arXiv subjects

Nikolay Gromov

Publications and source records attributed to Nikolay Gromov.

At least 55 records · Page 3Linked to original sources

arXiv2017

Integrability of Conformal Fishnet Theory

We study integrability of fishnet-type Feynman graphs arising in planar four-dimensional bi-scalar chiral theory recently proposed in arXiv:1512.06704 as a special double scaling limit of gamma-deformed $\mathcal{N}=4$ SYM theory. We show that the transfer matrix "building" the fishnet graphs emerges from the $R-$matrix of non-compact conformal $SU(2,2)$ Heisenberg spin chain with spins belonging to principal series representations of the four-dimensional conformal group. We demonstrate explicitly a relationship between this integrable spin chain and the Quantum Spectral Curve (QSC) of $\mathcal{N}=4$ SYM. Using QSC and spin chain methods, we construct Baxter equation for $Q-$functions of the conformal spin chain needed for computation of the anomalous dimensions of operators of the type $\text{tr}(ϕ_1^J)$ where $ϕ_1$ is one of the two scalars of the theory. For $J=3$ we derive from QSC a quantization condition that fixes the relevant solution of Baxter equation. The scaling dimensions of the operators only receive contributions from wheel-like graphs. We develop integrability techniques to compute the divergent part of these graphs and use it to present the weak coupling expansion of dimensions to very high orders. Then we apply our exact equations to calculate the anomalous dimensions with $J=3$ to practically unlimited precision at any coupling. These equations also describe an infinite tower of local conformal operators all carrying the same charge $J=3$. The method should be applicable for any $J$ and, in principle, to any local operators of bi-scalar theory. We show that at strong coupling the scaling dimensions can be derived from semiclassical quantization of finite gap solutions describing an integrable system of noncompact $SU(2,2)$ spins. This bears similarities with the classical strings arising in the strongly coupled limit of $\mathcal{N}=4$ SYM.

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arXiv2017

Introduction to the Spectrum of N=4 SYM and the Quantum Spectral Curve

This review is based on the lectures given by the author at the Les Houches Summer School 2016. It describes the recently developed Quantum Spectral Curve (QSC) for a non-perturbative planar spectrum of N=4 Super Yang-Mills theory in a pedagogical way starting from the harmonic oscillator and avoiding a long historical path. We give many examples and provide exercises. At the end we give a list of the recent and possible future applications of the QSC.

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arXiv2017

Quark--anti-quark potential in N=4 SYM

We construct a closed system of equations describing the quark--anti-quark potential at any coupling in planar N=4 supersymmetric Yang-Mills theory. It is based on the Quantum Spectral Curve method supplemented with a novel type of asymptotics. We present a high precision numerical solution reproducing the classical and one-loop string predictions very accurately. We also analytically compute the first 7 nontrivial orders of the weak coupling expansion. Moreover, we study analytically the generalized quark--anti-quark potential in the limit of large imaginary twist to all orders in perturbation theory. We demonstrate how the QSC reduces in this case to a one-dimensional Schrodinger equation. In the process we establish a link between the Q-functions and the solution of the Bethe-Salpeter equation.

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arXiv2017

Quantum Spectral Curve and the Numerical Solution of the Spectral Problem in AdS5/CFT4

We developed an efficient numerical algorithm for computing the spectrum of anomalous dimensions of the planar ${\cal N}=4$ Super-Yang--Mills at finite coupling. The method is based on the Quantum Spectral Curve formalism. In contrast to Thermodynamic Bethe Ansatz, worked out only for some very special operators, this method is applicable for generic states/operators and is much faster and precise due to its Q-quadratic convergence rate. To demonstrate the method we evaluate the dimensions $Δ$ of twist operators in $sl(2)$ sector directly for any value of the spin $S$ including non-integer values. In particular, we compute the BFKL pomeron intercept in a wide range of the 't Hooft coupling constant with up to $20$ significant figures precision, confirming two previously known from the perturbation theory orders and giving prediction for several new coefficients. Furthermore, we explore numerically a rich branch cut structure for complexified spin $S$.

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arXiv2016

On the Exact Interpolating Function in ABJ Theory

Based on the recent indications of integrability in the planar ABJ model, we conjecture an exact expression for the interpolating function h(λ_1,λ_2) in this theory. Our conjecture is based on the observation that the integrability structure of the ABJM theory given by its Quantum Spectral Curve is very rigid and does not allow for a simple consistent modification. Under this assumption, we revised the previous comparison of localization results and exact all loop integrability calculations done for the ABJM theory by one of the authors and Grigory Sizov, fixing h(λ_1,λ_2). We checked our conjecture against various weak coupling expansions, at strong coupling and also demonstrated its invariance under the Seiberg-like duality. This match also gives further support to the integrability of the model. If our conjecture is correct, it extends all the available integrability results in the ABJM model to the ABJ model.

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arXiv2015

Analytic Solution of Bremsstrahlung TBA II: Turning on the Sphere Angle

We find an exact analytical solution of the Y-system describing a cusped Wilson line in the planar limit of N=4 SYM. Our explicit solution describes anomalous dimensions of this family of observables for any value of the `t Hooft coupling and arbitrary R-charge L of the local operator inserted on the cusp in a near-BPS limit. Our finding generalizes the previous results of one of the authors & Sever and passes several nontrivial tests. First, for a particular case L=0 we reproduce the predictions of localization techniques. Second, we show that in the classical limit our result perfectly reproduces the existing prediction from classical string theory. In addition, we made a comparison with all existing weak coupling results and we found that our result interpolates smoothly between these two very different regimes of AdS/CFT. As a byproduct we found a generalization of the essential parts of the FiNLIE construction for the gamma-deformed case and discuss our results in the framework of the novel ${\bf P}μ$-formulation of the spectral problem.

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arXiv2015

Quantum spectral curve for arbitrary state/operator in AdS$_5$/CFT$_4$

We give a derivation of quantum spectral curve (QSC) - a finite set of Riemann-Hilbert equations for exact spectrum of planar N=4 SYM theory proposed in our recent paper Phys.Rev.Lett. 112 (2014). We also generalize this construction to all local single trace operators of the theory, in contrast to the TBA-like approaches worked out only for a limited class of states. We reveal a rich algebraic and analytic structure of the QSC in terms of a so called Q-system -- a finite set of Baxter-like Q-functions. This new point of view on the finite size spectral problem is shown to be completely compatible, though in a far from trivial way, with already known exact equations (analytic Y-system/TBA, or FiNLIE). We use the knowledge of this underlying Q-system to demonstrate how the classical finite gap solutions and the asymptotic Bethe ansatz emerge from our formalism in appropriate limits.

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arXiv2015

Quantum Spectral Curve for a Cusped Wilson Line in N=4 SYM

We show that the Quantum Spectral Curve (QSC) formalism, initially formulated for the spectrum of anomalous dimensions of all local single trace operators in N=4 SYM, can be extended to the generalized cusp anomalous dimension for all values of the parameters. We find that the large spectral parameter asymptotics and some analyticity properties have to be modified, but the functional relations are unchanged. As a demonstration, we find an all-loop analytic expression for the first two nontrivial terms in the small |phi \pm theta| expansion. We also present nonperturbative numerical results at generic angles which match perfectly 4-loop perturbation theory and the classical string prediction. The reformulation of the problem in terms of the QSC opens the possibility to explore many open questions. We attach to this paper several Mathematica notebooks which should facilitate future studies.

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arXiv2015

Quantum Spectral Curve at Work: From Small Spin to Strong Coupling in N=4 SYM

We apply the recently proposed quantum spectral curve technique to the study of twist operators in planar N=4 SYM theory. We focus on the small spin expansion of anomalous dimensions in the sl(2) sector and compute its first two orders exactly for any value of the 't Hooft coupling. At leading order in the spin S we reproduced Basso's slope function. The next term of order S^2 structurally resembles the Beisert-Eden-Staudacher dressing phase and takes into account wrapping contributions. This expansion contains rich information about the spectrum of local operators at strong coupling. In particular, we found a new coefficient in the strong coupling expansion of the Konishi operator dimension and confirmed several previously known terms. We also obtained several new orders of the strong coupling expansion of the BFKL pomeron intercept. As a by-product we formulated a prescription for the correct analytical continuation in S which opens a way for deriving the BFKL regime of twist two anomalous dimensions from AdS/CFT integrability.

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arXiv2015

NNLO BFKL Pomeron eigenvalue in N=4 SYM

We obtain an analytical expression for the Next-to-Next-to-Leading order of the Balitsky-Fadin-Kuraev-Lipatov (BFKL) Pomeron eigenvalue in planar SYM N=4 using Quantum Spectral Curve (QSC) integrability based method. The result is verified with more than 60 digits precision using the numerical method developed by us in a previous paper. As a byproduct we developed a general analytic method of solving the QSC perturbatively.

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arXiv2015

QCD Pomeron from AdS/CFT Quantum Spectral Curve

Using the methods of the recently proposed Quantum Spectral Curve (QSC) originating from integrability of ${\cal N}=4$ Super--Yang-Mills theory we analytically continue the scaling dimensions of twist-2 operators and reproduce the so-called pomeron eigenvalue of the Balitsky-Fadin-Kuraev-Lipatov (BFKL) equation. Furthermore, we recovered the Faddeev-Korchemsky Baxter equation for Lipatov's spin chain and also found its generalization for the next-to-leading order in the BFKL scaling. Our results provide a non-trivial test of QSC describing the exact spectrum in planar ${\cal N}=4$ SYM at infinitely many loops for a highly nontrivial non-BPS quantity and also opens a way for a systematic expansion in the BFKL regime.

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arXiv2014

Exact Slope and Interpolating Functions in ABJM Theory

Using the Quantum Spectral Curve approach we compute exactly an observable (called slope function) in the planar ABJM theory in terms of an unknown interpolating function h(λ) which plays the role of the coupling in any integrability based calculation in this theory. We verified our results with known weak coupling expansion in the gauge theory and with the results of semi-classical string calculations. Quite surprisingly at strong coupling the result is given by an explicit rational function of h(λ) to all orders. By comparing the structure of our result with that of an exact localization-based calculation for a similar observable in JHEP 1006 (2010) 011 we conjecture an exact expression for h(λ).

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arXiv2014

The Quantum Spectral Curve of the ABJM theory

Recently, it was shown that the spectrum of anomalous dimensions and other important observables in N = 4 SYM are encoded into a simple nonlinear Riemann-Hilbert problem: the Pμ-system or Quantum Spectral Curve. In this letter we present the Pμ-system for the spectrum of the ABJM theory. This may be an important step towards the exact determination of the interpolating function h(λ) characterising the integrability of the ABJM model. We also discuss a surprising symmetry between the Pμ-system equations for N = 4 SYM and ABJM.

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arXiv2013

Quantum spectral curve for AdS_5/CFT_4

We present a new formalism, alternative to the old TBA-like approach, for solution of the spectral problem of planar N = 4 SYM. It takes a concise form of a non-linear matrix Riemann-Hilbert problem in terms of a few Q-functions. We demonstrate the formalism for two types of observables - local operators at weak coupling and cusped Wilson lines in a near BPS limit.

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arXiv2013

On the Derivation of the Exact Slope Function

In this note we give a simple derivation of the exact slope function conjectured by Basso for the anomalous dimensions of Wilson operators in the sl2 sector of planar N=4 Super-Yang-Mills theory. We also discuss generalizations of this result for higher charges and other sectors.

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arXiv2012

Analytic Solution of Bremsstrahlung TBA

We consider the quark--anti-quark potential on the three sphere or the generalized cusp anomalous dimension in planar N=4 SYM. We concentrate on the vacuum potential in the near BPS limit with $L$ units of R-charge. Equivalently, we study the anomalous dimension of a super-Wilson loop with L local fields inserted at a cusp. The system is described by a recently proposed infinite set of non-linear integral equations of the Thermodynamic Bethe Ansatz (TBA) type. That system of TBA equations is very similar to the one of the spectral problem but simplifies a bit in the near BPS limit. Using techniques based on the Y-system of functional equations we first reduced the infinite system of TBA equations to a Finite set of Nonlinear Integral Equations (FiNLIE). Then we solve the FiNLIE system analytically, obtaining a simple analytic result for the potential! Surprisingly, we find that the system has equivalent descriptions in terms of an effective Baxter equation and in terms of a matrix model. At L=0, our result matches the one obtained before using localization techniques. At all other L's, the result is new. Having a new parameter, L, allows us to take the large L classical limit. We use the matrix model description to solve the classical limit and match the result with a string theory computation. Moreover, we find that the classical string algebraic curve matches the algebraic curve arising from the matrix model.

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arXiv2012

Solving the AdS/CFT Y-system

Using integrability and analyticity properties of the AdS5/CFT4 Y-system we reduce it to a finite set of nonlinear integral equations. The Z4 symmetry of the underlying coset sigma model, in its quantum version, allows for a deeper insight into the analyticity structure of the underlying Y-functions and T-functions, as well as for their analyticity friendly parameterization in terms of Wronskian determinants of Q-functions. As a check for the new equations, we reproduce the numerical results for the Konishi operator previously obtained from the original infinite Y-system.

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arXiv2012

Tailoring Three-Point Functions and Integrability IV. Theta-morphism

We compute structure constants in N=4 SYM at one loop using Integrability. This requires having full control over the two loop eigenvectors of the dilatation operator for operators of arbitrary size. To achieve this, we develop an algebraic description called the Theta-morphism. In this approach we introduce impurities at each spin chain site, act with particular differential operators on the standard algebraic Bethe ansatz vectors and generate in this way higher loop eigenvectors. The final results for the structure constants take a surprisingly simple form. For some quantities we conjecture all loop generalizations. These are based on the tree level and one loop patterns together and also on some higher loop experiments involving simple operators.

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