arXiv subjects

Fanny Eustachon

Publications and source records attributed to Fanny Eustachon.

4 recordsLinked to original sources

arXiv2026

The Lee-Yang model and its generalizations through the lens of long-range deformations

In two dimensions, the non-unitary class of conformal minimal models, $\mathcal{M}(2,2m+1)$, has been recently conjectured to arise as renormalization-group fixed points of scalar field theories with complex $i\varphi^{2m-1}$ interaction, $m\in \mathbb{N}$, $m\ge2$. We test a variation of this conjecture through the perturbative study of two separate long-range constructions based on respectively the minimal model and its potential Landau-Ginzburg formalism. For $m>2$, inconsistencies are found when subsequently relating both constructions. In contrast, the long-range Lee-Yang model, the $m=2$ case, is shown to be analogue to the long-range Ising model.

hep-th↗

arXiv2026

Critical and multicritical Lee-Yang fixed points in the local potential approximation

The multicritical generalizations of the Lee-Yang universality class arise as renormalization-group fixed points of scalar field theories with complex $i\varphi^{2n+1}$ interaction, $n\in\mathbb{N}$, just below their upper critical dimension. It has been recently conjectured that their continuation to two dimensions corresponds to the non-unitary conformal minimal models $\mathcal{M}(2,2n+3)$. Motivated by that, we revisit the functional renormalization group approach to complex $\mathcal{P}\mathcal{T}$-symmetric scalar field theories in the Local Potential Approximation, without or with wavefunction renormalization (LPA and LPA' respectively), aiming to explore the fate of the $i\varphi^{2n+1}$ theories from their upper critical dimension to two dimensions. The $i\varphi^{2n+1}$ fixed points are identified using a perturbative expansion of the functional fixed-point equation near their upper critical dimensions, and they are followed to lower dimensions by numerical integration of the full equation. A peculiar feature of the complex $\mathcal{P}\mathcal{T}$-symmetric potentials is that the fixed points are characterized by real but negative anomalous dimensions $\eta$, and in low dimension $d$, this can lead to a change of sign of the scaling dimensions $\Delta=(d-2+\eta)/2$, thus requiring a novel analysis of the analytical properties of the functional fixed-point equations. We are able to follow the Lee-Yang universality class ($n=1$) down to two dimensions, and numerically determine the scaling dimension of the fundamental field as a function of $d$. On the other hand, within the LPA', multicritical Lee-Yang fixed points with $n>1$ cannot be continued to $d=2$ due to the existence of unexpected non-perturbative fixed points that annihilate with the $i\varphi^{2n+1}$ fixed points.

hep-th↗

arXiv2025

Long-range minimal models

We study a class of nonlocal conformal field theories in two dimensions which are obtained as deformations of the Virasoro minimal models. The construction proceeds by coupling a relevant primary operator $\phi_{r,s}$ of the $m$-th minimal model to a generalized free field, in such a way that the interaction term has scaling dimension $2-\delta$. Flowing to the infrared, we reach a new class of CFTs that we call long-range minimal models. In the case $r=s=2$, the resulting line of fixed points, parametrized by $\delta$, can be studied using two perturbative expansions with different regimes of validity, one near the mean-field theory end, and one close to the long-range to short-range crossover. This is due to a straightforward generalization of an infrared duality which was proposed for the long-range Ising model ($m = 3$) in 2017. We find that the large-$m$ limit is problematic in both perturbative regimes, hence nonperturbative methods will be required in the intermediate range for all values of $m$. For the models based on $\phi_{1,2}$, the situation is rather different. In this case, only one perturbative expansion is known but it is well behaved at large $m$. We confirm this with a computation of infinitely many anomalous dimensions at two loops. Their large-$m$ limits are obtained from both numerical extrapolations and a method we develop which carries out conformal perturbation theory using Mellin amplitudes. For minimal models, these can be accessed from the Coulomb gas representations of the correlators. This method reveals analytic expressions for some integrals in conformal perturbation theory which were previously only known numerically.

hep-th↗

arXiv2024

Quantum vorticity: a not so effective field theory

We provide a comprehensive picture for the formulation of the perfect fluid in the modern effective field theory formalism at both the classical and quantum level. Due to the necessity of decomposing the hydrodynamical variables $(\rho, p, u^\mu)$ into other internal degrees of freedom, the procedure is inherently not unique. We discuss and compare the different inequivalent formulations. These theories possess a peculiarity: the presence of an infinite dimensional symmetry implying a vanishing dispersion relation $\omega = 0$ for the transverse modes. This sets the stage for UV-IR mixing in the quantum theory, which we study in the different formulations focussing on the incompressible limit. We observe that the dispersion relation gets modified by quantum effects to become $\omega \propto \mathbf{k}^2$, where the fundamental excitations can be viewed as vortex-anti-vortex pairs. The spectrum exhibits infinitely many types of degenerate quanta. The unusual sensitivity to UV quantum fluctuations renders the implementation of the defining infinite symmetry somewhat subtle. However we present a lattice regularization that preserves a deformed version of such symmetry.

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