Quantum aspects of GMS solutions of non-commutative field theory and large <Emphasis Type="Italic">N</Emphasis> limit of matrix models

We investigate quantum aspects of Gopakumar–Minwalla–Strominger (GMS) solutions of non-commutative field theory (NCFT) in the large non-commutativity limit, . Building upon a quantitative map between the operator formulation of 2- (respectively, (2+1)-) dimensional NCFTs and large-N matrix models of c=0 (respectively,c=1) non-critical strings, we show that GMS solutions are quantum mechanically sensible only if we make an appropriate joint scaling of and N. For 't Hooft's scaling, GMS solutions are replaced by large-N saddle-point solutions. GMS solutions are recovered from saddle-point solutions in the small 't Hooft coupling regime, but are destabilized in the large 't Hooft coupling regime by quantum effects. We make comparisons between these large-N effects and the recently studied infrared effects in NCFTs. We estimate the U(N) symmetry breaking effects of the gradient term and argue that they are suppressed only in the small 't Hooft coupling regime. Received: 2 January 2002 / Published online: 26 April 2002     

ZQCD and universal matching to domain walls

We discuss the one loop matching procedure in ZQCD. Universality and Casimir scaling leave – in terms of the 't Hooft coupling – just two combinations of parameters to be fixed numerically. These numbers are then the same for any number of colours.     

't Hooft loop in SU(2) Yang-Mills theory

We study the behavior of the spatial and temporal 't Hooft loop at zero and finite temperature in the 4D SU(2) Yang-Mills theory, using a new numerical method. In the deconfined phase T > T(c), the spatial 't Hooft loop exhibits a dual string tension, which vanishes at T(c) with a 3D Ising-like critical exponent.     

A note on anomaly matching for finite density QCD

We note that the QCD phases at large finite density respect 't Hooft anomaly matching conditions. Specifically the spectrum of the light excitations possesses the correct quantum numbers required to obey global anomaly constraints. We argue that 't Hooft constraints can be used at finite density along with non perturbative methods to help selecting the correct phase.     

Chasing electric flux in hot QCD

In this talk, I present the status of attempts to analyze the behavior of the so-called spatial 't Hooft loop, which can be taken as an order parameter for the deconfinement phase transition in pure SU(N) gauge theory. While lattice data show a strikingly universal scaling of extracted k–string tensions for various values of k and N, the analytic approach to these observables might need some refinement.     

Fermionic Entropy in Kerr Black Hole Space–Time Background

Making use of brick-wall model proposed by 't Hooft, we have obtained the free energy and the entropy of Fermionic field and given out their expressions under the Kerr space–time background.     

Composite antisymmetric-tensor Nambu-Goldstone bosons in a four-fermion interaction model and the Higgs mechanism

Starting from the Fierz transform of the two-flavour 't Hooft interaction (a four-fermion Lagrangian with antisymmetric Lorentz tensor interaction terms augmented by an NJL type Lorentz scalar interaction responsible for dynamical symmetry breaking and quark mass generation), we show that: (1) antisymmetric tensor Nambu-Goldstone bosons appear provided that the scalar and tensor couplings stand in the proportion of two to one, which ratio appears naturally in the Fierz transform of the two-flavour 't Hooft interaction; (2) non-Abelian vector gauge bosons coupled to this system acquire a non-zero mass. Axial-vector fields do not mix with antisymmetric tensor fields, so there is no mass shift there. Received: 3 September 1999 / Revised Version: 3 November 1999 / Published online: 6 April 2000     

Integrable model of Yang-Mills theory and quasi-instantons

Within the framework of Euclidean conformal invariant Yang-Mills theory with a scalar field, a two-dimensional Hamiltonian system integrable for a definite relation between the coupling constants is considered. A particular solution of the Hamilton-Jacobi equation leads to a system of first-order equations providing a nonself-dual instanton-like solution of the model concerned. As a generalization of the system, a quasi-self-duality equation is suggested which is integrated by means of the 't Hooft ansatz and results in quasi-self-dual instantons (quasi-instantons).     

Geometric Quantization and Two Dimensional QCD

In this article, we will discuss geometric quantization of two dimensional Quantum Chromodynamics with fermionic or bosonic matter fields. We identify the respective large-N _c phase spaces as the infinite dimensional Grassmannian and the infinite dimensional Disc. The Hamiltonians are quadratic functions, and the resulting equations of motion for these classical systems are nonlinear. In [33], it was shown that the linearization of the equations of motion for the Grassmannian gave the 't Hooft equation. We will see that the linearization in the bosonic case leads to the scalar analog of the 't Hooft equation found in [36]. Received: 13 August 1996 / Accepted: 20 May 1997     

Breakdown of the operator-product expansion in the 't Hooft model

We consider deep inelastic scattering in the 't Hooft model. Being solvable, this model allows us to directly compute the moments associated with the cross section at next-to-leading order in the 1/Q(2) expansion. We perform the same computation using the operator-product expansion. We find that all the terms match in both computations except for one in the hadronic side, which is proportional to a nonlocal operator. The basics of the result suggest that a similar phenomenon may occur in four dimensions in the large N(c) limit.     

Strong coupling for planar SYM theory: An all-order result

We propose a scheme for determining a generalised scaling function, namely the Sudakov factor in a peculiar double scaling limit for high spin and large twist operators belonging to the sl(2) sector of planar SYM. In particular, we perform explicitly the all-order computation at strong 't Hooft coupling regarding the first (contribution to the) generalised scaling function. Moreover, we compare our asymptotic results with the numerical solutions finding a very good agreement and evaluate numerically the non-asymptotic contributions. Eventually, we illustrate the agreement and prediction on the string side.     

Lattice gases and exactly solvable models

We detail the construction of a family of lattice gas automata based on a model of 't Hooft, proceeding by use of symmetry principles to define first the kinematics of the model and then the dynamics. A spurious conserved quantity appears; we use it to effect a radical transformation of the model into one whose spacetime configurations are equivalent to the two-dimensional states of an exactly solvable statistical mechanics model, the symmetric eight-vertex model with parameters restricted to a disorder variety. We comment on the implications of this identification for the original lattice gas.     

C-theorem for two dimensional chiral theories

We discuss an extension of the C-theorem to chiral theories. We show that two monotonically decreasing C-functions can be introduced. However, their difference is a constant of the renormalization group flow. This constant reproduces the 't Hooft anomaly matching conditions.     

Black hole thermodynamics from calculations in strongly coupled gauge theory

We develop an approximation scheme for the quantum mechanics of N D0-branes at finite temperature in the 't Hooft large- N limit. The entropy of the quantum mechanics calculated using this approximation agrees well with the Bekenstein-Hawking entropy of a ten-dimensional nonextremal black hole with 0-brane charge. This result is in accordance with the duality conjectured by Itzhaki, Maldacena, Sonnenschein, and Yankielowicz [Phys. Rev. D 58, 046004 (1998)]. Our approximation scheme provides a model for the density matrix which describes a black hole in the strongly coupled quantum mechanics.     

Magnetic monopoles and non-Abelian gauge theories

We review some properties of magnetic monopoles in non-Abelian gauge theories. Removal of Dirac string singularities and generalizations of the Wu-Yang solution that follow from this procedure are described. A discussion of the possible relevance of monopoles in strong interaction models and their role in quark confinement schemes is given. The magnetic monopole soliton discovered by 't Hooft and Polyakov, the first order formalism developed by Bogomolny, and extensions of these ideas are illustrated.Work supported in part by the U.S. Energy Research and Development Administration under Contract No. EY-76-C-02-2232B^*000.     

Thermal spectral functions of strongly coupled N = 4 supersymmetric Yang-Mills theory

We use the gauge-gravity duality conjecture to compute spectral functions of the stress-energy tensor in finite-temperature N = 4 supersymmetric Yang-Mills theory in the limit of large N(c) and large 't Hooft coupling. The spectral functions exhibit peaks characteristic of hydrodynamic modes at small frequency, and oscillations at intermediate frequency. The nonperturbative spectral functions differ qualitatively from those obtained in perturbation theory. The results may prove useful for lattice studies of transport processes in thermal gauge theories.     

Black Hole Entropy: Membrane Approach

The wall contribution character of the Bekenstein–Hawking entropy in the brick-wall model leads us to propose a new method of computing the entropy of a black hole. In our model, the entropy is attributed to the dynamical degrees of the field covering the two dimensional membranes just outside the horizon. A cutoff different from the model of 't Hooft is necessarily introduced. It can be treated as an increase in horizon because of the space–time fluctuations. It is also shown that our method can be applied to the nonstatic case, such as Vaidya–deSitter space–time, and the final result relies on a time-dependent cutoff different from the brick-wall model.     

Quantization and Renormalization of the Manifest Left–Right Symmetric Model of Electroweak Interactions

Quantization and renormalization of the left–right symmetric model is the main purpose of the paper. First the model at tree level with a Higgs sector containing one bidoublet and two triplets is precisely discussed. Then the canonical quantization and Faddeev–Popov Lagrangian are carried out ('t Hooft gauge). The BRST symmetry is discussed. Subsequently the on-mass-shell renormalization is performed and, as a test of consistency, the renormalization of the ZN_iN_j vertex is analyzed.     

Planar amplitudes in maximally supersymmetric Yang-Mills theory

The collinear factorization properties of two-loop scattering amplitudes in dimensionally regulated N=4 super-Yang-Mills theory suggest that, in the planar ('t Hooft) limit, higher-loop contributions can be expressed entirely in terms of one-loop amplitudes. We demonstrate this relation explicitly for the two-loop four-point amplitude and, based on the collinear limits, conjecture an analogous relation for n-point amplitudes. The simplicity of the relation is consistent with intuition based on the anti-de Sitter/conformal field theory correspondence that the form of the large-N(c) L-loop amplitudes should be simple enough to allow a resummation to all orders.