arXiv subjects

Nikolay Gromov

Publications and source records attributed to Nikolay Gromov.

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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arXiv2026

Integrability and the spectrum of two-dimensional fishnet CFT

We formulate a closed set of equations for the spectrum of two-dimensional bi-scalar fishnet conformal field theory, comprising Baxter equations and quantisation conditions, which we derive operatorially from the underlying sl(2) spin chain. These equations are reminiscent of the Quantum Spectral Curve (QSC) framework found in other holographic CFTs and are expected to provide a complete non-perturbative description of the spectrum at arbitrary coupling. We solve the QSC numerically at finite coupling and uncover a rich analytic structure, including state collisions and complex energy levels. Analytically, we introduce a new method to derive the Asymptotic Bethe Ansatz equations, which control the spectrum up to wrapping order and incorporate spinning states. We further extend our results to the twisted case, which may be particularly useful for future separation of variables analyses of correlation functions in this theory.

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arXiv2026

Short Strings in Three-Dimensional Anti-de Sitter Space: from Weak to Strong Coupling

We numerically solve the conjectured Quantum Spectral Curve for strings on AdS$_3\times$S$^3\times$T$^4$ with R--R charge from weak to strong coupling. At strong coupling, the spectrum organises into flat-space string mass levels with universal square-root scaling in the string tension at leading order, and additional Kaluza-Klein fine-splitting at subleading order. At weak coupling, the energies are determined by a nearest-neighbour Bethe Ansatz, with universal subleading corrections that are suppressed at large volume.

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arXiv2025

Gluing Quantum Spectral Curves: A Two-Copy osp(4|2) Construction

We propose a Quantum Spectral Curve for planar string theory on AdS3*S3*S3*S1 supported by pure Ramond-Ramond flux. Our proposal is built on symmetry considerations and integrability-based functional relations. To test our construction, we consider the large volume limit and successfully reproduce the cross- ing equations and the correct structure of the Bethe equations found in the literature. In a symmetric subsector, we find agreement with previously known results and furthermore extend the Asymptotic Bethe Ansatz to include massless modes. Beyond this sector, we identify an interesting puzzle regarding the compatibility of crossing equations with braiding unitarity for individual dressing phases, which warrants further investigation and may require additional physical insights or novel structures not previously encountered in related systems. As we expect the QSC to be exact in the planar limit, our proposal may open the way for non-perturbative analysis of this holographic system.

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arXiv2025

Regge Trajectories of N=4 SYM Part I: General Asymptotic Baxter-Bethe Ansatz

In this work, we derive a novel set of equations - the Asymptotic Baxter--Bethe Ansatz - that determine the asymptotic spectrum of Regge trajectories in the BFKL regime of N=4 SYM. In this challenging limit, our method yields multi-loop results in the 't Hooft coupling, with the perturbative accuracy increasing as the quantum numbers grow. Our formalism not only provides a straightforward path to obtain multi-loop perturbative data, as we demonstrate, but also enables the classification of trajectories, paving the way for systematic non-perturbative studies up to the strong-coupling regime.

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arXiv2024

Probing Line Defect CFT with Mixed-Correlator Bootstrability

We continue our study of the defect CFT on a Maldacena-Wilson line in N=4 Super-Yang-Mills theory using Bootstrability -- the conformal bootstrap supplemented with exact integrability data. In this paper, we extend this program to charged sectors of the theory, considering a mixed-correlator setup first introduced by Liendo, Meneghelli, and Mitev. The exact spectrum in all channels is given by integrability at any coupling. Additionally, we use exact expressions for some structure constants fixed by localisation and leverage the exact discrete symmetries of the theory. We analyse the remaining data with the numerical bootstrap, developing an algorithm optimised to scan over a large multidimensional space of OPE coefficients and carve the allowed region with the "cutting surface" procedure. We compute upper and lower bounds for 12 OPE coefficients for several values of the coupling. Our results are sharp for the lowest states in each sector but become quite wide for the excited states due to their near degeneracy. This highlights the need for studying the system with non-protected external states and for further input from integrability in the form of integrated correlators of non-protected operators.

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arXiv2024

Demystifying the Massless Sector in AdS_3 Quantum Spectral Curve

We show that in the asymptotic large-volume limit, the original proposal for Quantum Spectral Curve for AdS3 x S3 x T4 with R-R flux has a wider class of solutions, than studied previously. We argue that in this limit the QSC reduces to a finite set of Bethe equations for both massive and massless particle types. We also find that the QSC imposes more constraining conditions on the dressing phases than previously known and we present solutions of those equations.

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arXiv2024

Long Range Asymptotic Baxter-Bethe Ansatz for N=4 BFKL

We demonstrate that the Balitsky-Fadin-Kuraev-Lipatov regime of maximally supersymmetric Yang-Mills theory can be explicitly solved up to the L+1 order in weak coupling by uncovering a novel long-range asymptotic Baxter-Bethe ansatz for trajectories with L scalar fields. The set of equations we have found is reminiscent of the Beisert-Eden-Staudacher equations for local operators but instead applies to non-local operators corresponding to the horizontal Regge trajectories. We also verify and give new predictions for the light-ray operator spectrum by resummation of the leading singularities in our result.

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arXiv2024

New Approach to Strongly Coupled N = 4 SYM via Integrability

Finding a systematic expansion of the spectrum of free superstrings on AdS${}_5\times $S${}^5$, or equivalently strongly coupled N = 4 SYM in the planar limit, remains an outstanding challenge. No first principle string theory methods are readily available, instead the sole tool at our disposal is the integrability-based Quantum Spectral Curve (QSC). For example, through the QSC the first five orders in the strong coupling expansion of the conformal dimension of an infinite family of short operators have been obtained. However, when using the QSC at strong coupling one must often rely on numerics, and the existing methods for solving the QSC rapidly lose precision as we approach the strong coupling regime. In this paper, we introduce a new framework that utilises a novel set of QSC variables with a regular strong coupling expansion. We demonstrate how to use this approach to construct a new numerical algorithm that remains stable even at a 't Hooft coupling as large as $10^6$ (or g ~ 100). Employing this approach, we derive new analytic results for some states in the sl(2) sector and beyond. We present a new analytic prediction for a coefficient in the strong coupling expansion of the conformal dimension for the lowest trajectory at a given twist L. For non-lowest trajectories, we uncover a novel feature of mixing with operators outside the sl(2) sector, which manifests as a new type of analytic dependence on the twist.

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arXiv2024

Boundary Overlaps from Functional Separation of Variables

In this paper we show how the Functional Separation of Variables (FSoV) method can be applied to the problem of computing overlaps with integrable boundary states in integrable systems. We demonstrate our general method on the example of a particular boundary state, a singlet of the symmetry group, in an su(3) rational spin chain in an alternating fundamental--anti-fundamental representation. The FSoV formalism allows us to compute in determinant form not only the overlaps of the boundary state with the eigenstates of the transfer matrix, but in fact with any factorisable state. This includes off-shell Bethe states, whose overlaps with the boundary state have been out of reach with other methods. Furthermore, we also found determinant representations for insertions of so-called Principal Operators (forming a complete algebra of all observables) between the boundary and the factorisable state as well as certain types of multiple insertions of Principal Operators. Concise formulas for the matrix elements of the boundary state in the SoV basis and su(N) generalisations are presented. Finally, we managed to construct a complete basis of integrable boundary states by repeated action of conserved charges on the singlet state. As a result, we are also able to compute the overlaps of all of these states with integral of motion eigenstates.

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arXiv2024

Fast QSC Solver: tool for systematic study of N=4 Super-Yang-Mills spectrum

Integrability methods give us access to a number of observables in the planar N=4 SYM. Among them, the Quantum Spectral Curve (QSC) governs the spectrum of anomalous dimensions. Low lying states were successfully studied in the past using the QSC. However, with the increased demand for a systematic study of a large number of states for various applications, there is a clear need for a fast QSC solver which can easily access a large number of excited states. Here, we fill this gap by developing a new algorithm and applied it to study all 219 states with the bare dimension $Δ_0 \leq 6$ in a wide range of couplings. The new algorithm has an improved performance at weak coupling and allows to glue numerics smoothly the available perturbative data, resolving the previous obstruction. Further ~ 8-fold efficiency gain comes from C++ implementation over the best available Mathematica implementation. We have made the code and the data to be available via a GitHub repository. The method is generalisable for non-local observables as well as for other theories such as deformations of N=4 SYM and ABJM. It may find applications in the separation of variables and bootstrability approaches to the correlation functions. Some applications to correlators at strong coupling are also presented.

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arXiv2023

Computing Four-Point Functions with Integrability, Bootstrap and Parity Symmetry

The combination of integrability and crossing symmetry has proven to give tight non-perturbative bounds on some planar structure constants in $\mathcal{N}$=4 SYM, particularly in the setup of defect observables built on a Wilson-Maldacena line. Whereas the precision is good for the low lying states, higher in the spectrum it drops due to the degeneracies at weak coupling when considering a single correlator. As this could be a clear obstacle in restoring higher point functions, we studied the problem of bounding directly a 4-point function at generic cross ratio, showing how to adapt for this purpose the numerical bootstrap algorithms based on semidefinite programming. Another tool we are using to further narrow the bounds is a parity symmetry descending from the $\mathcal{N}$=4 SYM theory, which allowed us to reduce the number of parameters. We also give an interpretation for the parity in terms of the Quantum Spectral Curve at weak coupling. Our numerical bounds give an accurate determination of the 4-point function for physical values of the cross ratio, with at worst 5-6 digits precision at weak coupling and reaching more than 11 digits for 't Hooft coupling $\frac{\sqrtλ}{4 π} \sim 4$.

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arXiv2023

Exploring the Quantum Spectral Curve for AdS${}_3$/CFT${}_2$

Despite the rich and fruitful history of the integrability approach to string theory on the $AdS_3\times S^3\times T^4$ background, it has not been possible to extract many concrete predictions from integrability, except in a strict asymptotic regime of large quantum numbers, due to the severity of wrapping effects. The situation changed radically with two independent and identical proposals for the Quantum Spectral Curve (QSC) for this system in a background of pure Ramond-Ramond flux. This formulation is expected to capture all wrapping effects exactly and describe the full planar spectrum. Massless modes conjecturally manifest themselves in a new property of this QSC: the non-quadratic nature of the branch-cut singularities of the QSC Q-functions. This feature implies new technical challenges in solving the QSC equations as compared to the well-studied case of N=4 SYM. In this paper we resolve these difficulties and obtain the first ever predictions for generic unprotected string excitations. We explain how to extract a systematic expansion around the analogue of the weak 't Hooft coupling limit in N=4 SYM and also obtain high-precision numerical results. This concrete data and others obtainable from the QSC could help to identify the so-far mysterious dual CFT.

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arXiv2022

Integrated correlators from integrability: Maldacena-Wilson line in $\mathcal{N}=4$ SYM

We present a systematic method for the derivation of a relation which connects the correlation function of operators on the straight Maldacena-Wilson line with the integrability data for the cusp anomalous dimension. As we show, the derivation requires very careful treatment of the UV divergences. Our method opens a way to derive infinitely many constraints on integrals of multi-point correlation functions, relating them with the integrability data for the generalised cusp anomalous dimension governed by the Quantum Spectral Curve. Such constraints have been shown recently to be very powerful in combination with the numerical conformal bootstrap, leading to very narrow non-perturbative bounds on conformal data beyond the spectrum.

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arXiv2022

Form-factors and complete basis of observables via separation of variables for higher rank spin chains

Integrable sl(N) spin chains, which we consider in this paper, are not only the prototypical example of quantum integrable systems but also systems with a wide range of applications. For these models we use the Functional Separation of Variables (FSoV) technique with a new tool called Character Projection to compute all matrix elements of a complete set of operators, which we call principal operators, in the basis diagonalising the tower of conserved charges as determinants in Q-functions. Building up on these results we then derive similar determinant forms for the form-factors of combinations of multiple principal operators between arbitrary factorizable states, which include, in particular, off-shell Bethe vectors and Bethe vectors with arbitrary twists. We prove that the set of principal operators generates the complete spin chain Yangian. Furthermore, we derive the representation of these operators in the SoV bases allowing one to compute correlation functions with an arbitrary number of principal operators. Finally, we show that the available combinations of multiple insertions includes Sklyanin`s SoV B operator. As a result, we are able to derive the B operator for sl(N) spin chains using a minimal set of ingredients, namely the FSoV method and the structure of the SoV basis.

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arXiv2022

Quantum Spectral Curve for AdS$_3$/CFT$_2$: a proposal

We conjecture the Quantum Spectral Curve equations for string theory on $AdS_3 \times S^3 \times T^4$ with RR charge and its CFT$_2$ dual. We show that in the large-length regime, under additional mild assumptions, the QSC reproduces the Asymptotic Bethe Ansatz equations for the massive sector of the theory, including the exact dressing phases found in the literature. The structure of the QSC shares many similarities with the previously known AdS$_5$ and AdS$_4$ cases, but contains a critical new feature - the branch cuts are no longer quadratic. Nevertheless, we show that much of the QSC analysis can be suitably generalised producing a self-consistent system of equations. While further tests are necessary, particularly outside the massive sector, the simplicity and self-consistency of our construction suggests the completeness of the QSC.

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arXiv2022

Bootstrability in Defect CFT: Integrated Correlators and Sharper Bounds

We continue to develop Bootstrability -- a method merging Integrability and Conformal Bootstrap to extract CFT data in integrable conformal gauge theories such as $\mathcal{N}$=4 SYM. In this paper, we consider the 1D defect CFT defined on a $\frac{1}{2}$-BPS Wilson line in the theory, whose non-perturbative spectrum is governed by the Quantum Spectral Curve (QSC). In addition, we use that the deformed setup of a cusped Wilson line is also controlled by the QSC. In terms of the defect CFT, this translates into two nontrivial relations connecting integrated 4-point correlators to cusp spectral data, such as the Bremsstrahlung and Curvature functions -- known analytically from the QSC. Combining these new constraints and the spectrum of the $10$ lowest-lying states with the Numerical Conformal Bootstrap, we obtain very sharp rigorous numerical bounds for the structure constant of the first non-protected state, giving this observable with seven digits precision for the 't Hooft coupling in the intermediate coupling region $\frac{\sqrtλ}{4π}\sim 1$, with the error decreasing quickly at large 't Hooft coupling. Furthermore, for the same structure constant we obtain a $4$-loop analytic result at weak coupling. We also present results for excited states.

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arXiv2021

Integrability and Conformal Bootstrap: One Dimensional Defect CFT

In this letter we study how the exact non-perturbative integrability methods in 4D N=4 Super-Yang-Mills can work efficiently together with the numerical conformal bootstrap techniques to go beyond the spectral observables and access previously unreachable quantities such as correlation functions at finite coupling. In the setup of 1D defect CFT living on a Maldacena-Wilson line, we managed to compute with good precision a non-supersymmetric structure constant for a wide range of the `t Hooft coupling. Our result is particularly precise at strong coupling and matches well with the recent analytic results of Meneghelli and Ferrero.

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