arXiv subjects

Simone Giombi

Publications and source records attributed to Simone Giombi.

At least 19 recordsLinked to original sources

arXiv2026

Impurities Near the Light Cone

The lightlike Wilson line cusp underlies the Sudakov double logarithm and is a central ingredient in gauge-theory factorization. We ask what replaces this behavior for general conformal line defects in Lorentzian signature. We argue that, when the defects admit local endpoint operators, the cusp anomalous dimension has a finite large-boost limit fixed by the scaling dimensions of the corresponding defect-creation operators. We further analyze the distinct analytic continuations of the cusp, elucidate their physical interpretations, and derive a positivity condition on the Lorentzian cusp anomalous dimension. We test these predictions in several perturbative examples, including pinning-field defects and spin impurities, and discuss their possible implications for gauge theories.

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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 $\epsilon$-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 $\epsilon$-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

Boundary criticality in the Gross-Neveu-Yukawa model at higher orders

We extend the study of boundary criticality in the Gross-Neveu-Yukawa universality class beyond leading order. Using the hyperbolic space formulation of boundary conformal field theories, we compute the first subleading corrections at large $N$ to the free energies of the ``normal", ``ordinary" and ``special" boundary universality classes. We also determine the order $1/N$ correction to the dimension of the boundary fermion at the normal fixed point. In the Gross-Neveu-Yukawa theory in $d=4-\epsilon$, we perform a higher-order analysis of the boundary free energy, and use it to extract estimates for the boundary central charge in $d=3$. The large $N$ and $\epsilon$-expansion results are shown to be precisely consistent in overlapping regimes, providing nontrivial consistency checks for the identification of the boundary universality classes. Our calculations rely on a combination of AdS harmonic analysis and boundary conformal field theory techniques.

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arXiv2026

Bouncing singularities and thermal correlators on line defects

Thermal correlators in holographic conformal field theories are known to exhibit singularities in complex time, sometimes referred to as ``bouncing singularities", which are believed to be related to bulk geodesics probing the black hole interior. These singularities correspond to exponentially suppressed contributions in the high-frequency limit of the thermal correlators. We revisit in detail the calculation of retarded two-point functions of local operators dual to bulk scalar fields in the planar AdS black hole background. We confirm that these correlators develop bouncing singularities, and highlight the agreement of two independent methods: a large frequency WKB analysis with infalling boundary conditions at the horizon; and an asymptotic OPE analysis that relies only on the near-boundary expansion, without any direct input from the black hole interior. We then extend these calculations to the case of the retarded two-point function of displacement operators on a Wilson line in the finite temperature gauge theory. This is computed holographically by solving the wave equation for the transverse fluctuations of the dual string worldsheet in the planar AdS black hole background. We find that these defect correlators also exhibit bouncing singularities, and again observe exact agreement between the WKB analysis sensitive to the black hole interior and the asymptotic OPE analysis. This agreement suggests that the bouncing singularities and the corresponding OPE data encode a universal high-frequency structure of the retarded correlators, and we propose a factorization formula that encodes the deviations from this universality.

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arXiv2026

The phase of de Sitter higher spin gravity

The one-loop Euclidean partition function on the sphere is known to exhibit a nontrivial phase for massless fields of spin greater than one. Such a phase appears to be in tension with a state counting interpretation of the partition function and its relation to the de Sitter entropy. It has been recently argued that the phase associated with the gravitational path integral can be cancelled by including the contribution of an observer. In this note, we compute the total phase of Vasiliev higher spin gravity on the sphere by summing over the contributions of all spins. We evaluate the resulting infinite sum using two different regularization schemes, obtaining consistent results. We find that for the non-minimal Vasiliev theory, which includes massless fields of all integer spins, the total phase vanishes in all dimensions. This result suggests that the sphere partition function of these theories may be consistent with a counting interpretation, without explicitly including an observer.

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arXiv2025

Line Defects with a Cusp in Fermionic CFTs

We study line defects with a cusp in fermionic CFTs arising as fixed points of scalar-fermion theories with Yukawa interactions. These include the Gross-Neveu-Yukawa model and some of its generalizations with additional scalar fields, which can be thought of as UV completions of fermionic theories with quartic interactions. We compute the cusp anomalous dimension in these models to one-loop order in the epsilon expansion near four dimensions, and also to leading order in the large $N$ expansion in $2<d<4$. We discuss several observables that can be extracted from the cusp anomalous dimension, such as the dimensions of the defect changing and defect creation operators, the Casimir energy appearing in the fusion of defects, and the normalization coefficients of the two-point functions of displacement and tilt operators. We provide some estimates of the values of these observables in $d=3$ using the one-loop epsilon expansion and Pad\'e approximants.

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arXiv2025

Higher loops in AdS: applications to boundary CFT

The Euclidean Anti-de Sitter (AdS) space provides a natural framework for studying boundary conformal field theory (BCFT). We analyze the conformal boundary conditions of the critical O$(N)$ model in $d=4-\epsilon$ dimensions using the $\epsilon$-expansion, and extract some BCFT observables through higher-loop calculations in AdS. Specifically, in the so-called "ordinary" universality class, we determine the free energy to four-loop order and the one-point function of the lightest O$(N)$ singlet operator to three-loop order. In the symmetry breaking "normal" universality class, we derive the two-loop free energy and compute the leading correction to the one-point function of the lightest O($N$) vector. We apply Pad\'e approximants to extract the corresponding conformal data in three dimensions. In particular, from a suitable dimensional continuation of the free energy in AdS, we obtain estimates for the boundary central charge of the BCFT in $d=3$.

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arXiv2024

Sphere free energy of scalar field theories with cubic interactions

The dimensional continuation approach to calculating the free energy of $d$-dimensional Euclidean CFT on the round sphere $S^d$ has been used to develop its $4-\epsilon$ expansion for a number of well-known non-supersymmetric theories, such as the $O(N)$ model. The resulting estimate of the sphere free energy $F$ in the 3D Ising model has turned out to be in good agreement with the numerical value obtained using the fuzzy sphere regularization. In this paper, we develop the $6-\epsilon$ expansions for CFTs on $S^d$ described by scalar field theory with cubic interactions and use their resummations to estimate the values of $F$. In particular, we study the theories with purely imaginary coupling constants, which describe non-unitary universality classes arising when certain conformal minimal models are continued above two dimensions. The Yang-Lee model $M(2,5)$ is described by a field theory with one scalar field, while the $D$-series $M(3,8)$ model is described by two scalar fields. We also study the $OSp(1|2)$ symmetric cubic theory of one commuting and two anti-commuting scalar fields, which appears to describe the critical behavior of random spanning forests. In the course of our work, we revisit the calculations of beta functions of marginal operators containing the curvature. We also use another method for approximating $F$, which relies on perturbation theory around the bilocal action near the long-range/short-range crossover. The numerical values it gives for $F$ tend to be in good agreement with other available methods.

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arXiv2024

Non-planar corrections in ABJM theory from quantum M2 branes

The quantization of semiclassical strings in AdS spacetimes yields predictions for the strong-coupling behaviour of the scaling dimensions of the corresponding operators in the planar limit of the dual gauge theory. Finding non-planar corrections requires computing string loops (corresponding to torus and higher genus surfaces), which is a challenging task. It turns out that in the case of the $U_k(N) \times U_{-k}(N)$ ABJM theory there is an alternative approach: one may semiclassically quantize M2 branes in AdS$_{4}\times S^7/\mathbb{Z}_{k}$ which are wrapped around the 11d circle of radius $1/k= \lambda/N$. Such M2 branes are the M-theory generalization of the strings in AdS$_4\times $CP$^3$. In this work, we show that by expanding in large M2 brane tension $ T_2 \sim \sqrt{kN} $ for fixed $k$, followed by an expansion in large $k$, we can predict the large $\lambda$ asymptotics of the non-planar corrections to the dimensions of the dual ABJM operators. As a specific example, we consider the M2 brane configuration that generalizes the long folded string with large spin in AdS$_4$, and compute the 1-loop correction to its energy. This calculation allows us to determine non-planar corrections to the universal scaling function or cusp anomalous dimension. We extend our analysis to the semiclassical M2 branes that generalize the "short" and "long" circular strings with two equal angular momenta in CP$^3$. The "short" M2 brane corresponds to a dual operator whose dimension at strong coupling scales as $\Delta \sim \lambda^{1/4} + \dots$, and we derive the leading non-planar correction to it.

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arXiv2024

RG Interfaces from Double-Trace Deformations

We study a class of interface conformal field theories obtained by taking a large $N$ CFT and turning on a relevant double-trace deformation over half space. At low energies, this leads to a conformal interface separating two CFTs which are related by RG flow. We set up the large $N$ expansion of these models by employing a Hubbard-Stratonovich transformation over half space, and use this approach to compute some of the defect CFT data. We also calculate the free energy of the theory in the case of spherical interface, which encodes a conformal anomaly coefficient for even dimensional interface, and the analog of the $g$-function for odd-dimensional interface. These models have a dual description in terms of a gravitational theory in AdS where a bulk scalar field satisfies different boundary conditions on each half of the AdS boundary. We review this construction and show that the results of the large $N$ expansion on the CFT side are in precise agreement with the holographic predictions.

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arXiv2023

(2,0) theory on $S^5 \times S^1$ and quantum M2 branes

The superconformal index $Z$ of the 6d (2,0) theory on $S^5 \times S^1$ (which is related to the localization partition function of 5d SYM on $S^5$) should be captured at large $N$ by the quantum M2 brane theory in the dual M-theory background. Generalizing the type IIA string theory limit of this relation discussed in arXiv:2111.15493 and arXiv:2304.12340, we consider semiclassically quantized M2 branes in a half-supersymmetric 11d background which is a twisted product of thermal AdS$_7$ and $S^4$. We show that the leading non-perturbative term at large $N$ is reproduced precisely by the 1-loop partition function of an "instanton" M2 brane wrapped on $S^1\times S^2$ with $S^2\subset S^4$. Similarly, the (2,0) theory analog of the BPS Wilson loop expectation value is reproduced by the partition function of a "defect" M2 brane wrapped on thermal AdS$_3\subset$ AdS$_7$. We comment on a curious analogy of these results with similar computations in arXiv:2303.15207 and arXiv:2307.14112 of the partition function of quantum M2 branes in AdS$_4 \times S^7/\mathbb Z_k$ which reproduced the corresponding localization expressions in the ABJM 3d gauge theory.

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arXiv2023

Boundary reparametrizations and six-point functions on the AdS$_2$ string

We compute the tree-level connected six-point function of identical scalar fluctuations of the AdS$_2$ string worldsheet dual to the half-BPS Wilson line in planar ${\cal N}=4$ Super Yang-Mills. The calculation can be carried out analytically in the conformal gauge approach, where the boundary reparametrization mode of the string plays a crucial role. We also study the analytic continuation of the six-point function to an out-of-time-order configuration, which is related to a 3-to-3 scattering amplitude in flat space. As a check of our results, we also numerically compute the six-point function using the Nambu-Goto action in static gauge, finding agreement with the conformal gauge answer.

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arXiv2023

Instanton contributions to the ABJM free energy from quantum M2 branes

We present a quantum M2 brane computation of the instanton prefactor in the leading non-perturbative contribution to the ABJM 3-sphere free energy at large $N$ and fixed level $k$. Using supersymmetric localization, such instanton contribution was found earlier to take the form $F^{\rm inst}(N,k) = - ({\sin^{2} \frac{2\pi}{k}} )^{-1} \, \exp (-2\pi \sqrt\frac{2N}{k}) + \cdots$ . The exponent comes from the action of an M2 brane instanton wrapped on $S^3/{\mathbb Z}_k$, which represents the M-theory uplift of the $\mathbb{C}P^1$ instanton in type IIA string theory on AdS$_4 \times \mathbb{C}P^3$. The IIA string computation of the leading large $k$ term in the instanton prefactor was recently performed in arXiv:2304.12340. Here we find that the exact value of the prefactor $({\sin^{2} \frac{2\pi}{k}})^{-1} $ is reproduced by the 1-loop term in the M2 brane partition function expanded near the $S^3/\mathbb{Z}_k$ instanton configuration. As in the Wilson loop example in arXiv:2303.15207, the quantum M2 brane computation is well defined and produces a finite result in exact agreement with localization.

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arXiv2023

Notes on a Surface Defect in the $O(N)$ Model

We study a surface defect in the free and critical $O(N)$ vector models, defined by adding a quadratic perturbation localized on a two-dimensional subspace of the $d$-dimensional CFT. We compute the beta function for the corresponding defect renormalization group (RG) flow, and provide evidence that at long distances the system flows to a nontrivial defect conformal field theory (DCFT). We use epsilon and large $N$ expansions to compute several physical quantities in the DCFT, finding agreement across different expansion methods. We also compute the defect free energy, and check consistency with the so-called $b$-theorem for RG flows on surface defects.

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arXiv2023

Wilson loops at large $N$ and the quantum M2 brane

The Wilson loop operator in the $U(N)_k \times U(N)_{-k}$ ABJM theory at large $N$ and fixed level $k$ has a dual description in terms of a wrapped M2 brane in the M-theory background AdS$_4 \times S^7/\mathbb Z_k$. We consider the localization result for the $1\over 2$-BPS circular Wilson loop expectation value $W$ in this regime, and compare it to the prediction of the M2 brane theory. The leading large $N$ exponential factor is matched as expected by the classical action of the M2 brane solution with AdS$_2\times S^1$ geometry. We show that the subleading $k$-dependent prefactor in $W$ is also exactly reproduced by the one-loop term in the partition function of the wrapped M2 brane (with all Kaluza-Klein modes included). This appears to be the first case of an exact matching of the overall numerical prefactor in the Wilson loop expectation value against the dual holographic result. It provides an example of a consistent quantum M2 brane computation, suggesting various generalizations.

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arXiv2022

Chaos and the reparametrization mode on the AdS$_2$ string

We study the holographic correlators corresponding to scattering of fluctuations of an open string worldsheet with AdS$_2$ geometry. In the out-of-time-order configuration, the correlators display a Lyapunov growth that saturates the chaos bound. We show that in a double-scaling limit interpolating between the Lyapunov regime and the late time exponential decay, the out-of-time-order correlator (OTOC) can be obtained exactly, and it has the same functional form found in the analogous calculation in JT gravity. The result can be understood as coming from high energy scattering near the horizon of a AdS$_2$ black hole, and is essentially controlled by the flat space worldsheet S-matrix. While previous works on the AdS$_2$ string employed mainly a static gauge approach, here we focus on conformal gauge and clarify the role of boundary reparametrizations in the calculation of the correlators. We find that the reparametrization mode is governed by a non-local action which is distinct from the Schwarzian action arising in JT gravity, and in particular leads to $SL(2,\mathbb{R})$ invariant boundary correlators. The OTOC in the double-scaling limit, however, has the same functional form as that obtained from the Schwarzian, and it can be computed using the reparametrization action and resumming a subset of diagrams that are expected to dominate in the limit. One application of our results is to the defect CFT defined by the half-BPS Wilson loop in ${\cal N}=4$ SYM. In this context, we show that the exact result for the OTOC in the double-scaling limit is in precise agreement with a recent analytic bootstrap prediction to three-loop order at strong coupling.

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arXiv2022

Line Defects in Fermionic CFTs

We study line defects in the fermionic CFTs in the Gross-Neveu-Yukawa universality class in dimensions $2<d<4$. These CFTs may be described as the IR fixed points of the Gross-Neveu-Yukawa (GNY) model in $d=4-\epsilon$, or as the UV fixed points of the Gross-Neveu (GN) model, which can be studied using the large $N$ expansion in $2<d<4$. These models admit natural line defects obtained by integrating over a line either the scalar field in the GNY description, or the fermion bilinear operator in the GN description. We compute the beta function for the defect RG flow using both the epsilon expansion and the large $N$ approach, and find IR stable fixed points for the defect coupling, thus providing evidence for a non-trivial IR DCFT. We also compute some of the DCFT observables at the fixed point, and check that the $g$-function associated with the circular defect is consistent with the $g$-theorem for the defect RG flow.

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arXiv2022

Long Range, Large Charge, Large $N$

We study operators with large charge $j$ in the $d$-dimensional $O(N)$ model with long range interactions that decrease with the distance as $1/r^{d+s}$, where $s$ is a continuous parameter. We consider the double scaling limit of large $N$, large $j$ with $j/N=\hat{j}$ fixed, and identify the semiclassical saddle point that captures the two-point function of the large charge operators in this limit. The solution is given in terms of certain ladder conformal integrals that have recently appeared in the literature on fishnet models. We find that the scaling dimensions for general $s$ interpolate between $\Delta_j \sim \frac{(d-s)}{2}j$ at small $\hat{j}$ and $\Delta_j \sim \frac{(d+s)}{2}j$ at large $\hat{j}$, which is a qualitatively different behavior from the one found in the short range version of the $O(N)$ model. We also derive results for the structure constants and 4-point functions with two large charge and one or two finite charge operators. Using a description of the long range models as defects in a higher dimensional local free field theory, we also obtain the scaling dimensions in a complementary way, by mapping the problem to a cylinder in the presence of a chemical potential for the conserved charge.

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