacelike past and future infinities, $\mathscr{I}^\pm$. We show that the variational problem is well-posed if one specifies a conformal class up to three-dimensional diffeomorpshims at $\mathscr{I}^\pm$, provided one adds at $\mathscr{I}^\pm$ suitable local terms. These are analogues of the AdS covariant counterterms of holographic renormalisation. Radiation is possible only when the conformal class at infinity is non-trivial. Bulk diffeomorphisms that asymptote to conformal Killing vectors at $\mathscr{I}^\pm$ lead to gravitational charges that are conserved under radial translations, while transformations that asymptote to a general three-dimensional vector imply that the gravitational charges satisfy flux-balance laws. We also present quantities that are invariant under temporal translations, if gravitational flux is absent, but otherwise satisfy flux-balance laws. We derive these results using first principles application of Noether's method as well as covariant phase space methods. We apply our formalism to several exact solutions, including the Robinson-Trautman-dS class, which we use to demonstrate the existence of conserved charges even in the absence of asymptotic conformal Killing vectors and the existence of monotonic charges, including the Bondi mass.

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arXiv2024

AdS amplitudes as CFT correlators

We show that AdS amplitudes are CFT correlators to all orders in the loop expansion by showing that they obey the conformal Ward identities. In particular, we provide explicit formulas for the constants and functions of cross-ratios that determine the CFT correlators in terms of bulk data.

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arXiv2024

Flat space spinning massive amplitudes from momentum space CFT

We discuss the flat space limit of AdS using the momentum space representation of CFT correlators. The flat space limit involves sending the AdS radius and the dimensions of operators dual to massive fields to infinity while also scaling appropriately the sources of the dual operators. In this limit, d-dimensional CFT correlators become (d+1)-dimensional scattering amplitudes. We exemplify our discussion with the computation of the flat-space limit of the CFT 3-point function of a conserved current, a non-conserved charged vector operator and its conjugate. The flat-space limit should yield the scattering amplitude of an Abelian gauge field with two massive vector fields. This scattering amplitude computes the electromagnetic form factors of the electromagnetic current in a spin-1 state, and these form factors encode the electromagnetic properties of the massive vector field (charge, magnetic moment and quadruple moment). In terms of the CFT, the flat-space limit amounts to zooming in the infrared region of the triple-K integrals that determine the 3-point function, while also scaling to infinity the order of (some of) the Bessel functions that feature in the triple-K integrals. In this limit the triple-K integral becomes proportional to the energy-preserving delta function, and the flat space limit correctly yields the corresponding flat space scattering amplitude in complete detail.

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arXiv2024

Renormalisation of IR divergences and holography in de Sitter

We formulate a renormalisation procedure for IR divergences of tree-level in-in late-time de Sitter correlators. These divergences are due to the infinite volume of spacetime and are analogous to the divergences that appear in AdS dealt with by holographic renormalisation. Regulating the theory using dimensional regularisation, we show that one can remove all infinities by adding local counterterms at the future boundary of dS in the Schwinger-Keldysh path integral. The counterterms amount to renormalising the late-time bulk field. We frame the discussion in terms of bulk scalar fields in dS, using tree-level correlators of massless and conformal scalars for illustration. The relation to AdS via analytic continuation is discussed, and we show that different versions of the analytic continuation appearing in the literature are equivalent to each other. In AdS, one needs to add counterterms that are related to conformal anomalies, and also to renormalise the source part of the bulk field. The analytic continuation to dS projects out the traditional AdS counterterms, and links the renormalisation of the sources to the renormalisation of the late-time bulk field. We use these results to establish holographic formulae that relate tree-level dS in-in correlators to CFT correlators at up to four points, and we provide two proofs: one using the connection between the dS wavefunction and the partition function of the dual CFT, and a second by direct evaluation of the in-in correlators using the Schwinger-Keldysh formalism. The renormalisation of the bulk IR divergences is mapped by these formulae to UV renormalisation of the dual CFT via local counterterms, providing structural support for a possible duality. We also recast the regulated holographic formulae in terms of the AdS amplitudes of shadow fields, but show that this relation breaks down when renormalisation is required.

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arXiv2024

The Ambient Space Formalism

We present a new formalism to solve the kinematical constraints due to Weyl invariance for CFTs in curved backgrounds and/or non-trivial states, and we apply it to thermal CFTs and to CFTs on squashed spheres. The ambient space formalism is based on constructing a class of geometric objects that are Weyl covariant and identifying them as natural building blocks of correlation functions. We construct (scalar) $n$-point functions and we illustrate the formalism with a detailed computation of 2-point functions. We compare our results for thermal 2-point functions with results that follow from thermal OPEs and holographic computations, finding exact agreement. In our holographic computation we also obtain the OPE coefficient of the leading double-twist contribution, and we discuss how the double-twist coefficients may be computed from the multi-energy-momentum contributions, given knowledge of the analytic structure of the correlator. The 2-point function for the CFT on squashed spheres is a new result. We also discuss the relation of our work to flat holography.

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arXiv2023

An embedding formalism for CFTs in general states on curved backgrounds

We present a generalisation of the embedding space formalism to conformal field theories (CFTs) on non-trivial states and curved backgrounds, based on the ambient metric of Fefferman and Graham. The ambient metric is a Lorentzian Ricci-flat metric in $d+2$ dimensions and replaces the Minkowski metric of the embedding space. It is canonically associated with a $d$-dimensional conformal manifold, which is the physical spacetime where the CFT${}_d$ lives. We propose a construction of CFT${}_d$ $n$-point functions in non-trivial states and on curved backgrounds using appropriate geometric invariants of the ambient space as building blocks. This captures the contributions of non-vanishing 1-point functions of multi-stress-energy tensors, at least in holographic CFTs. We apply the formalism to 2-point functions of thermal CFT, finding exact agreement with a holographic computation and expectations based on thermal operator product expansions (OPEs), and to CFTs on squashed spheres where no prior results are known and existing methods are difficult to apply, demonstrating the utility of the method.

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arXiv2023

Bulk renormalization and the AdS/CFT correspondence

We develop a systematic renormalization procedure for QFT in anti-de Sitter spacetime. UV infinities are regulated using a geodesic point-splitting method, which respects AdS isometries, while IR infinities are regulated by cutting off the radial direction (as in holographic renormalization). The renormalized theory is defined by introducing $Z$ factors for all parameters in the Lagrangian and the boundary conditions of bulk fields (sources of dual operators), and a boundary counterterm action, $S_{\rm ct}$, such that the limit of removing the UV and IR regulators exists. The results are in general scheme dependent (mirroring the analogous result in flat space) and require renormalization conditions. These may be provided by the dual CFT (or by string theory in AdS). Our analysis amounts also to a first principles derivation of the Feynman rules regarding Witten diagrams. The presence and treatment of IR divergences is essential for correctly accounting for anomalous dimensions of dual operators. We apply the method to scalar $Φ^4$ theory and obtain the renormalized 2-point function of the dual operator to 2-loops, and the renormalized 4-point function to 1-loop order, for operators of any dimension $Δ$ and bulk spacetime dimension up to $d+1=7$.

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arXiv2022

Momentum space CFT correlators of non-conserved spinning operators

We analyse the 3-point CFT correlators involving non-conserved spinning operators in momentum space. We derive a general expression for the conformal Ward identities defining the 3-point functions involving two generic spin $s$ non-conserved operators and a spin 1 conserved current. We give explicit expressions for the 3-point function when the two non-conserved operators have spins 1 and 2 and generic conformal dimensions. We also systematically analyse the divergences appearing in these 3-point functions when the conformal dimensions of the two non-conserved operators coincide.

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arXiv2022

Position-Space Renormalisation of the Energy-Momentum Tensor

There is increasing interest in the study of nonperturbative aspects of three-dimensional quantum field theories (QFT). They appear as holographic dual to theories of (strongly coupled) gravity. For instance, in Holographic Cosmology, the two-point function of the Energy-Momentum Tensor (EMT) of a particular class of three-dimensional QFTs can be mapped into the power spectrum of the Cosmic Microwave Background in the gravitational theory. However, the presence of divergent contact terms poses challenges in extracting a renormalised EMT two-point function on the lattice. Using a $ϕ^4$ theory of adjoint scalars valued in the $\mathfrak{su}(N)$ Lie Algebra as a proof-of-concept motivated by Holographic Cosmology, we apply a novel method for filtering out such contact terms by making use of infinitely differentiable "bump" functions which enforce a smooth window that excludes contributions at zero spatial separation. The process effectively removes the local contact terms and allows us to extract the continuum limit behaviour of the renormalised EMT two-point function.

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arXiv2022

A handbook of holographic 4-point functions

We present a comprehensive discussion of tree-level holographic $4$-point functions of scalar operators in momentum space. We show that each individual Witten diagram satisfies the conformal Ward identities on its own and is thus a valid conformal correlator. When the $β= Δ- d/2$ are half-integral, with $Δ$ the dimensions of the operators and $d$ the spacetime dimension, the Witten diagrams can be evaluated in closed form and we present explicit formulae for the case $d=3$ and $Δ=2,3$. These correlators require renormalization, which we carry out explicitly, and lead to new conformal anomalies and beta functions. Correlators of operators of different dimension may be linked via weight-shifting operators, which allow new correlators to be generated from given `seed' correlators. We present a new derivation of weight-shifting operators in momentum space and uncover several subtleties associated with their use: such operators map exchange diagrams to a linear combination of exchange and contact diagrams, and special care must be taken when renormalization is required.

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arXiv2022

Charges, conserved quantities and fluxes in de Sitter spacetime

We discuss the definition of conserved quantities in asymptotically locally de Sitter spacetimes. One may define an analogue of holographic charges at future and past infinity and at other Cauchy surfaces $I_t$ as integrals over the intersection of timelike surfaces $C$ and the Cauchy surface $I_t$. In general, the charges $Q^t$ defined on the Cauchy surface $I_t$ depend on $C$, but if gravitational flux is absent the charges are independent of $C$. On the other hand, if there is a net gravitational flux entering or leaving the spacetime region bounded by $C_1, C_2$ and two Cauchy surfaces then $ΔQ^t(C_1, C_2) = Q^t(C_1)-Q^t(C_2)$ changes by the same amount.

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arXiv2022

Massive holographic QFTs in de Sitter

We study strongly coupled mass-deformed-CFT on a fixed de Sitter spacetime in three dimensions via holography. We elucidate the global causal structure of the four-dimensional spacetime dual to the de Sitter invariant vacuum state. The conformal boundaries of de Sitter appear as spacelike defects sourced by the mass deformation, which extend into the bulk as curvature singularities in AdS. We compute all one- and two-point functions of the deformed-CFT stress tensor and a scalar operator order-by-order in the mass deformation for a simple holographic model. These correlation functions admit a spectral representation as a sum of simple poles corresponding to normalisable modes in the bulk.

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arXiv2022

Renormalization of the $3D$ $SU(N)$ scalar energy-momentum tensor using the Wilson flow

In the holographic approach to cosmology, cosmological observables are described in terms of correlators of a three-dimensional boundary quantum field theory. As a concrete model, we study the $3D$ massless $SU(N)$ scalar matrix field theory with a $ϕ^4$ interaction. On the lattice, the energy-momentum tensor (EMT) in this theory can mix with the operator $ϕ^2$. We utilize the Wilson Flow to renormalize the EMT on the lattice, and present numerical results for the mixing coefficient for $N = 2$. Obtaining the renormalized EMT will allow us to make predictions for the CMB power spectra in the regime where the dual QFT is non-perturbative.

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arXiv2021

Renormalization of the energy-momentum tensor in three-dimensional scalar $SU(N)$ theories using the Wilson flow

A nonperturbative determination of the energy-momentum tensor is essential for understanding the physics of strongly coupled systems. The ability of the Wilson flow to eliminate divergent contact terms makes it a practical method for renormalizing the energy-momentum tensor on the lattice. In this paper, we utilize the Wilson flow to define a procedure to renormalize the energy-momentum tensor for a three-dimensional massless scalar field in the adjoint of $SU(N)$ with a $φ^4$ interaction on the lattice. In this theory the energy-momentum tensor can mix with $φ^2$ and we present numerical results for the mixing coefficient for the $N=2$ theory.

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