arXiv subjects

Lorenzo Di Pietro

Publications and source records attributed to Lorenzo Di Pietro.

At least 19 recordsLinked to original sources

arXiv2026

Bremsstrahlung function from Goldstone bosons in AdS$_2$

We study quantum field theory on the AdS$_2$ worldsheet of the fundamental string dual to the half-BPS Wilson line of $\mathcal{N}=4$ super Yang-Mills. We consider a recently proposed gauge-fixed string fluctuation Lagrangian around the AdS$_2$ minimal surface, and focus on the nonlinearly realized $SO(6)/SO(5)$ symmetry. The boundary two-point function of the associated tilt operators, whose normalization coefficient is proportional the Bremsstrahlung function, can be related to the bulk two-point function of the broken-symmetry Noether current through the boundary operator expansion. We evaluate the one-loop diagrams contributing to the current correlator, discussing the role of dimensional regularization and recovering the known strong-coupling correction to the Bremsstrahlung function directly from AdS$_2$ worldsheet quantum field theory.

hep-th↗

arXiv2026

Symmetry extension by condensation defects II: general dimensions and higher-groups

We discuss a class of symmetry structures in general spacetime dimension that arise when gauging symmetries in theories with a cubic 't Hooft anomaly. The anomaly mixes two Abelian discrete symmetries $A$ and $B$ with a characteristic class for an additional symmetry $C$, and we gauge $A\times B$. The novelty of this construction is that the resulting symmetry structure involves certain condensation defects of the dual symmetry $\widehat{A}\times\widehat{B}$. Specifically, these defects generate an invertible symmetry that extends $C$, either as an ordinary group extension or as a higher-group, depending on the characteristic class. We describe the corresponding charged operators and states, and illustrate the mechanism in several examples.

hep-th↗

arXiv2026

Symmetry extension by condensation defects in five-dimensional gauge theories

We investigate the symmetry structure of five-dimensional Yang-Mills theories with $\mathfrak{su}(N)$ gauge algebra. These theories feature intertwined 0-, 1-, and 2-form symmetries, depending on the global variant one is considering. In the $SU(N)$ theory, there is a mixed 't Hooft anomaly between the instantonic 0-form symmetry and the electric 1-form symmetry. We show that in the $PSU(N)$ theory this translates into a $\mathbb{Z}_N$ extension of the instantonic symmetry, generated by an invertible condensation defect of the magnetic 2-form symmetry. We identify the charged configurations as linked 't Hooft surfaces, while pointlike instanton operators remain insensitive to the extension. We generalize our analysis to the $SU(N)/\mathbb{Z}_k$ global form and show that similar results hold, embedded now in a 3-group structure for generic $k$. We then apply our findings to $SO(3)$ supersymmetric Yang-Mills theory. We determine the global form of the enhanced instantonic symmetry of its superconformal UV completion, showing that it arises through a similar symmetry extension mechanism from the parent $E_1$ theory, which is the UV completion of $SU(2)$ supersymmetric Yang-Mills theory. Finally, we recast our results in the language of the symmetry topological field theory. As a warm-up, we also analyze Maxwell theory, highlighting analogous features involving continuous symmetries and composite currents.

hep-th↗

arXiv2026

Dressing and Screening in Anti-de Sitter

Motivated by a question of defining gauge-invariant observables in cosmology and by the close connection between perturbation theory in de Sitter (dS) and Anti-de Sitter (AdS), we study scalar electrodynamics in AdS in setups that are largely unexplored but relevant for dS physics. For photons with standard (Dirichlet) boundary conditions, we analyze charged scalars whose boundary conditions break the $U(1)$ symmetry. This leads to a nonstandard Higgs mechanism in which the gauge field acquires a one-loop mass without a classical vacuum expectation value. Using recent advances in perturbation theory in AdS, we compute this mass explicitly and evaluate charged-scalar four-point functions. We also provide an alternative derivation based on boundary Ward identities. For photons with alternate (Neumann) boundary conditions, where local charged operators are not gauge invariant, we construct physical observables by dressing charged fields with geodesic Wilson lines. These dressed operators have well-behaved conformal properties and unphysical photon modes decouple from their correlation functions. Explicit one-loop computations further reveal the decoupling of boundary field strengths, for which we provide a nonperturbative argument based on higher-form symmetry. Along the way, we explain the physical consequences of spontaneous breaking of higher-form symmetry in AdS, including the role of the tilt operator, the relation between one-form symmetry and endpoints of Wilson lines at the boundary, and a generalized-symmetry interpretation of conserved currents dual to bulk gauge fields.

hep-th↗

arXiv2026

Analyticity and Unitarity for Cosmological Correlators

We study the fundamentals of quantum field theory on a rigid de Sitter space. We show that the perturbative expansion of late-time correlation functions to all orders can be equivalently generated by a non-unitary Lagrangian on a Euclidean AdS geometry. This finding simplifies dramatically perturbative computations, as well as allows us to establish basic properties of these correlators, which comprise a Euclidean CFT. We use this to infer the analytic structure of the spectral density that captures the conformal partial wave expansion of a late-time four-point function, to derive an OPE expansion, and to constrain the operator spectrum. Generically, dimensions and OPE coefficients do not obey the usual CFT notion of unitarity. Instead, unitarity of the de Sitter theory manifests itself as the positivity of the spectral density. This statement does not rely on the use of Euclidean AdS Lagrangians and holds non-perturbatively. We illustrate and check these properties by explicit calculations in a scalar theory by computing first tree-level, and then full one-loop-resummed exchange diagrams. An exchanged particle appears as a resonant feature in the spectral density which can be potentially useful in experimental searches.

hep-th↗

arXiv2025

F-theorem for Quantum Field Theories in Anti-de Sitter Space

We introduce a regularized free energy $\mathcal{F}_{\text{AdS}}$ for massive quantum field theories (QFTs) on Anti-de Sitter space (AdS). We conjecture this quantity to be monotonic under the renormalization group (RG) flow induced by boundary perturbations, generalizing the known boundary $F$-theorem to non-conformal setups. We test this conjecture in several examples and provide a proof in two dimensions. We also discuss applications to long-range critical points, obtaining bounds on the sphere free energy of long- and short-range Ising models in three dimensions.

hep-th↗

arXiv2025

A Bootstrap Study of Confinement in AdS

Yang-Mills theory in AdS$_{4}$ with Dirichlet boundary conditions is expected to undergo a transition as the AdS radius varies, since the boundary data is incompatible with confinement in flat space. Various mechanisms have been proposed for the disappearance of the Dirichlet boundary condition. From the boundary viewpoint, the associated $3d$ CFT is a deformation of a generalised free theory of non-Abelian conserved currents, with the deformation governed by the bulk gauge coupling. We test these scenarios by deriving non-perturbative constraints from the numerical conformal bootstrap of the four-point function of non-Abelian conserved currents. We rule out the scenario in which the boundary current decouples. Bounds on the lightest scalar operators disfavour a bulk Higgs mechanism and instead point to a transition driven by a scalar singlet becoming marginal. We also obtain bounds on other scalar operators and on the current central charge, and we refine character-based techniques incorporating parity and charge-conjugation symmetry to determine the operator spectrum of the $3d$ Generalised Free Vector theory. These results may be of independent interest beyond Yang-Mills theory in AdS.

hep-th↗

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.

hep-th↗

arXiv2025

BCFT One-point Functions of Coulomb Branch Operators

We show that supersymmetry can be used to compute the BCFT one-point function coefficients for chiral primary operators, in 4d $\mathcal{N}=2$ SCFTs with $\frac{1}{2}$-BPS boundary conditions. The main ingredient is the hemisphere partition function, with the boundary condition on the equatorial $S^3$. A supersymmetric Ward identity relates derivatives with respect to the chiral coupling constants to the insertion of the primaries at the pole of the hemisphere. Exact results for the one-point functions can be then obtained in terms of the localization matrix model. We discuss in detail the example of the super Maxwell theory in the bulk, interacting with 3d $\mathcal{N}=2$ SCFTs on the boundary. In particular we derive the action of the SL(2,$\mathbb{Z}$) duality on the one-point functions.

hep-th↗

arXiv2025

$\mathcal{N}=2$ Super Yang-Mills in AdS$_4$ and $F_{\text{AdS}}$-maximization

We investigate the dynamics of four-dimensional $\mathcal{N}=2$ $SU(2)$ super Yang--Mills theory on an AdS background. We propose that the boundary conditions that preserve the AdS super-isometries are determined by maximizing the real part of the AdS partition function $F_{\text{AdS}}=-\log Z_{\text{AdS}}$. At weak coupling $ΛL \ll 1$ the maximization singles out the Dirichlet boundary condition with an $SU(2)$ boundary global symmetry, corresponding to the classical vacuum at the origin of the Coulomb branch with fully un-higgsed gauge group. We find that for $ΛL \sim \mathcal{O}(1)$ new boundary conditions are favored, with gauge-group higgsed down to $U(1)$, matching the expectation from the flat space limit. We use supersymmetric localization to compute $Z_{\text{AdS}}$ nonperturbatively. We further provide evidence for a relation between $F_{\text{AdS}}$ and the $\mathcal{N}=2$ prepotential in AdS background.

hep-th↗

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.

hep-th↗

arXiv2025

Cosmological Correlators at Finite Coupling

We study finite-coupling effects of QFT on a rigid de Sitter (dS) background taking the $O(N)$ vector model at large $N$ as a solvable example. Extending standard large $N$ techniques to the dS background, we analyze the phase structure and late-time four-point functions. Explicit computations reveal that the spontaneous breaking of continuous symmetries is prohibited due to strong IR effects, akin to flat two-dimensional space. Resumming loop diagrams, we compute the late-time four-point functions of vector fields at large $N$, demonstrating that their spectral density is meromorphic in the spectral plane and positive along the principal series. These results offer highly nontrivial checks of unitarity and analyticity for cosmological correlators.

hep-th↗

arXiv2024

Looking through the QCD Conformal Window with Perturbation Theory

We study the conformal window of QCD using perturbation theory, starting from the perturbative upper edge and going down as much as we can towards the strongly coupled regime. We do so by exploiting the available five-loop computation of the $\overline{\rm MS}$ $β$-function and employing Borel resummation techniques both for the ordinary perturbative series and for the Banks-Zaks conformal expansion. Large-$n_f$ results are also used. We argue that the perturbative series for the $\overline{\rm MS}$ $β$-function is most likely asymptotic and non-Borel resummable, yet Borel resummation techniques allow to improve on ordinary perturbation theory. We find substantial evidence that QCD with $n_f=12$ flavours flows in the IR to a conformal field theory. Though the evidence is weaker, we find indications that also $n_f=11$ might sit within the conformal window. We also compute the value of the mass anomalous dimension $γ$ at the fixed point and compare it with the available lattice results. The conformal window might extend for lower values of $n_f$, but our methods break down for $n_f<11$, where we expect that non-perturbative effects become important. A similar analysis is performed in the Veneziano limit.

hep-th↗

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.

hep-th↗

arXiv2024

Taming Mass Gap with Anti-de-Sitter Space

Anti-de-Sitter space acts as an infra-red cut off for asymptotically free theories, allowing interpolation between a weakly-coupled small-sized regime and a strongly-coupled flat-space regime. We scrutinize the interpolation for theories in two dimensions from the perspective of boundary conformal theories. We show that the appearance of a singlet marginal operator destabilizes a gapless phase existing at a small size, triggering a boundary renormalization group flow to a gapped phase that smoothly connects to flat space. We conjecture a similar mechanism for confinement in gauge theories.

hep-th↗

arXiv2024

Conformal boundary conditions for a 4d scalar field

We construct unitary, stable, and interacting conformal boundary conditions for a free massless scalar in four dimensions by coupling it to edge modes living on a boundary. The boundary theories we consider are bosonic and fermionic QED$_3$ with $N_f$ flavors and a Chern-Simons term at level $k$, in the large-$N_f$ limit with fixed $k/N_f$. We find that interacting boundary conditions only exist when $k\neq 0$. To obtain this result we compute the $β$ functions of the classically marginal couplings at the first non-vanishing order in the large-$N_f$ expansion, and to all orders in $k/N_f$ and in the couplings. To check vacuum stability we also compute the large-$N_f$ effective potential. We compare our results with the the known conformal bootstrap bounds.

hep-th↗

arXiv2024

Anomalies and Persistent Order in the Chiral Gross-Neveu model

We study the $2d$ chiral Gross-Neveu model at finite temperature $T$ and chemical potential $μ$. The analysis is performed by relating the theory to a $SU(N)\times U(1)$ Wess-Zumino-Witten model with appropriate levels and global identifications necessary to keep track of the fermion spin structures. At $μ=0$ we show that a certain $\mathbb{Z}_2$-valued 't Hooft anomaly forbids the system to be trivially gapped when fermions are periodic along the thermal circle for any $N$ and any $T>0$. We also study the two-point function of a certain composite fermion operator which allows us to determine the remnants for $T>0$ of the inhomogeneous chiral phase configuration found at $T=0$ for any $N$ and any $μ$. The inhomogeneous configuration decays exponentially at large distances for anti-periodic fermions while it persists for $T>0$ and any $μ$ for periodic fermions, as expected from anomaly considerations. A large $N$ analysis confirms the above findings.

hep-th↗

arXiv2023

Vacuum stability, fixed points, and phases of QED$_3$ at large $N_f$

We consider three-dimensional Quantum Electrodynamics in the presence of a Chern-Simons term at level $k$ and $N_f$ flavors, in the limit of large $N_f$ and $k$ with $k/N_f$ fixed. We consider either bosonic or fermionic matter fields, with and without quartic terms at criticality: the resulting theories are critical and tricritical bosonic QED$_3$, Gross-Neveu and fermionic QED$_3$. For all such theories we compute the effective potentials and the $β$ functions of classically marginal couplings, at the leading order in the large $N_f$ limit and to all orders in $k/N_f$ and in the couplings. We determine the RG fixed points and discuss the quantum stability of the corresponding vacua. While critical bosonic and fermionic QED$_3$ are always stable CFTs, we find that tricritical bosonic and Gross-Neveu QED$_3$ exist as stable CFTs only for specific values of $k/N_f$. Finally, we discuss the phase diagrams of these theories as a function of their relevant deformations.

hep-th↗