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Leonardo Pipolo de Gioia

Publications and source records attributed to Leonardo Pipolo de Gioia.

8 recordsLinked to original sources
arXiv2026

Two roads to fortuity in ABJM theory

A recently proposed addition to the holographic dictionary connects extremal black holes to fortuitous operators -- those which are only supersymmetric for sufficiently small values of the central charge. The most efficient techniques for finding them come from studying the cohomology of a nilpotent supercharge. We explore two aspects of this problem in weakly-coupled ABJM theory, where the gauge group is $\mathrm{U}(N) \times \mathrm{U}(N)$ and the Chern-Simons level is taken to be large. Adapting an algorithm which has been used to great effect in $\mathcal{N} = 4$ Super Yang-Mills, we enumerate 244 low-lying fortuitous operators and sort them into multiplets of the centralizer algebra. This leads to the construction of two leading fortuitous representatives for $N = 3$ which are subleading for $N = 2$. In the second part of this work, we identify a truncation of ABJM theory where the action of the one-loop supercharge matches the one in the BMN subsector of $\mathcal{N} = 4$ Super Yang-Mills. This allows a known infinite tower of representatives to be lifted from one theory to the other.

hep-th↗
arXiv2026

Fortuitous ABJM Operators as Black Holes

Given a superconformal gauge theory at a fixed loop order, BPS states can be studied in two ways --- by enumerating cohomology classes of a nilpotent supercharge or by diagonalizing the anomalous dimension matrix. The second one allows for a deeper look at how holographic theories distinguish between operators based on whether they are dual to horizonless geometries or black holes. To this end, we carry out the diagonalization in $\mathrm{U}(N)_k \times \mathrm{U}(N)_{-k}$ ABJM theory with $N$ as a formal parameter. This makes it possible to define trajectories of operators and focus on the fortuitous ones which are characterized by being BPS at only finitely many values of $N$. In contrast to $\mathcal{N} = 4$ Super Yang-Mills, where it has been numerically prohibitive to study more than one of these, ABJM gives us access to 16 such trajectories along with their descendants. We show that they take an especially simple form at large $N$ where they agree with the predictions of integrability. We also show that many of them, as with black holes, can only be dressed by certain types of gravitons and comment on how this exercise in cohomology also has implications for properties of the full operators. Finally, we show that the gap to the first non-BPS state in ABJM theory qualitatively differs from that of $\mathcal{N} = 4$ Super Yang-Mills in the expected way.

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arXiv2026

From Gross-Manes to Alday-Maldacena

Minimal surfaces govern the classical limit of several important observables in string theory. Two basic examples are the Gross--Manes saddle for high-energy string scattering in flat space and the Alday--Maldacena surface for gluon scattering at strong coupling in ${\cal N}=4$ SYM. In this paper we study a family of null polygonal minimal surfaces in AdS interpolating between these two regimes by moving the cusps from a small region deep in the bulk to the AdS boundary. We do this both numerically and -- in interesting simplifying limits -- analytically. In particular, we derive the leading AdS-radius correction around flat space and show that the resulting classical amplitude agrees with the recent prediction of Alday, Armanini, Häring, and Zhiboedov, supporting an underlying worldsheet description of their bootstrap construction.

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arXiv2025

Infinite towers of 2d symmetry algebras from Carrollian limit of 3d CFT

We consider the Carrollian limit of OPE blocks of scalar primaries, spin-1 currents and the stress tensor in 3-dimensional conformal field theory (CFT$_3$). We demonstrate that these OPE blocks decompose into OPE blocks of towers of $\mathfrak{sl}(2,\mathbb{C})$ modes labeled by negative integer dimensions. We present two applications of this construction. We first show that the current-scalar-scalar and stress tensor-scalar-scalar OPE blocks in CFT$_3$ reduce to $\mathfrak{sl}(2,\mathbb{C})$ OPE blocks from which towers of conformally soft photon and graviton theorems can be derived. We then show that the CFT$_3$ OPE blocks of, respectively, current and stress tensor components dual to positive helicity gluons and gravitons in AdS$_4$ become $\mathfrak{sl}(2,\mathbb{C})$ blocks of conformally soft gluons and gravitons which imply the $S$ and $w_{1 + \infty}$ algebras of celestial CFT.

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arXiv2024

Celestial amplitudes from conformal correlators with bulk-point kinematics

We show that two- and three-point celestial (C)CFT$_{d-1}$ amplitudes can be directly obtained from correlation functions in a unitary Lorentzian CFT$_d$ on $\mathbb{R}\times S^{d-1}$. The recipe involves a rescaling of the operators, followed by an expansion around a bulk point configuration and a transformation to an $S^{d-1}$ conformal primary basis. The first two steps project the CFT$_d$ correlators onto distributions on $S^{d-1}$. The final step implements a dimensional reduction yielding CCFT$_{d-1}$ amplitudes that are manifestly vanishing for all in/out configurations and Poincaré invariant. The dimensional reduction may be implemented either by evaluating certain time integral transforms around the bulk-point limit, or by analytically continuing the CFT$_d$ operator dimensions and restricting the operators to $S^{d-1}$ time slices separated by $π$ in global time. The latter prescription generates the correct normalization for both two- and three-point functions. On the other hand, the celestial three-point amplitudes obtained via the former prescription are found to only agree after evaluating a residue at an integer linear combination of the CFT$_d$ conformal dimensions. The correct normalization may also be obtained by considering a different integration path in the uplift of the complexified time plane to its universal cover.

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arXiv2023

Celestial Sector in CFT: Conformally Soft Symmetries

We show that time intervals of width $Δτ$ in 3-dimensional conformal field theories (CFT$_3$) on the Lorentzian cylinder admit an infinite dimensional symmetry enhancement in the limit $Δτ\rightarrow 0$. The associated vector fields are approximate solutions to the conformal Killing equations in the strip labelled by a function and a conformal Killing vector on the sphere. An Inonu-Wigner contraction yields a set of symmetry generators obeying the extended BMS$_4$ algebra. We analyze the shadow stress tensor Ward identities in CFT$_d$ on the Lorentzian cylinder with all operator insertions in infinitesimal time intervals separated by $π$. We demonstrate that both the leading and subleading conformally soft graviton theorems in $(d-1)$-dimensional celestial CFT (CCFT$_{d-1}$) can be recovered from the transverse traceless components of these Ward identities in the limit $Δτ\rightarrow 0$. A similar construction allows for the leading conformally soft gluon theorem in CCFT$_{d-1}$ to be recovered from shadow current Ward identities in CFT$_d$.

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arXiv2022

Eikonal Approximation in Celestial CFT

We identify an eikonal regime in celestial CFT$_2$ in which massless 2-2 scattering is dominated by t-channel exchange. We derive a formula for the celestial amplitude that resums exchanges of arbitrary integer spin to all orders in the coupling. The resulting eikonal phase takes the same form as in flat space with the powers of center-of-mass energy replaced by weight-shifting operators on the celestial sphere. We independently compute the celestial two-point function for a scalar propagating in a shockwave background and show that to leading order in the gravitational coupling and for a suitable choice of the source, the result agrees with the prediction from the celestial eikonal formula for graviton exchange. We demonstrate that this two-point function can be directly obtained from the corresponding formula in AdS$_4$ in a flat space limit. We finally establish a general relation between scalar celestial amplitudes in celestial CFT$_{d-1}$ and the flat space limit of scalar AdS$_{d+1}$ Witten diagrams.

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