arXiv subjects

Alessandro Piazza

Publications and source records attributed to Alessandro Piazza.

8 recordsLinked to original sources

arXiv2026

The Virasoro Bootstrap: from the $c\sim1$ desert to coupled Potts

We develop a numerical conformal bootstrap for two-dimensional CFTs with $c>1$ based on Virasoro conformal blocks, computed with Zamolodchikov's recursion and optimal polynomial interpolation. As a first test we isolate an island around three decoupled Ising models. We then consider three 3-state Potts models coupled through their energy operators, a candidate irrational CFT. Mixed correlators isolate the decoupled theory in an island, and different gap assumptions, motivated by perturbation theory, yield a peninsula that contains the coupled fixed point but not the decoupled one. Finally, we explore the standard single-correlator bound on the lowest-dimension scalar primary in the OPE of two identical scalars. We find that for central charges just above $c=1$ the bound collapses over a wide range of external dimensions. This excludes any theory whose lightest scalar is absent from its own OPE and lies in this range, and supports the conjecture that no compact CFT exists in this region. We explain several features of these bounds analytically.

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arXiv2026

Bootstrapping Holographic Theories in the Planar Limit

We combine the numerical conformal bootstrap with supersymmetric localization to constrain the spectrum of holographic superconformal field theories in the planar large $N$ limit for finite 't Hooft coupling $λ$. We consider the stress tensor multiplet four-point function in $\mathcal{N}=4$ $SU(N)$ super-Yang-Mills (SYM), which is holographically dual to closed string scattering, as well as the flavor multiplet correlator in a certain $ 4d $ $\mathcal{N}=2$ $U\!Sp(2N)$ gauge theory with $SO(8)$ flavor symmetry, which is dual to open string scattering. In both cases, we combine dispersive sum rules with integrated constraints from supersymmetric localization to compute an upper bound on the scaling dimension of the lowest scalar single-trace operator for all $λ$. For $\mathcal{N}=4$ SYM, we find that our bounds are close to the known integrability result for all $λ$. For the $\mathcal{N}=2$ theory, where integrability is not yet available, we find that our bounds are close to weak and strong coupling predictions in the relevant regimes.

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arXiv2026

Bounds on scattering amplitudes of non-identical scalar particles in 4d

We initiate the study of two-to-two scattering amplitudes involving two distinct scalar particles in $d = 4$ spacetime dimensions using the primal S-matrix bootstrap. We impose a $\mathbb{Z}_2 \times \mathbb{Z}_2$ global symmetry under which the two particles are the lightest ones carrying charges $(-,+)$ and $(+,-)$, guaranteeing their absolute stability and absence of triangular anomalous thresholds. For unequal masses, the presence of a pseudo-physical cut whose discontinuity is not directly constrained by physical unitarity qualitatively changes the bootstrap problem. We find several observables to be unbounded, while others obey non-trivial one-sided bounds or become bounded once another observable is fixed. In the equal-mass limit, where the pseudo-physical region disappears, two-sided bounds are recovered. As a proof of concept, we show that supplying information about the pseudo-physical discontinuity through an Omnès parametrisation also restores boundedness. Our results provide a starting point for future studies of physical processes such as pion-kaon and pion-nucleon scattering.

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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.

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arXiv2025

The random free field scalar theory

Quantum field theories with quenched disorder are so hard to study that even exactly solvable free theories present puzzling aspects. We consider a free scalar field $ϕ$ in $d$ dimensions coupled to a random source $h$ with quenched disorder. Despite the presence of a mass scale governing the disorder distribution, we derive a new description of the theory that allows us to show that the theory is gapless and invariant under conformal symmetry, which acts in a non-trivial way on $ϕ$ and $h$. This manifest CFT description reveals the presence of exotic continuous symmetries, such as nilpotent bosonic ones, in the quenched theory. We also reconsider Cardy's CFT description defined through the replica trick. In this description, the nilpotent symmetries reveal a striking resemblance with Parisi-Sourlas supersymmetries. We provide explicit maps of correlation functions between such CFTs and the original quenched theory. The maps are non-trivial and show that conformal behaviour is manifest only when considering suitable linear combinations of averages of products of correlators. We also briefly discuss how familiar notions like normal ordering of composite operators and OPE can be generalized in the presence of the more complicated local observables in the quenched theory.

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arXiv2025

Bootstrapping the Simplest Deconfined Quantum Critical Point

We study the $N=3$ case of the $CP^{N-1}$ model, which is a field theory of $N$ complex scalars in $3d$ coupled to an Abelian gauge field with $SU(N) \times U(1)$ global symmetry. Recent evidence suggests the $N=2$ theory is not critical, which makes the $N=3$ theory the simplest possibility of deconfined quantum criticality. We apply the conformal bootstrap to correlators of charge $q=0,1,2$ scalar operators under the $U(1)$ symmetry, which gives us access also to $q=3,4$ operators. After imposing that only the lowest $q=0,1,2$ scalar operators are relevant, we find that the bootstrap bounds are saturated by the large $N$ prediction for $q=1,2,3,4$ scalar monopole operator scaling dimensions, which were shown earlier to be accurate even for small $N$, as well as a lattice prediction for the $q=0$ non-monopole scalar operator. We also predict the scaling dimensions of the lowest spinning monopole operators, which we match to the large charge prediction for spinning operators. This suggests that the critical $CP^{2}$ model is described by this bootstrap bound.

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arXiv2024

On the $1/c$ expansion in $2d$ CFTs with degenerate operators

We analytically determine the large central charge asymptotic expansion of the Virasoro conformal blocks entering in four-point functions with external degenerate operators on a sphere in $2d$ CFTs, and study its resurgence properties as a function of the conformal cross-ratio $z$. We focus on the cases of four heavy $(2,1)$ degenerate operators, and two $(2,1)$ heavy degenerate ones plus two arbitrary light operators. The $1/c$ asymptotic series is Borel summable for generic values of $z$, but it jumps when a Stokes line is crossed. Starting from the $1/c$ series of the identity block, we show how a resurgent analysis allows us to completely determine the other Virasoro block and in fact to reconstruct the full correlator. We also show that forbidden singularities, known to exist in correlators with two heavy and two light operators, appear with four heavy operators as well. In both cases, they are turning points emanating Stokes lines, artefacts of the asymptotic expansion, and we show how they are non perturbatively resolved. More general correlators and implications for gravitational theories in $\text{AdS}_{3}$ are briefly discussed. Our results are based on new asymptotic expansions for large parameters $(a,b,c)$ of certain hypergeometric functions $\,_2 F_1(a,b,c;z)$ which can be useful in general.

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arXiv2024

Exploring Replica-Potts CFTs in Two Dimensions

We initiate a numerical conformal bootstrap study of CFTs with $S_n \ltimes (S_Q)^n$ global symmetry. These include CFTs that can be obtained as coupled replicas of two-dimensional critical Potts models. Particular attention is paid to the special case $S_3 \ltimes (S_3)^3$, which governs the critical behaviour of three coupled critical 3-state Potts models, a multi-scalar realisation of a (potentially) non-integrable CFT in two dimensions. The model has been studied in earlier works using perturbation theory, transfer matrices, and Monte Carlo simulations. This work represents an independent non-perturbative analysis. Our results are in agreement with previous determinations: we obtain an allowed peninsula within parameter space for the scaling dimensions of the three lowest-lying operators in the theory, which contains the earlier predictions for these scaling dimensions. Additionally, we derive numerous bounds on admissible scaling dimensions in the theory, which are compatible with earlier results. Our work sets the necessary groundwork for a future precision study of these theories in the conformal bootstrap.

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