arXiv subjects

Konstantinos Siampos

Publications and source records attributed to Konstantinos Siampos.

At least 19 recordsLinked to original sources

arXiv2026

Non-Abelian Thirring model at large $N$

We consider the non-Abelian bosonized Thirring model for a semi-simple group $G$ at level $k$, with deformation parameter $λ$. We compute the two-point correlation functions of current and composite current operators to cubic order in $λ$, assuming large values of the quadratic Casimir $c_G$ of the group $G$ in the adjoint representation. From these, we extract the $β$-function and the anomalous dimensions of both the current and composite current operators, showing the absence of an additional critical point of order $k/c_G$. Our findings align with those of Destri & de Vega for the Fermionic non-Abelian Thirring model, but contradict the claim in Dashen & Frishman regarding the existence of an additional fixed point of order $1/c_G$.

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arXiv2025

Scale without conformal invariance from integrable deformations of coset CFTs

We construct the $λ$-model on $SU(3)_k/U(2)_k$ and we compute the one-loop $β$-function for the deformation parameter $λ$. Its non-compact version for $SU(2,1)_{-k}/U(2)_{-k}$ is also considered, whose target space admits an asymptotic region that can be reached when one of the coordinates becomes large. The asymptotic model can be seen as an integrable deformation of the $SU(2)_k/U(1)$ WZW model together with a linear dilaton and a free boson, where integrability is inherited from the parental $λ$-model. By taking an asymptotic double-scaling limit of the $SU(2,1)_{-k}/U(2)_{-k}$ model, we obtain a two-dimensional field theory that is scale-invariant but not conformally invariant at one-loop order. Crucially, this deformation does not admit a Kerr-Schild form, unlike the cases studied in arXiv:2109.05040. However, in a suitable asymptotic regime, scale invariance is enhanced to full conformal invariance. Finally, we construct Type-II supergravity embeddings of the asymptotic model for specific values of the deformation parameter.

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arXiv2025

On the geometric origin of the energy-momentum tensor improvement terms

In a flat background, the canonical energy momentum tensor of Lorentz and conformally invariant matter field theories can be improved to a symmetric and traceless tensor that gives the same conserved charges. We argue that the geometric origin of this improvement process is unveiled when the matter theory is coupled to Metric-Affine Gravity. In particular, we show that the Belinfante-Rosenfeld improvement terms correspond to the matter theory's hypermomentum. The improvement terms in conformally invariant matter theories are also related to the hypermomentum however a general proof would require an extended investigation. We demonstrate our results through various examples, such as the free massless scalar, the Maxwell field, Abelian $p$-forms, the Dirac field and a non-unitary massless scalar field. Possible applications of our method for theories that break Lorentz or special conformal invariance are briefly discussed.

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arXiv2025

Integrability of the $λ$-deformation of the PCM with spectators

We construct a generalisation of the $λ$-deformation of the Principal Chiral Model (PCM) where we deform just a subgroup $F$ of the full symmetry group $G$. We find that demanding Lax integrability imposes a crucial restriction, namely that the coset $F\backslash G$ must be symmetric. Surprisingly, we also find that (when $F$ is non-abelian) integrability requires that the term in the action involving only the spectator fields should have a specific $λ$-dependence, which is a curious modification of the procedure expected from the known $F=G$ case. The resulting Lax connection has a novel analytical structure, with four single poles as opposed to the two poles of the cases of the PCM and of the standard $λ$-deformation. We also explicitly work out the example of $G=SU(2)$ and $F=U(1)$, discussing its renormalisation group flow to two loops.

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arXiv2024

Supersymmetric backgrounds from $λ$-deformations

We provide the first supersymmetric embedding of an integrable $λ$-deformation to type-II supergravity. Specifically, that of the near horizon of the NS1-NS5 brane intersection, geometrically corresponding to $AdS_3 \times S^3 \times T^4$. We show that the deformed background preserves 1/4 of the maximal supersymmetry. In the Penrose limit we show that it preserves no-more than one half of the maximal supersymmetry.

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arXiv2023

Chern-Simons action and the Carrollian Cotton tensors

In three-dimensional pseudo-Riemannian manifolds, the Cotton tensor arises as the variation of the gravitational Chern-Simons action with respect to the metric. It is Weyl-covariant, symmetric, traceless and covariantly conserved. Performing a reduction of the Cotton tensor with respect to Carrollian diffeomorphisms in a suitable frame, one discloses four sets of Cotton Carrollian relatives, which are conformal and obey Carrollian conservation equations. Each set of Carrollian Cotton tensors is alternatively obtained as the variation of a distinct Carroll-Chern-Simons action with respect to the degenerate metric and the clock form of a strong Carroll structure. The four Carroll-Chern-Simons actions emerge in the Carrollian reduction of the original Chern-Simons ascendant. They inherit its anomalous behaviour under diffeomorphisms and Weyl transformations. The extremums of these Carrollian actions are commented and illustrated.

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arXiv2023

Integrable models based on non-semi-simple groups and plane wave target spacetimes

We initiate the construction of integrable $λ$-deformed WZW models based on non-semisimple groups. We focus on the four-dimensional case whose underlying symmetries are based on the non-semisimple group $E_2^c$. The corresponding gravitational backgrounds of Lorentzian signature are plane waves which can be obtained as Penrose limits of the $λ$-deformed $SU(2)$ background times a timelike coordinate for appropriate choices of the $λ$-matrix. We construct two such deformations which we demonstrate to be integrable. They both deform the Nappi-Witten plane wave and are inequivalent. Nevertheless, they have the same underlying symmetry algebra which is a Saletan-type contraction of that for the $λ$-deformed $SU(2)$ background with a timelike direction. We also construct a plane wave from the Penrose limit of the $λ$-deformation of the $\nicefrac{SU(2)}{U(1)}$ coset CFT times a timelike coordinate which represents the deformation of a logarithmic CFT constructed in the past. Finally, we briefly consider contractions based on the simplest Yang-baxter $σ$-models.

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arXiv2023

Dynamically restoring conformal invariance in (integrable) $σ$-models

Integrable $λ$-deformed $σ$-models are characterized by an underlying current algebra/coset model CFT deformed, at the infinitesimal level, by current/parafermion bilinears. We promote the deformation parameters to dynamical functions of time introduced as an extra coordinate. It is conceivable that by appropriately constraining them, the beta-functions vanish and consequently the $σ$-model stays conformal. Remarkably, we explicitly materialize this scenario in several cases having a single and even multiple deformation parameters. These generically obey a system of non-linear second-order ordinary differential equations. They are solved by the fixed points of the RG flow of the original $σ$-model. Moreover, by appropriately choosing initial conditions we may even interpolate between the RG fixed points as the time varies from the far past to the far future.Finally, we present an extension of our analysis to the Yang--Baxter deformed PCMs.

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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.

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arXiv2021

Kerr-Schild perturbations of coset CFTs as scale invariant integrable $σ$-models

Kerr-Schild perturbations in General Relativity provide a fruitful way of constructing new exact solutions starting from known ones, elucidating also the structure of the spacetimes. We initiate such a study in the context of string theory and supergravity. Specifically, we explicitly construct Kerr-Schild perturbations of coset CFTs based on low dimensionality orthogonal groups. We show that these give rise to scale, but not Weyl, invariant integrable $σ$-models. We explicitly demonstrate that these models can also be derived from a particular limiting procedure of $λ$-deformed coset CFTs based on non-compact groups. The target space of the simplest $σ$-model describes a two-dimensional scale invariant black hole for which we also provide two different embeddings to type-II supergravity.

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arXiv2021

Novel integrable interpolations

A novel class of integrable $σ$-models interpolating between exact coset conformal field theories in the IR and hyperbolic spaces in the UV is constructed. We demonstrate the relation to the asymptotic limit of $λ$-deformed models for cosets of non-compact groups. An integrable model interpolating between two spacetimes with cosmological and black hole interpretations and exact conformal field theory descriptions is also provided. In the process of our work, a new zoom-in limit, distinct from the well known non-Abelian T-duality limit, is found.

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arXiv2021

$λ$-deformations in the upper-half plane

We formulate $λ$-deformed $σ$-models as QFTs in the upper-half plane. For different boundary conditions we compute correlation functions of currents and primary operators, exactly in the deformation parameter $λ$ and for large values of the level $k$ of the underlying WZW model. To perform our computations we use either conformal perturbation theory in association with Cardy's doubling trick, as well as meromorphicity arguments and a non-perturbative symmetry in the parameter space $(λ,k)$, or standard QFT techniques based on the free field expansion of the $σ$-model action, with the free fields obeying appropriate boundary conditions. Both methods have their own advantages yielding consistent and rich, compared to those in the absence of a boundary, complementary results. We pay particular attention, albeit not exclusively, to integrability preserving boundary conditions.

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arXiv2021

RG flows of integrable $σ$-models and the twist function

In the study of integrable non-linear $σ$-models which are assemblies and/or deformations of principal chiral models and/or WZW models, a rational function called the twist function plays a central role. For a large class of such models, we show that they are one-loop renormalizable, and that the renormalization group flow equations can be written directly in terms of the twist function in a remarkably simple way. The resulting equation appears to have a universal character when the integrable model is characterized by a twist function.

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arXiv2020

A free field perspective of $λ$-deformed coset CFT's

We continue our study of $λ$-deformed $σ$-models by setting up a $1/k$ perturbative expansion around the free field point for cosets, in particular for the $λ$-deformed $SU(2)/U(1)$ coset CFT. We construct an interacting field theory in which all deformation effects are manifestly encoded in the interaction vertices. Using this we reproduce the known $β$-function and the anomalous dimension of the composite operator perturbing away from the conformal point. We introduce the $λ$-dressed parafermions which have an essential Wilson-like phase in their expressions. Subsequently, we compute their anomalous dimension, as well as their four-point functions, as exact functions of the deformation and to leading order in the $k$ expansion. Correlation functions with an odd number of these parafermions vanish as in the conformal case.

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arXiv2020

An exact symmetry in $λ$-deformed CFTs

We consider $λ$-deformed current algebra CFTs at level $k$, interpolating between an exact CFT in the UV and a PCM in the IR. By employing gravitational techniques, we derive the two-loop, in the large $k$ expansion, $β$-function. We find that this is covariant under a remarkable exact symmetry involving the coupling $λ$, the level $k$ and the adjoint quadratic Casimir of the group. Using this symmetry and CFT techniques, we are able to compute the Zamolodchikov metric, the anomalous dimension of the bilinear operator and the Zamolodchikov $C$-function at two-loops in the large $k$ expansion, as exact functions of the deformation parameter. Finally, we extend the above results to $λ$-deformed parafermionic algebra coset CFTs which interpolate between exact coset CFTs in the UV and a symmetric coset space in the IR.

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arXiv2020

Strong integrability of $λ$-deformed models

We study the notion of strong integrability for classically integrable $λ$-deformed CFTs and coset CFTs. To achieve this goal we employ the Poisson brackets of the spatial Lax matrix which we prove that it assumes the Maillet $r/s$-matrix algebra. As a consequence the system in question are integrable in the strong sense. Furthermore, we show that the derived Maillet $r/s$-matrix algebras can be realized in terms of twist functions, at the poles of which we recover the underlying symmetry algebras.

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arXiv2019

$λ$-deformations of left-right asymmetric CFTs

We compute the all-loop anomalous dimensions of current and primary field operators in deformed current algebra theories based on a general semi-simple group, but with different (large) levels for the left and right sectors. These theories, unlike their equal level counterparts, possess a new non-trivial fixed point in the IR. By computing the exact in $λ$ two- and three-point functions for these operators we deduce their OPEs and their equal-time commutators. Using these we argue on the nature of the CFT at the IR fixed point. The associated to the currents Poisson brackets are a two-parameter deformation of the canonical structure of the isotropic PCM.

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arXiv2019

Double and cyclic $λ$-deformations and their canonical equivalents

We prove that the doubly lambda-deformed sigma-models, which include integrable cases, are canonically equivalent to the sum of two single lambda-deformed models. This explains the equality of the exact beta-functions and current anomalous dimensions of the doubly lambda-deformed sigma-models to those of two single lambda-deformed models. Our proof is based upon agreement of their Hamiltonian densities and of their canonical structure. Subsequently, we show that it is possible to take a well defined non-Abelian type limit of the doubly-deformed action. Last, but not least, by extending the above, we construct multi-matrix integrable deformations of an arbitrary number of WZW models.

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