arXiv subjects

Fabiana De Cesare

Publications and source records attributed to Fabiana De Cesare.

8 recordsLinked to original sources

arXiv2026

QFT as a set of ODEs: higher dimensions

Correlation functions of local operators in Quantum Field Theory (QFT) in Anti-de Sitter space (AdS) are completely fixed by the QFT data: the set of scaling dimensions $Δ_i$ and OPE coefficients $C_{ijk}$ of the boundary operators, and the bulk-boundary (BOE) coefficients $b^{\hatΦ}_i$ encoding how bulk fields decompose into boundary operators. In this work, we generalize the ordinary differential equations (ODEs) that govern the variation of the QFT data under a bulk relevant deformation, originally derived for AdS$_2$ \cite{Loparco:2026fki}, to the cases of AdS$_3$ and AdS$_4$. We demonstrate that these flow equations natively capture the mechanism of merger-annihilation when a boundary operator hits marginality, as well as level repulsion when different $Δ_i$'s approach each other. Furthermore, we address the practical implementation of the framework: we propose substituting the ODE for the OPE coefficients with the crossing equation for greater efficiency, and we observe that Padé approximants dramatically improve the convergence of the sums over boundary operators, at least in free theories. Altogether, these advances lay the groundwork for the future application of the flow equations to the study of strongly coupled QFTs in AdS and their flat space limits.

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arXiv2026

Conformal QED in AdS as a BCFT

We study conformal Quantum Electrodynamics (QED) coupled to either $N_f$ massless fermions or $N_s$ conformally coupled scalars in Euclidean Anti-de Sitter (AdS$_d$) space for $d < 4$. Using the $ε$-expansion around $d=4$, we investigate the associated Boundary Conformal Field Theories (BCFTs) defined by imposing either Dirichlet or Neumann boundary conditions on the gauge field. We compute the regularized AdS free energy at the interacting fixed point up to next-to-leading order and extract some of the boundary conformal data at one loop, including the anomalous dimensions of the lightest singlet scalar operators. For Dirichlet boundary conditions, extrapolation of our $ε$-expansion results indicate that one of these scalar operators, which is irrelevant near $d=4$, reaches marginality within the range $3 < d < 4$. This suggests that the Dirichlet boundary condition may not define a stable BCFT in $d=3$.

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arXiv2026

Disturbing news about the $d=2+ε$ expansion II. Assessing the recombination scenario

In [De Cesare, Rychkov (2025)], we revisited the $d=2+ε$ expansion in the $O(N)$ Non-Linear Sigma Model (NLSM), emphasizing the existence of a protected operator which is a closed form with $N-1$ indices. The scaling dimension of this operator stays exactly equal to $N-1$, independently of $ε$. Its existence is problematic for the identification of the NLSM fixed point in $d=2+ε$ with the Wilson-Fisher fixed point family obtained by analytically continuing from near $d=4$, which does not possess such a protected operator. Multiplet recombination is one scenario discussed in [De Cesare, Rychkov (2025)], which could allow to connect the two families continuously (although not analytically). In this scenario, the protected dimension is lifted at some critical value of $ε$, thanks to the short conformal multiplet of scaling dimension $N-1$ eating a long conformal multiplet of higher scaling dimension. In this followup work, we assess this scenario for the cases $N=3$ and $N=4$. We identify the lowest candidates for the long multiplet which could be eaten, and compute their one-loop anomalous dimensions. We find that at one loop, scaling dimensions of these candidates grow with $ε$, while it should decrease down to $N$ for the recombination to occur. We conclude that multiplet recombination is unlikely.

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arXiv2025

QCD in AdS

We study QCD on AdS space with scalars or fermions in the fundamental representation, extending earlier results on pure Yang-Mills theory. In the latter, the Dirichlet boundary condition is conjectured to disappear via merger and annihilation, as signaled by the lightest scalar singlet operator approaching marginality as the coupling increases. With matter, there are two candidate operators for this mechanism. We compute their one-loop anomalous dimensions via broken conformal Ward identities and Witten diagrams. In the confining phase, with Dirichlet (Neumann) boundary condition, their anomalous dimensions are negative (positive), consistent with the disappearance (persistence) of the associated boundary CFT in the flat-space limit. In the conformal window, one of these operators becomes the displacement operator of the IR CFT, as signaled by the vanishing of its one-loop anomalous dimension in the perturbative Banks-Zaks regime. Possible scenarios for the lower edge of the conformal window are discussed. Finally, we consider general boundary conditions on fermions and discuss their relation to chiral symmetry breaking in flat space.

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arXiv2025

Disturbing news about the $d=2+ε$ expansion

The $O(N)$ Non-Linear Sigma Model (NLSM) in $d=2+ε$ has long been conjectured to describe the same conformal field theory (CFT) as the Wilson-Fisher (WF) $O(N)$ fixed point obtained from the $λ(ϕ^2)^2$ model in $d=4-ε$. In this work, we put this conjecture into question, building on the recent observation [Jones (2024)] that the NLSM CFT possesses a protected operator with dimension $N-1$, which is instead absent in the WF $O(N)$ CFT. We investigate the possibility of lifting this operator via multiplet recombination - the only known mechanism that could resolve this mismatch while preserving a connection between the two theories. We also explore an alternative scenario in which the NLSM $O(N)$ fixed point in $d=2+ε$ is not continuously connected to the WF $O(N)$ CFT, and instead corresponds to a different universality class. For $N=3$, this could be related to the hedgehog-suppressed critical point, which describes the Néel-VBS phase transition in 3D.

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arXiv2025

Exploring Confinement in Anti-de Sitter Space

We study Yang-Mills theory on four dimensional Anti-de Sitter space. The Dirichlet boundary condition cannot exist at arbitrarily large radius because it would give rise to colored asymptotic states in flat space. As observed in [1] this implies a deconfinement-confinement transition as the radius is increased. We gather hints on the nature of this transition using perturbation theory. We compute the anomalous dimensions of the lightest scalar operators in the boundary theory, finding that the singlet gets a larger negative anomalous dimension compared to the adjoint. We also compute the correction to the coefficient $C_J$ and we estimate that the singlet operator reaches marginality before the value of the coupling at which $C_J=0$. These results favor the scenario of merger and annihilation as the most promising candidate for the transition. For the Neumann boundary condition, the lightest scalar operator is found to have a positive anomalous dimension, in agreement with the idea that this boundary condition extrapolates smoothly to flat space. The perturbative calculations are made possible by a drastic simplification of the gauge field propagator in Fried-Yennie gauge. We also derive a general result for the leading-order anomalous dimension of the displacement operator for a generic perturbation in Anti-de Sitter, showing that it is related to the beta function of bulk couplings.

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arXiv2024

Five-dimensional CFTs from the $ε$-expansion

We look for UV fixed points of non-abelian $SU(n_c)$ gauge theories in $4+2ε$ dimensions with $n_f$ Dirac fermions in the fundamental representation, using the available five-loop $\overline{\rm MS}$ $β$-function and employing Padé-Borel resummation techniques and Padé approximants to the series expansion in $ε$. We find evidence for a $5d$ UV-fixed point for $SU(2)$ theories with $n_f\leq 4$. We also compute the anomalous dimensions $γ$ and $γ_g$ of respectively the fermion mass bilinear and the gauge kinetic term operator at the UV fixed point.

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arXiv2022

Free Energy on the Sphere for Non-Abelian Gauge Theories

We compute the $S^d$ partition function of the fixed point of non-abelian gauge theories in continuous $d$, using the $ε$-expansion around $d=4$. We illustrate in detail the technical aspects of the calculation, including all the factors arising from the gauge-fixing procedure, and the method to deal with the zero-modes of the ghosts. We obtain the result up to NLO, i.e. including two-loop vacuum diagrams. Depending on the sign of the one-loop beta function, there is a fixed point with real gauge coupling in $d>4$ or $d<4$. In the first case we extrapolate to $d=5$ to test a recently proposed construction of the UV fixed point of $5d$ $SU(2)$ Yang-Mills via a susy-breaking deformation of the $E_1$ SCFT. We find that the $F$ theorem allows the proposed RG flow. In the second case we extrapolate to $d=3$ to test whether QCD$_3$ with gauge group $SU(n_c)$ and $n_f$ fundamental matter fields flows to a CFT or to a symmetry-breaking phase. We find that within the regime with a real gauge coupling near $d=4$ the CFT phase is always favored. For lower values of $n_f$ we compare the average of $F$ between the two complex fixed points with its value at the symmetry-breaking phase to give an upper bound of the critical value $n_f^*$ below which the symmetry-breaking phase takes over.

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