arXiv subjects

Yuri Makeenko

Publications and source records attributed to Yuri Makeenko.

At least 37 records · Page 2Linked to original sources

arXiv2011

An interplay between static potential and Reggeon trajectory for QCD string

I consider two cases where QCD string is described by an effective theory of long strings: the static potential and meson scattering amplitudes in the Regge regime. I show how they can be solved in the mean-field approximation, justified by the large number of space-time dimensions, and argue that it turns out to be exact. I compare contributions from QCD string and perturbative QCD and discuss experimental consequences for the scattering amplitudes.

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arXiv2010

Effective String Theory and QCD Scattering Amplitudes

QCD string is formed at the distances larger than the confinement scale and can be described by the Polchinski--Strominger effective string theory with a nonpolynomial action, which has nevertheless a well-defined semiclassical expansion around a long-string ground state. We utilize modern ideas about the Wilson-loop/scattering-amplitude duality to calculate scattering amplitudes and show that the expansion parameter in the effective string theory is small in the Regge kinematical regime. For the amplitudes we obtain the Regge behavior with a linear trajectory of the intercept (d-2)/24 in d dimensions, which is computed semiclassically as a momentum-space Luscher term, and discuss an application to meson scattering amplitudes in QCD.

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arXiv2010

Semiclassical Regge trajectories of noncritical string and large-N QCD

By properly treating the path integral over the boundary value of the Liouville field (associated with reparametrizations of the boundary contour) in open string theory, we derive consistent off-shell scattering amplitudes in d=26 dimensions. In d<26 we consider a recently proposed boundary ansatz which reproduces a semiclassical correction to the classical string (known as the Luscher term) and obtain in the semiclassical approximation a linear Regge trajectory with the intercept (d-2)/24. We associate it with the quark-antiquark Regge trajectory in large-N QCD and explain why it dominates over perturbative QCD when t > -few GeV^2.

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arXiv2010

Path Integral over Reparametrizations: Levy Flights versus Random Walks

We investigate the properties of the path integral over reparametrizations (= the boundary value of the Liouville field in open string theory). Discretizing the path integral, we apply the Metropolis-Hastings algorithm to numerical simulations of a proper (subordinator) stochastic process and find that typical trajectories are not Brownian but rather have discontinuities of the type of Levy's flights. We study a fractal structure of these trajectories and show that their Hausdorff dimension is zero. We confirm thereby the discretization and heuristic consideration of QCD scattering amplitudes by analytical and numerical calculations. We also perform Monte Carlo simulations of the path integral over reparametrization in the effective-string ansatz for a circular Wilson loop and discuss their subtleties associated with the discretization of Douglas' functional.

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arXiv2010

Quantum corrections from a path integral over reparametrizations

We study the path integral over reparametrizations that has been proposed as an ansatz for the Wilson loops in the large-$N$ QCD and reproduces the area law in the classical limit of large loops. We show that a semiclassical expansion for a rectangular loop captures the Lüscher term associated with $d=26$ dimensions and propose a modification of the ansatz which reproduces the Lüscher term in other dimensions, which is observed in lattice QCD. We repeat the calculation for an outstretched ellipse advocating the emergence of an analog of the Lüscher term and verify this result by a direct computation of the determinant of the Laplace operator and the conformal anomaly.

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arXiv2009

A Brief Introduction to Wilson Loops and Large N

A pedagogical introduction to Wilson loops, lattice gauge theory and the 1/N-expansion of QCD is presented. The three introductory lectures were given at the 37th ITEP Winter School of Physics, Moscow, February 9-16, 2009.

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arXiv2009

Wilson Loops and QCD/String Scattering Amplitudes

We generalize modern ideas about the duality between Wilson loops and scattering amplitudes in ${\cal N}=4$ SYM to large $N$ QCD by deriving a general relation between QCD meson scattering amplitudes and Wilson loops. We then investigate properties of the open-string disk amplitude integrated over reparametrizations. When the Wilson loop is approximated by the area behavior, we find that the QCD scattering amplitude is a convolution of the standard Koba-Nielsen integrand and a kernel. As usual poles originate from the first factor, whereas no (momentum dependent) poles can arise from the kernel. We show that the kernel becomes a constant when the number of external particles becomes large. The usual Veneziano amplitude then emerges in the kinematical regime where the Wilson loop can be reliably approximated by the area behavior. In this case we obtain a direct duality between Wilson loops and scattering amplitudes when spatial variables and momenta are interchanged, in analogy with the $\cal N$=4 SYM case.

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arXiv2009

Implementation of the Duality between Wilson loops and Scattering Amplitudes in QCD

We generalize modern ideas about the duality between Wilson loops and scattering amplitudes in ${\cal N}$=4 SYM to large-N (or quenched) QCD. We show that the area-law behavior of asymptotically large Wilson loops is dual to the Regge-Veneziano behavior of scattering amplitudes at high energies and fixed momentum transfer, when quark mass is small and/or the number of particles is large. We elaborate on this duality for string theory in a flat space, identifying the asymptotes of the disk amplitude and the Wilson loop of large-N QCD.

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arXiv2008

Topics in Cusped/Lightcone Wilson Loops

I review several old/new approaches to the string/gauge correspondence for the cusped/lightcone Wilson loops. The main attention is payed to SYM perturbation theory calculations at two loops and beyond and to the cusped loop equation. These three introductory lectures were given at the 48 Cracow School of Theoretical Physics: "Aspects of Duality", June 13-22, 2008, Zakopane, Poland.

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arXiv2007

Wilson Loops in 2D Noncommutative Euclidean Gauge Theory: 2. 1/θExpansion

We analyze the $1/θ$ and 1/N expansions of the Wilson loop averages $ _{U_θ(N)}$ in the two-dimensional noncommutative $U_θ(N)$ gauge theory with the parameter of noncommutativity $θ$. For a generic rectangular contour $C$, a concise integral representation is derived (non-perturbatively both in the coupling constant $g^{2}$ and in $θ$) for the next-to-leading term of the $1/θ$ expansion. In turn, in the limit when $θ$ is much larger than the area $A(C)$ of the surface bounded by $C$, the large $θ$ asymptote of this representation is argued to yield the next-to-leading term of the $1/θ$ series. For both of the expansions, the next-to-leading contribution exhibits only a power-like decay for areas $A(C)>>σ^{-1}$ (but $A(C)<<θ$) much larger than the inverse of the string tension $σ$ defining the range of the exponential decay of the leading term. Consequently, for large $θ$, it hinders a direct stringy interpretation of the subleading terms of the 1/N expansion in the spirit of Gross-Taylor proposal for the $θ=0$ commutative D=2 gauge theory.

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arXiv2006

Cusped SYM Wilson loop at two loops and beyond

We calculate the anomalous dimension of the cusped Wilson loop in ${\cal N}=4$ supersymmetric Yang-Mills theory to order $λ^2$ ($λ=g^2_{YM}N$). We show that the cancellation between the diagrams with the three-point vertex and the self-energy insertion to the propagator which occurs for smooth Wilson loops is not complete for cusped loops, so that an anomaly term remains. This term contributes to the cusp anomalous dimension. The result agrees with the anomalous dimensions of twist-two conformal operators with large spin. We verify the loop equation for cusped loops to order $λ^2$, reproducing the cusp anomalous dimension this way. We also examine the issue of summing ladder diagrams to all orders. We find an exact solution of the Bethe-Salpeter equation, summing light-cone ladder diagrams, and show that for certain values of parameters it reduces to a Bessel function. We find that the ladder diagrams cannot reproduce for large $λ$ the $\sqrtλ$-behavior of the cusp anomalous dimension expected from the AdS/CFT correspondence.

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arXiv2004

The First Thirty Years of Large-N Gauge Theory

I review some developments in the large-N gauge theory since 1974. The main attention is payed to: multicolor QCD, matrix models, loop equations, reduced models, 2D quantum gravity, free random variables, noncommutative theories, AdS/CFT correspondence.

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arXiv2002

Light-Cone Wilson Loops and the String/Gauge Correspondence

We investigate a Π-shape Wilson loop in N=4 super Yang--Mills theory, which lies partially at the light-cone, and consider an associated open superstring in AdS_5 x S^5. We discuss how this Wilson loop determines the anomalous dimensions of conformal operators with large Lorentz spin and present an explicit calculation in perturbation theory to order λ. We find the minimal surface in the supergravity approximation, that reproduces the Gubser, Klebanov and Polyakov prediction for the anomalous dimensions at large λ=g_YM^2 N, and discuss its quantum-mechanical interpretation.

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arXiv2000

Reduced Models and Noncommutative Gauge Theories

This is a short review of the relation between the Reduced Models and Noncommutative Yang-Mills Theories (NCYM) based on the work done in collaboration with J. Ambjorn, J. Nishimura and R. Szabo. Contents: 1.Twisted Eguchi-Kawai model (TEK), 2.Mapping onto NCYM, 3.Morita equivalence, 4.Fundamental matter, 5.Wilson loops in NCYM, 6.D-brane interpretation. Talk given at the 11th International Seminar "Quarks'2000", Pushkin, Russia, May 13-21, 2000 and the E.S.Fradkin Memorial Conference, Moscow, June 5-10, 2000.

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arXiv2000

Large-N Gauge Theories

Four pedagogical Lectures at the NATO-ASI on "Quantum Geometry" in Akureyri, Iceland, August 1999. Contents: 1. O(N) Vector Models, 2. Large-N QCD, 3. QCD in Loop Space, 4. Large-N Reduction

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arXiv1999

Formulation of Matrix Theory at Finite Temperature

The interaction between static D0-branes at finite temperature is considered in the matrix theory and the superstring theory. The results agree in both cases to the leading order in the supersymmetry violation by temperature, where the one-loop approximation is reliable. The effective static potential is short-ranged and attractive. Talk at the 32nd International Symposium Ahrenshoop on the Theory of Elementary Particles, Buckow, Germany, September 1-5, 1998.

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arXiv1997

Supersymmetric Matrix Models and the Meander Problem

We consider matrix-model representations of the meander problem which describes, in particular, combinatorics for foldings of closed polymer chains. We introduce a supersymmetric matrix model for describing the principal meander numbers. This model is of the type proposed by Marinari and Parisi for discretizing a superstring in D=1 while the supersymmetry is realized in D=0 as a rotational symmetry between bosonic and fermionic matrices. Using non-commutative sources, we reformulate the meander problem in a Boltzmannian Fock space whose annihilation and creation operators obey the Cuntz algebra. We discuss also the relation between the matrix models describing the meander problem and the Kazakov-Migdal model on a D-dimensional lattice.

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arXiv1997

Three Introductory Lectures in Helsinki on Matrix Models of Superstrings

These are short notes of three introductory lectures on recently proposed matrix models of Superstrings and M theory given at 5th Nordic Meeting on Supersymmetric Field and String Theories in Helsinki (March 10-12, 1997). Contents: M(atrix) theory of BFSS, From IIA to IIB with IKKT, The NBI matrix model.

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