arXiv subjects

Amit Sever

Publications and source records attributed to Amit Sever.

At least 19 recordsLinked to original sources

arXiv2026

Quark Anti-Quark Fusion and Walking RG Flows

We study the fusion of two conjugate conformal line defects on the sphere. At small separation, their spectrum is governed by a universal Fusion Master Equation. Below a critical coupling, the fused defect has two conformal fixed points; at criticality, they collide and move into the complex plane, producing walking RG behaviour. Although individual energy levels then drift with the UV scale and are scheme dependent, the $SL(2,\mathbb{R})$ Casimir continues to commute with the Hamiltonian below that scale. This organises the spectrum into conformal families and fixes a universal, scheme-independent density of states. We derive this structure in the planar ladder model and obtain an exact finite-coupling description of conjugate $1/2$-BPS Wilson-line fusion in planar ${\cal N}=4$ SYM using the Quantum Spectral Curve. We test our results against perturbation theory and semiclassical string theory.

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arXiv2025

Correlators of Line Defect and Local Operator in Conformal Field Theories with a Slightly Broken Higher-Spin Symmetry

We study three-dimensional conformal field theories with a large-$N$ limit. Leveraging the framework of slightly broken higher-spin symmetry, we bootstrap correlation functions between the single-trace, local operators and straight, conformal line defects with boundaries. These correlation functions, which depend on a single conformal cross-ratio, encapsulate all bulk-defect operator product expansion coefficients. Concentrating on the quasi-fermionic theory, we explicitly compute all correlators involving the spin-zero and spin-one conserved currents, along with an infinite family of correlators involving the higher-spin currents. Furthermore, we demonstrate that the dependence of these correlators on the defect's shape is fully determined by our bootstrap constraints.

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arXiv2025

Universal Constraints for Conformal Line Defects

We present a novel framework for deriving integral constraints for correlators on conformal line defects. These constraints emerge from the non-linearly realized ambient-space conformal symmetry. To validate our approach, we examine several examples and compare them against existing data for the four-point function of the displacement operator. Additionally, we provide a few new predictions that extend the current understanding of these correlators.

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arXiv2024

Planar RG Flows on Line Defects

We study a class of renormalization group flows on line defects that can be described by a generalized free field with ordered planar contractions on the line. They are realized, for example, in large $N$ gauge theories with matter in the fundamental representation and arise generically in non-relativistic CFTs. We analyze the flow exactly and compute the change in the $g$-function between the UV and IR fixed points. We relate the result to the change in the two-point function of the displacement operator and check the monotonicity of the defect entropy along the flow analytically. Finally, we give a general realization of this type of flow starting from the direct sum of the IR fixed point and a trivial line. This type of defect renormalization group flow parallels the well-studied case of double-trace flow.

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arXiv2023

Bootstrapping Smooth Conformal Defects in Chern-Simons-Matter Theories

The expectation value of a smooth conformal line defect in a CFT is a conformal invariant functional of its path in space-time. For example, in large $N$ holographic theories, these fundamental observables are dual to the open string partition function in AdS. In this paper, we develop a bootstrap method for studying them and apply it to conformal line defects in Chern-Simons matter theories. In these cases, the line bootstrap is based on three minimal assumptions -- conformal invariance of the line defect, large $N$ factorization, and the spectrum of the two lowest-lying operators at the end of the line. On the basis of these assumptions, we solve the one-dimensional CFT on the line and systematically compute the defect expectation value in an expansion around the straight line. We find that the conformal symmetry of a straight defect is insufficient to fix the answer. Instead, imposing the conformal symmetry of the defect along an arbitrary curved line leads to a functional bootstrap constraint. The solution to this constraint is found to be unique.

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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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arXiv2022

Line operators in Chern-Simons-Matter theories and Bosonization in Three Dimensions II -Perturbative Analysis and All-loop Resummation

We study mesonic line operators in Chern-Simons theories with bosonic or fermionic matter in the fundamental representation. In this paper, we elaborate on the classification and properties of these operators using all loop resummation of large $N$ perturbation theory. We show that these theories possess two conformal line operators in the fundamental representation. One is a stable renormalization group fixed point, while the other is unstable. They satisfy first-order chiral evolution equations, in which a smooth variation of the path is given by a factorized product of two mesonic line operators. The boundary operators on which the lines can end are classified by their conformal dimension and transverse spin, which we compute explicitly at finite 't Hooft coupling. We match the operators in the bosonic and fermionic theories.

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arXiv2022

Line Operators in Chern-Simons-Matter Theories and Bosonization in Three Dimensions

We study Chern-Simons theories at large $N$ with either bosonic or fermionic matter in the fundamental representation. The most fundamental operators in these theories are mesonic line operators, the simplest example being Wilson lines ending on fundamentals. We classify the conformal line operators along an arbitrary smooth path as well as the spectrum of conformal dimensions and transverse spins of their boundary operators at finite 't Hooft coupling. These line operators are shown to satisfy first-order chiral evolution equations, in which a smooth variation of the path is given by a factorized product of two line operators. We argue that this equation together with the spectrum of boundary operators are sufficient to uniquely determine the expectation values of these operators. We demonstrate this by bootstrapping the two-point function of the displacement operator on a straight line. We show that the line operators in the theory of bosons and the theory of fermions satisfy the same evolution equation and have the same spectrum of boundary operators.

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arXiv2021

An Operator Product Expansion for Form Factors III. Finite Coupling and Multi-Particle Contributions

Form factors in planar $\mathcal{N}=4$ super-Yang-Mills theory have a dual description in terms of periodic Wilson loops. This duality maps the multi-collinear expansion of the former to an operator product expansion of the latter. The coefficients of this expansion are decomposed in terms of several elementary building blocks and can be determined at finite 't Hooft coupling using bootstrap and integrability techniques. Some of these blocks are known from an analogous expansion of scattering amplitudes. In addition to these, the expansion for form factors includes a new type of building block, called {\it form factor transitions}, that encode information about the local operator. In the present paper, we consider the form factor of the chiral part of the stress-tensor supermultiplet. We bootstrap the corresponding form factor transitions of two-particle flux-tube states and use them to predict the leading term in the collinear expansion at finite coupling. The transitions we find can be expressed in terms of a quantity that previously appeared in a seemingly unrelated context, namely the octagon kernel. Lastly, we use a factorized ansatz to determine the multi-particle form factor transitions at finite coupling, which we use to predict the first subleading term in the collinear expansion. A perfect match is found between our predictions and the available perturbative data.

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arXiv2021

Probing multi-particle unitarity with the Landau equations

We consider the $2\to 2$ scattering amplitude of identical massive particles. We identify the Landau curves in the multi-particle region $16m^2 \leq s, t < 36m^2$. We systematically generate and select the relevant graphs and numerically solve the associated Landau equations for the leading singularity. We find an infinite sequence of Landau curves that accumulates at finite $s$ and $t$ on the physical sheet. We expect that such accumulations are generic for $s,t > 16m^2$. Our analysis sheds new light on the complicated analytic structure of nonperturbative relativistic scattering amplitudes.

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arXiv2021

Rigorous bounds on the Analytic $S$-matrix

We consider a dual $S$-matrix Bootstrap approach in $d\geq 3$ space-time dimensions which relies solely on the rigorously proven analyticity, crossing, and unitarity properties of the scattering amplitudes. As a proof of principle, we provide rigorous upper and lower numerical bounds on the quartic coupling for the scattering of identical scalar particles in four dimensions.

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arXiv2021

An Operator Product Expansion for Form Factors II. Born level

Form factors in planar N=4 Super-Yang-Mills theory admit a type of non-perturbative operator product expansion (OPE), as we have recently shown in arXiv:2009.11297. This expansion is based on a decomposition of the dual periodic Wilson loop into elementary building blocks: the known pentagon transitions and a new object that we call form factor transition, which encodes the information about the local operator. In this paper, we compute the two-particle form factor transitions for the chiral part of the stress-tensor supermultiplet at Born level; they yield the leading contribution to the OPE. To achieve this, we explicitly construct the Gubser-Klebanov-Polyakov two-particle singlet states. The resulting transitions are then used to test the OPE against known perturbative data and to make higher-loop predictions.

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arXiv2020

An Operator Product Expansion for Form Factors

We propose an operator product expansion for planar form factors of local operators in $\mathcal{N}=4$ SYM theory. This expansion is based on the dual conformal symmetry of these objects or, equivalently, the conformal symmetry of their dual description in terms of periodic Wilson loops. A form factor is decomposed into a sequence of known pentagon transitions and a new universal object that we call the "form factor transition". This transition is subject to a set of non-trivial bootstrap constraints, which we expect to be sufficient to fully determine it. We evaluate the form factor transition for MHV form factors of the chiral half of the stress tensor supermultiplet at leading order in perturbation theory and use it to produce OPE predictions at any loop order. We match the one-loop and two-loop predictions with data available in the literature.

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arXiv2020

An Analytical Toolkit for the S-matrix Bootstrap

We revisit analytical methods for constraining the nonperturbative $S$-matrix of unitary, relativistic, gapped theories in $d \geq 3$ spacetime dimensions. We assume extended analyticity of the two-to-two scattering amplitude and use it together with elastic unitarity to develop two natural expansions of the amplitude. One is the threshold (non-relativistic) expansion and the other is the large spin expansion. The two are related by the Froissart-Gribov inversion formula. When combined with crossing and a local bound on the discontinuity of the amplitude, this allows us to constrain scattering at finite energy and spin in terms of the low-energy parameters measured in the experiment. Finally, we discuss the modern numerical approach to the $S$-matrix bootstrap and how it can be improved based on the results of our analysis.

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arXiv2020

Colour-Twist Operators I: Spectrum and Wave Functions

We introduce a new class of operators in any theory with a 't Hooft large-$N$ limit that we call colour-twist operators. They are defined by twisting the colour-trace with a global symmetry transformation and are continuously linked to standard, un-twisted single-trace operators. In particular, correlation functions between operators that are twisted by an R-symmetry of ${\cal N}=4$ SYM extend those in the $\gamma$-deformed theory. The most general deformation also breaks the Lorentz symmetry but preserves integrability in the examples we consider. In this paper, we focus on colour-twist operators in the fishnet model. We exemplify our approach for the simplest colour-twist operators with one and two scalar fields, which we study non-perturbatively using field-theoretical as well as integrability methods, finding a perfect match. We also propose the quantisation condition for the Baxter equation appearing in the integrability calculation in the fishnet model. The results of this paper constitute a crucial step towards building the separation of variable construction for the correlation functions by means of the Quantum Spectral Curve approach.

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arXiv2019

The Holographic Dual of Strongly \gamma-deformed N=4 SYM Theory: Derivation, Generalization, Integrability and Discrete Reparametrization Symmetry

Recently, we constructed the first-principle derivation of the holographic dual of N=4 SYM in the double-scaled $\gamma$-deformed limit directly from the CFT side. The dual fishchain model is a novel integrable chain of particles in AdS5. It can be viewed as a discretized string and revives earlier string-bit approaches. The original derivation was restricted to the operators built out of one of two types of scalar fields. In this paper, we extend our results to the general operators having any number of scalars of both types, except for a very special case when their numbers are equal. Interestingly, the extended model reveals a new discrete reparametrization symmetry of the "world-sheet", preserving all integrals of motion. We use integrability to formulate a closed system of equations, which allows us to solve for the spectrum of the model in full generality, and present non-perturbative numerical results. We show that our results are in agreement with the Asymptotic Bethe Ansatz of the fishnet model up to the wrapping order at weak coupling.

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arXiv2019

Quantum Fishchain in $AdS_5$

In our previous paper we derived the holographic dual of the planar fishnet CFT in four dimensions. The dual model becomes classical in the strongly coupled regime of the CFT and takes the form of an integrable chain of particles in five dimensions. Here we study the theory at the quantum level. By applying the canonical quantization procedure with constraints, we show that the model describes a quantum chain of particles propagating in $AdS_5$. We prove the duality at the full quantum level in the ${\mathfrak u}(1)$ sector and reproduce exactly the spectrum for the cases when it is known analytically.

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arXiv2019

The Holographic Fishchain

We present the first-principle derivation of a weak-strong duality between the fishnet theory in four dimensions and a discretized string-like model living in five dimensions. At strong coupling, the dual description becomes classical and we demonstrate explicitly the classical integrability of the model. We test our results by reproducing the strong coupling limit of the $4$-point correlator computed before non-perturbatively from the conformal partial wave expansion. Due to the extreme simplicity of our model, it could provide an ideal playground for holography with no super-symmetry. Furthermore, since the fishnet model and ${\cal N}=4$ SYM theory are continuously linked our consideration could shed light on the derivation of AdS/CFT for the latter.

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