Yuri Makeenko

Finite N matrix models of noncommutative gauge theory

We describe a unitary matrix model which is constructed from discrete analogs of the usual projective modules over the noncommutative torus and use it to construct a lattice version of noncommutative gauge theory. The model is a discretization of the noncommutative gauge theories that arise from toroidal compactification of Matrix theory and it includes a recent proposal for a non-perturbative definition of noncommutative Yang-Mills theory in terms of twisted reduced models. The model is interpreted as a manifestly star-gauge invariant lattice formulation of noncommutative gauge theory, which reduces to ordinary Wilson lattice gauge theory for particular choices of parameters. It possesses a continuum limit which maintains both finite spacetime volume and finite noncommutativity scale. We show how the matrix model may be used for studying the properties of noncommutative gauge theory.

Nonperturbative dynamics of noncommutative gauge theory

Abstract We present a nonperturbative lattice formulation of noncommutative Yang–Mills theories in arbitrary even dimension. We show that lattice regularization of a noncommutative field theory requires finite lattice volume which automatically provides both an ultraviolet and an infrared cutoff. We demonstrate explicitly Morita equivalence of commutative U( p ) gauge theory with p · n f flavours of fundamental matter fields on a lattice of size L with twisted boundary conditions and noncommutative U(1) gauge theory with n f species of matter on a lattice of size p · L with single-valued fields. We discuss the relation with twisted large N reduced models and construct observables in noncommutative gauge theory with matter.

Light-Cone Wilson Loops and the String/Gauge Correspondence

We investigate a ?-shape Wilson loop in = 4 super Yang?Mills theory, which lies partially at the light-cone, and consider an associated open superstring in AdS5 ? S5. 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 ?. We find the minimal surface in the supergravity approximation, that reproduces the Gubser, Klebanov and Polyakov prediction for the anomalous dimensions at large ? = gYM2N, and discuss its quantum-mechanical interpretation.

Properties of D-branes in matrix model of IIB superstring

Abstract We discuss the properties of D-brane configurations in the matrix model of the type IIB superstring recently proposed by Ishibashi, Kawai, Kitazawa and Tsuchiya. We calculate the central charges in the supersymmetry algebra at infinite N and associate them with one- and five-branes present in IIB superstring theory. We consider classical solutions associated with static three- and five-branes and calculate their interactions at one loop in the matrix model. We discuss some aspects of the matrix-model formulation of the IIB superstring.

TOWARDS A NON-PERTURBATIVE FORMULATION OF IIB SUPERSTRINGS BY MATRIX MODELS

Abstract We address the problem of a non-perturbative formulation of superstring theory by means of the recently proposed matrix models. For the model by Ishibashi, Kawai, Kitazawa and Tsuchiya (IKKT), we perform one-loop calculation of the interaction between operator-like solutions identified with D-brane configurations of type IIB superstrings (in particular, for parallel moving and rotated static p-branes). Comparing to the superstring calculations, we show that the matrix model reproduces the superstring results only at small velocities or large distances, corresponding to keeping only the lowest mass open-string modes. We propose a modification of the IKKT matrix model introducing an integration over an additional Hermitian matrix required to have positive definite eigenvalues, which is similar to the square root of the metric in the continuum Schild formulation of IIB superstrings. We show that for this new matrix action the Nambu-Goto version of the Green-Schwarz action is reproduced even at quantum level.

Large-N Gauge Theories

Four pedagogical lectures on 0(N) vector models, large-N QCD, QCD in loop space, large-N reduction.

Cusped SYM Wilson loop at two loops and beyond

Abstract We calculate the anomalous dimension of the cusped Wilson loop in N = 4 supersymmetric Yang–Mills theory to order λ 2 ( λ = g YM 2 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 conclude that without interaction diagrams the ladder diagrams cannot reproduce the behavior of the cusp anomalous dimension expected for large λ from the AdS/CFT correspondence.

String theory in electromagnetic fields

A review of various aspects of superstrings in background electromagnetic fields is presented. Topics covered include the Born-Infeld action, spectrum of open strings in background gauge fields, the Schwinger mechanism, finite-temperature formalism and Hagedorn behaviour in external fields, Debye screening, D-brane scattering, thermodynamics of D-branes, and noncommutative field and string theories on D-branes. The electric field instabilities are emphasized throughout and contrasted with the case of magnetic fields. A new derivation of the velocity-dependent potential between moving D-branes is presented, as is a new result for the velocity corrections to the one-loop thermal effective potential.

More about one-loop effective action of open superstring in AdS5 × S5

A bstractWe reconsider the calculation of the one-loop effective action for an open Green-Schwarz superstring in the AdS5 × S5 background for a circular boundary loop. By an explicit computation of the ratio of relevant determinants, describing semi-classical fluctuations about the minimal surface in AdS and flat spaces, we show that it does not depend upon the AdS regularizing parameter ϵ. The only dependence upon ϵ resides in the reparametrization path integral of the exponential of the classical boundary action. We analyze how the result depends on the choice of the boundary condition imposed on fluctuating fields and show that, despite the fact that the contribution of individual angular modes changes, the product over the modes remains unchanged.

The QCD scattering amplitude from area behaved Wilson loops

Abstract We explicitly construct the dominant saddle-point trajectory in the sum-over-path representation of meson scattering amplitudes in large N QCD for area-behaved Wilson loops and show that it dominates in the Regge regime. The graphic representation of the leading trajectory is very similar to the diagrams widely used to illustrate meson scattering.