arXiv subjects

Adar Sharon

Publications and source records attributed to Adar Sharon.

At least 19 recordsLinked to original sources

arXiv2026

Towers of Operators in CFTs and Convexity Bounds at Large Charge

In arXiv:2406.19441, it was shown that for 3d CFTs with a moduli space along which a $U(1)$ symmetry is spontaneously broken, the minimum scaling dimension at large charge $Q$ scales as $\Delta_{\min}(Q)=\alpha_1 Q+\alpha_0+O(1/Q)$. Motivated by the holographic swampland program, we study possible bounds on the coefficients $\alpha_i$. For $\alpha_0$, the weak gravity conjecture motivates the CFT charge convexity conjecture, which requires the bound $\alpha_0\leq 0$. Using the moduli space EFT we prove this bound for the $\textit{projected}$ $\Delta_{\min}(Q)$, obtained by fixing a single charge $Q$ and minimizing the dimension while allowing all other charges to vary. This provides a WGC-motivated bound that is explicitly provable using CFT methods. On the other hand, we show that $\alpha_1$ admits no universal bound apart from the trivial bound $\alpha_1\geq 0$. We also compute $\alpha_1$ and $\alpha_0$ in several new 3d $\mathcal{N}=1$ theories via the $\epsilon$-expansion and large-$N$ methods.

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arXiv2025

Unveiling dynamical quantum error correcting codes via non-invertible symmetries

Dynamical stabilizer codes (DSCs) have recently emerged as a powerful generalization of static stabilizer codes for quantum error correction, replacing a fixed stabilizer group with a sequence of non-commuting measurements. This dynamical structure unlocks new possibilities for fault tolerance but also introduces new challenges, as errors must now be tracked across both space and time. In this work, we provide a physical and topological understanding of DSCs by establishing a correspondence between qudit Pauli measurements and non-invertible symmetries in 4+1-dimensional 2-form gauge theories. Sequences of measurements in a DSC are mapped to a fusion of the operators implementing these non-invertible symmetries. We show that the error detectors of a DSC correspond to endable surface operators in the gauge theory, whose endpoints define line operators, and that detectable errors are precisely those surface operators that braid non-trivially with these lines. Finally, we demonstrate how this framework naturally recovers the spacetime stabilizer code associated with a DSC.

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arXiv2025

Non-Local Conserved Currents and Continuous Non-Invertible Symmetries

We embark on a systematic study of continuous non-invertible symmetries, focusing on 1+1d CFTs. We describe a generalized version of Noether's theorem, where continuous non-invertible symmetries are associated to $\textit{non-local}$ conserved currents: point-like operators attached to extended topological defects. The generalized Noether's theorem unifies several constructions of continuous non-invertible symmetries in the literature, and allows us to exhibit many more examples in diverse theories of interest. We first review known examples which are non-intrinsic (i.e., invertible up to gauging), and then describe $\textit{new}$ examples in Wess-Zumino-Witten models and products of minimal models. For some of these new examples, we show that these continuous non-invertible symmetries are intrinsic if we demand that a certain global symmetry is preserved. The continuous non-invertible symmetries in products of minimal models also allow us to construct new examples of defect conformal manifolds in a single copy of a minimal model. Finally, we comment on continuous non-invertible symmetries in higher dimensions.

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arXiv2024

6d Large Charge and 2d Virasoro Blocks

We compute observables in the interacting rank-one 6d $\mathcal{N}=(2,0)$ SCFT at large R-charge. We focus on correlators involving $\Phi^n$, namely symmetric products of the bottom component of the supermultiplet containing the stress-tensor. By using the moduli space effective action and methods from the large-charge expansion, we compute the OPE coefficients $\langle\Phi^n\Phi^m\Phi^{n+m}\rangle$ in an expansion in 1/n. The coefficients of the expansion are only partially determined from the 6d perspective, but we manage to fix them order-by-order in 1/n numerically by utilizing the 6d/2d correspondence. This is made possible by the fact that this $6d$ observable can be extracted in 2d from a specific double-scaling limit of the vacuum Virasoro block, which can be efficiently computed numerically. We also extend the computation to higher-rank SCFTs, and discuss various applications of our results to 6d as well as 2d.

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arXiv2024

Hunting 3d $\mathcal{N}=1$ SQED in the $\epsilon$-expansion

It was recently shown that $3d$ $\mathcal{N}=1$ supersymmetric Wess-Zumino models can be studied in the $\epsilon$-expansion by analytically continuing the number of fermionic degrees of freedom to be half-integer. In this work we study the extension of this strategy to gauge theories. We consider $U(1)$ gauge theories with $N_g$ neutral Majorana fermions $\chi_a$, $N_f$ charge-1 bosons $\phi_i$ and $N_f\times N_g$ charge-1 Dirac fermions $\psi_{ia}$ in the $d=4-2\epsilon$ expansion. Analytically continuing to $N_g=\frac12$ schematically matches the Lagrangian and matter content of $3d$ $\mathcal{N}=1$ SQED, and we check whether this match can be made rigorous. We compute anomalous dimensions of $\chi_a$ up to two loops and of meson operators up to one loop at the fixed points, and compare to expectations from SUSY. While we find obstructions to SUSY at small $N_f$, at large $N_f$ the observables approach the expected values at a SUSY fixed point. This may allow for checks of $3d$ $\mathcal{N}=1$ IR dualities between gauge theories.

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arXiv2024

Moduli Spaces in CFT: Large Charge Operators

Using the large-charge expansion, we prove a necessary condition for a CFT to exhibit conformal symmetry breaking, under the assumption that a continuous global symmetry is ${\it also}$ broken on the moduli space: there must be a tower of charged local operators whose scaling dimensions are asymptotically linear in the charge. In supersymmetric theories with a continuous R-symmetry and a holomorphic moduli space, the existence of such a tower of operators follows trivially from a BPS condition: their scaling dimensions are then exactly linear in the R-charge. We illustrate the more general statement in several examples of three-dimensional ${\cal N}=1$ CFTs, where the leading linear behavior receives nontrivial corrections. By considering a suitable scaling limit, we also relate the spectrum of states with large charge on the cylinder (isomorphic to local operators) to the spectrum of massive particles on the moduli space.

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arXiv2024

Moduli Spaces in CFT: Bootstrap Equation in a Perturbative Example

Conformal field theories that exhibit spontaneous breaking of conformal symmetry (a moduli space of vacua) must satisfy a set of bootstrap constraints, involving the usual data (scaling dimensions and OPE coefficients) as well as new data such as the spectrum of asymptotic states in the broken vacuum and form factors. The simplest bootstrap equation arises by expanding a two-point function of local operators in two channels, at short distance using the OPE and at large distance using the EFT in the broken vacuum. We illustrate this equation in what is arguably the simplest perturbative model that exhibits conformal symmetry breaking, namely the real $ABC$ model in $d = 4 -\epsilon$ dimensions. We investigate the convergence properties of the bootstrap equation and check explicitly many of the non-trivial relations that it imposes on theory data.

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arXiv2024

On the Fate of Stringy Non-Invertible Symmetries

Non-invertible symmetries in quantum field theory (QFT) generalize the familiar product rule of groups to a more general fusion rule. In many cases, gauged versions of these symmetries can be regarded as dual descriptions of invertible gauge symmetries. One may ask: are there any other types of non-invertible gauge symmetries? In theories with gravity we find a new form of non-invertible gauge symmetry that emerges in the limit of fundamental, tensionless strings. These stringy non-invertible gauge symmetries appear in standard examples such as non-abelian orbifolds. Moving away from the tensionless limit always breaks these symmetries. We also find that both the conventional form of non-invertible gauge symmetries and these stringy generalizations are realized in AdS/CFT. Although generically broken, approximate non-invertible symmetries have implications for Swampland constraints: in certain cases they can be used to prove the existence of towers of states related to the Distance Conjecture, and can sometimes explain the existence of slightly sub-extremal states which fill in the gaps in the sublattice Weak Gravity Conjecture.

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arXiv2023

A Large Twist Limit for Any Operator

We argue that for any single-trace operator in ${\cal N}=4$ SYM theory there is a large twist double-scaling limit in which the Feynman graphs have an iterative structure. Such structure can be recast using a graph-building operator. Generically, this operator mixes between single-trace operators with different scaling limits. The mixing captures both the finite coupling spectrum and corrections away from the large twist limit. We first consider a class of short operators with gluons and fermions for which such mixing problems do not arise, and derive their finite coupling spectra. We then focus on a class of long operators with gluons that do mix. We invert their graph-building operator and prove its integrability. The picture that emerges from this work opens the door to a systematic expansion of ${\cal N}=4$ SYM theory around the large twist limit.

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arXiv2023

A counterexample to the CFT convexity conjecture

Motivated by the weak gravity conjecture, arXiv:2108.04594 conjectured that in any CFT, the minimal operator dimension at fixed charge is a convex function of the charge. In this letter we construct a counterexample to this convexity conjecture, which is a clockwork-like model with some modifications to make it a weakly-coupled CFT. We also discuss further possible applications of this model and some modified versions of the conjecture which are not ruled out by the counterexample.

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arXiv2023

More on chaos at weak coupling

We discuss aspects of the quantum Lyapunov exponent $\lambda_L$ in theories with an exactly marginal SYK-like random interaction, where $\lambda_L$ can be computed as a continuous function of the interaction strength $\mathcal{J}$. In $1d$, we prove a conjecture from arXiv:2111.06108 which states that at small $\mathcal{J}$, $\lambda_L$ can be found by considering a specific limit of the four-point function in the decoupled theory. We then provide additional evidence for the $2d$ version of this conjecture by discussing new examples of Lyapunov exponents which can be computed at weak coupling.

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arXiv2022

Onset of Quantum Chaos in Random Field Theories

We study the quantum Lyapunov exponent $\lambda_L$ in theories with spacetime-independent disorder. We first derive self-consistency equations for the two- and four-point functions for products of $N$ models coupled by disorder at large $N$, generalizing the equations appearing in SYK-like models. We then study families of theories in which the disorder coupling is an exactly marginal deformation, allowing us to follow $\lambda_L$ from weak to strong coupling. We find interesting behaviors, including a discontinuous transition into chaos, mimicking classical KAM theory.

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arXiv2022

Convexity of Charged Operators in CFTs with Multiple Abelian Symmetries

Motivated by the Weak Gravity Conjecture in the context of holography in AdS, it has been proposed that operators charged under global symmetries in CFTs, in three dimensions or higher, should satisfy certain convexity properties on their spectrum. A key element of this proposal is the charge at which convexity must appear, which was proposed to never be parametrically large. In this paper, we develop this constraint in the context of multiple Abelian global symmetries. We propose the statement that the convex directions in the multi-dimensional charge space should generate a sub-lattice of the total lattice of charged operators, such that the index of this sub-lattice cannot be made parametrically large. In the special case of two-dimensional CFTs, the index can be made parametrically large, which we prove by an explicit example. However, we also prove that in two dimensions there always exist convex directions generating a sub-lattice with an index bounded by the current levels of the global symmetry. Therefore, in two dimensions, the conjecture should be slightly modified to account for the current levels, and then it can be proven. In more than two dimensions, we show that the index of the sub-lattice generated by marginally convex charge vectors associated to BPS operators only, can be made parametrically large. However, we do not find evidence for parametric delay in convexity once all operators are considered.

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arXiv2021

The onset of quantum chaos in disordered CFTs

We study the Lyapunov exponent $\lambda_L$ in quantum field theories with spacetime-independent disorder interactions. Generically $\lambda_L$ can only be computed at isolated points in parameter space, and little is known about the way in which chaos grows as we deform the theory away from weak coupling. In this paper we describe families of theories in which the disorder coupling is an exactly marginal deformation, allowing us to follow $\lambda_L$ from weak to strong coupling. We find surprising behaviors in some cases, including a discontinuous transition into chaos. We also derive self-consistency equations for the two- and four-point functions for products of $N$ nontrivial CFTs deformed by disorder at leading order in $1/N$.

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arXiv2021

Non-rational Narain CFTs from codes over $F_4$

We construct a map between a class of codes over $F_4$ and a family of non-rational Narain CFTs. This construction is complementary to a recently introduced relation between quantum stabilizer codes and a class of rational Narain theories. From the modular bootstrap point of view we formulate a polynomial ansatz for the partition function which reduces modular invariance to a handful of algebraic easy-to-solve constraints. For certain small values of central charge our construction yields optimal theories, i.e. those with the largest value of the spectral gap.

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arXiv2021

Squashing, Mass, and Holography for 3d Sphere Free Energy

We consider the sphere free energy $F(b;m_I)$ in $\mathcal{N}=6$ ABJ(M) theory deformed by both three real masses $m_I$ and the squashing parameter $b$, which has been computed in terms of an $N$ dimensional matrix model integral using supersymmetric localization. We show that setting $m_3=i\frac{b-b^{-1}}{2}$ relates $F(b;m_I)$ to the round sphere free energy, which implies infinite relations between $m_I$ and $b$ derivatives of $F(b;m_I)$ evaluated at $m_I=0$ and $b=1$. For $\mathcal{N}=8$ ABJ(M) theory, these relations fix all fourth order and some fifth order derivatives in terms of derivatives of $m_1,m_2$, which were previously computed to all orders in $1/N$ using the Fermi gas method. This allows us to compute $\partial_b^4 F\vert_{b=1}$ and $\partial_b^5 F\vert_{b=1}$ to all orders in $1/N$, which we precisely match to a recent prediction to sub-leading order in $1/N$ from the holographically dual $AdS_4$ bulk theory.

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arXiv2020

Full Phase Diagram of a UV Completed $\mathcal{N}=1$ Yang-Mills-Chern-Simons Matter Theory

We study the large $N$ phase diagram of an asymptotically free UV completion of $\mathcal{N}=1$ $SU(N)$ super-Yang-Mills-Chern-Simons theory coupled to a single massive fundamental scalar multiplet with a quartic superpotential coupling. We compute the effective superpotential at small gauge coupling $\lambda\equiv N/k$, and combine this with previous results in the literature to obtain the full phase diagram in this regime. We find that tuning the UV parameters allows us to reach various phases and fixed points of Chern-Simons theory that were recently discovered using large $N$ techniques, as well as new phases that characterize the Yang-Mills theory. We also conjecture the form of the phase diagram for general values of $\lambda$ and for finite $N$.

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arXiv2020

Transition of Large $R$-Charge Operators on a Conformal Manifold

We study the transition between phases at large $R$-charge on a conformal manifold. These phases are characterized by the behaviour of the lowest operator dimension $\Delta(Q_R)$ for fixed and large $R$-charge $Q_R$. We focus, as an example, on the $D=3$, $\mathcal{N}=2$ Wess-Zumino model with cubic superpotential $W=XYZ+\frac{\tau}{6}(X^3+Y^3+Z^3)$, and compute $\Delta(Q_R,\tau)$ using the $\epsilon$-expansion in three interesting limits. In two of these limits the (leading order) result turns out to be \begin{equation*} \Delta(Q_R,\tau)= \begin{cases} \left(\text{BPS bound}\right)\left[1+O(\epsilon |\tau|^2Q_R)\right], & Q_R\ll \left\{ \frac{1}{\epsilon},\, \frac{1}{\epsilon|\tau|^2}\right\}\\ \frac{9}{8}\left(\frac{\epsilon|\tau|^2}{2+|\tau|^2}\right)^{\frac{1}{D-1}}Q_R^{\frac{D}{D-1}} \left[1+O\left(\left(\epsilon |\tau|^2Q_R\right)^{-\frac{2}{D-1}}\right)\right], & Q_R\gg \left\{ \frac{1}{\epsilon},\, \frac{1}{\epsilon|\tau|^2}\right\} \end{cases} \end{equation*} which leads us to the double-scaling parameter, $\epsilon |\tau|^2Q_R$, which interpolates between the "near-BPS phase" ($\Delta(Q)\sim Q$) and the "superfluid phase" ($\Delta(Q)\sim Q^{D/(D-1)}$) at large $R$-charge. This smooth transition, happening near $\tau=0$, is a large-$R$-charge manifestation of the existence of a moduli space and an infinite chiral ring at $\tau=0$. We also argue that this behavior can be extended to three dimensions with minimal modifications, and so we conclude that $\Delta(Q_R,\tau)$ experiences a smooth transition around $Q_R\sim 1/|\tau|^2$. Additionally, we find a first-order phase transition for $\Delta(Q_R,\tau)$ as a function of $\tau$, as a consequence of the duality of the model. We also comment on the applicability of our result down to small $R$-charge.

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