arXiv subjects

Konstantinos Sfetsos

Publications and source records attributed to Konstantinos Sfetsos.

At least 19 recordsLinked to original sources

arXiv2025

Adjoint ferromagnets

We derive the phase structure and thermodynamics of ferromagnets consisting of elementary magnets carrying the adjoint representation of $SU(N)$ and coupled through two-body quadratic interactions. Such systems have a continuous $SU(N)$ symmetry as well as a discrete conjugation symmetry. We uncover a rich spectrum of phases and transitions, involving a paramagnetic and two distinct ferromagnetic phases that can coexist as stable and metastable states in different combinations over a range of temperatures. The ferromagnetic phases break $SU(N)$ invariance in various channels, leading to spontaneous magnetization. Interestingly, the conjugation symmetry also breaks over a range of temperatures and group ranks $N$, providing a realization of a spontaneously broken discrete symmetry.

cond-mat.stat-mech↗

arXiv2025

Nonabelian ferromagnets with three-body interactions

We study the thermodynamics of nonabelian ferromagnets consisting of atoms in the fundamental representation of $SU(N)$ and interacting with two-body and three-body interactions. Using a mean field approach, we uncover an intricate phase structure, depending on the relative strength and sign of the two-body and three-body coupling constants. In the case where two-body interactions are ferromagnetic and three-body ones are antiferromagnetic, we uncover a rich cascade of phase transitions, the appearance of phases with two distinct polarization directions being the most striking novel feature. Our results are relevant to magnetic systems where higher-body interactions cannot be neglected.

hep-th↗

arXiv2025

Ferromagnets from higher $SU(N)$ representations

We present a general formalism for deriving the thermodynamics of ferromagnets consisting of "atoms" carrying an arbitrary irreducible representation of $SU(N)$ and coupled through long-range two-body quadratic interactions. Using this formalism, we derive the thermodynamics and phase structure of ferromagnets with atoms in the doubly symmetric or doubly antisymmetric irreducible representations. The symmetric representation leads to a paramagnetic and a ferromagnetic phase with transitions similar to the ones for the fundamental representation studied before. The antisymmetric representation presents qualitatively new features, leading to a paramagnetic and two distinct ferromagnetic phases that can coexist over a range of temperatures, two of them becoming metastable. Our results are relevant to magnetic systems of atoms with reduced symmetry in their interactions compared to the fundamental case.

hep-th↗

arXiv2024

Triple critical point and emerging temperature scales in $SU(N)$ ferromagnetism at large $N$

The non-Abelian ferromagnet recently introduced by the authors, consisting of atoms in the fundamental representation of $SU(N)$, is studied in the limit where $N$ becomes large and scales as the square root of the number of atoms $n$. This model exhibits additional phases, as well as two different temperature scales related by a factor $N\!/\!\ln N$. The paramagnetic phase splits into a "dense" and a "dilute" phase, separated by a third-order transition and leading to a triple critical point in the scale parameter $n/N^2$ and the temperature, while the ferromagnetic phase exhibits additional structure, and a new paramagnetic-ferromagnetic metastable phase appears at the larger temperature scale. These phases can coexist, becoming stable or metastable as temperature varies. A generalized model in which the number of $SU(N)$-equivalent states enters the partition function with a nontrivial weight, relevant, e.g., when there is gauge invariance in the system, is also studied and shown to manifest similar phases, with the dense-dilute phase transition becoming second-order in the fully gauge invariant case.

hep-th↗

arXiv2024

Phase transitions in the decomposition of $SU(N)$ representations

We study the multiplicity of irreducible representations in the decomposition of $n$ fundamentals of $SU(N)$ weighted by a power of their dimension in the large $n$ and large $N$ double scaling limit. A nontrivial scaling is obtained by keeping $n/N^2$ fixed, which plays the role of an order parameter. We find that the system generically undergoes a fourth order phase transition in this parameter, from a dense phase to a dilute phase. The transition is enhanced to third order for the unweighted multiplicity, and disappears altogether when weighting with the first power of the dimension. This corresponds to the infinite temperature partition function of non-Abelian ferromagnets, and the results should be relevant to the thermodynamic limit of such ferromagnets at high temperatures.

hep-th↗

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.

hep-th↗

arXiv2023

Ferromagnetic phase transitions in $SU(N)$

We study the thermodynamics of a non-abelian ferromagnet consisting of "atoms" each carrying a fundamental representation of $SU(N)$, coupled with long-range two-body quadratic interactions. We uncover a rich structure of phase transitions from non-magnetized, global $SU(N)$-invariant states to magnetized ones breaking global invariance to $SU(N-1) \times U(1)$. Phases can coexist, one being stable and the other metastable, and the transition between states involves latent heat exchange, unlike in usual $SU(2)$ ferromagnets. Coupling the system to an external non-abelian magnetic field further enriches the phase structure, leading to additional phases. The system manifests hysteresis phenomena both in the magnetic field, as in usual ferromagnets, and in the temperature, in analogy to supercooled water. Potential applications are in fundamental situations or as a phenomenological model.

hep-th↗

arXiv2023

Composing arbitrarily many $SU(N)$ fundamentals

We compute the multiplicity of the irreducible representations in the decomposition of the tensor product of an arbitrary number $n$ of fundamental representations of $SU(N)$, and we identify a duality in the representation content of this decomposition. Our method utilizes the mapping of the representations of $SU(N)$ to the states of free fermions on the circle, and can be viewed as a random walk on a multidimensional lattice. We also derive the large-$n$ limit and the response of the system to an external non-abelian magnetic field. These results can be used to study the phase properties of non-abelian ferromagnets and to take various scaling limits.

hep-th↗

arXiv2023

Spinning strings: $λ$-deformation and non-Abelian T-dual limit

The simplest example of the $λ$-deformation connects the SU(2) Wess-Zumino-Witten model with the non-Abelian T-dual (NATD) of the SU(2) principal chiral model. We analyze spinning strings with one spin propagating through the $λ$-deformation of the target space of the interpolation. We show that the situation apart from the NATD limit parallels the undeformed case. We demonstrate that regular spinning strings are either folded or circular, and that nearly degenerate spinning strings are either nearly point-like, fast, or slow. The effects of the $λ$-deformation are both the overall increment of the energy of spinning strings and the enlargement of the gap between the energies of folded and circular strings. In the NATD limit, we prove that circular strings disappear and that fast strings realize the dispersion relation of Gubser-Klebanov-Polyakov strings.

hep-th↗

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.

hep-th↗

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.

hep-th↗

arXiv2022

Scattering in integrable pp-wave backgrounds: S-matrix and absence of particle production

Particle production in integrable field theories may exist depending on the vacuum around which excitations are defined. To tackle this and analogous issues with conventional field theoretical tools, we consider the integrable $λ$-deformed model for $SU(2)$ together with a timelike coordinate. We construct the corresponding four-dimensional plane wave background keeping also post-plane wave corrections, as well as all the non-trivial $λ$-dependence. After imposing the light-cone gauge and the Virasoro constraints, we obtain an interacting field theory for the transverse physical modes which are massive. We explicitly demonstrate the absence of particle production to leading order in the large $k$-expansion. This is based crucially on the form of the interaction vertices and their dependence on the $λ$-deformation parameter. In addition, we compute the $S$-matrix for the two-particle elastic scattering exactly in $λ$ and to leading order in the large $k$-expansion. Our method can be applied to any integrable theory with at least one isometry.

hep-th↗

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.

hep-th↗

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.

hep-th↗

arXiv2021

On the stability of $AdS$ backgrounds with $λ$-deformed factors

We investigate the stability of the non-supersymmetric solutions of type-IIB supergravity having an unwarped $AdS$ factor and $λ$-deformed subspaces found in arXiv:1911.12371. Among the plethora of solutions we study the perturbative stability of backgrounds with an $AdS_n$, with $n = 3,4,6$, factor. Our analysis is performed from a lower dimensional effective theory which we construct. We uncover the regions and isolated points in the parameter space of potential perturbative stability.

hep-th↗

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.

hep-th↗

arXiv2021

AdS solutions and $λ$-deformations

We elevate $λ$-deformed $σ$-models into full type-II supergravity backgrounds. We construct several solutions which contain undeformed $AdS_n$ spaces, with $n=2,3,4$ and $6$, as an integrable part. In that respect, our examples are the first in the literature in this context and bring $λ$-deformations in contact with the AdS/CFT correspondence. The geometries are supported by appropriate dilaton and RR-fields. Most of the solutions admit non-Abelian T-dual limits.

hep-th↗

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.

hep-th↗