Exact Solution of Noncommutative Field Theory in Background Magnetic Fields

We obtain the exact non-perturbative solution of a scalar field theory defined on a space with noncommuting position and momentum coordinates. The model describes non-locally interacting charged particles in a background magnetic field. It is an exactly solvable quantum field theory which has non-trivial interactions only when it is defined with a finite ultraviolet cutoff. We propose that small perturbations of this theory can produce solvable models with renormalizable interactions.Comment: 9 Pages AMSTeX; Typos correcte

Exact Solution of the One-Dimensional Non-Abelian Coulomb Gas at Large N

The problem of computing the thermodynamic properties of a one-dimensional gas of particles which transform in the adjoint representation of the gauge group and interact through non-Abelian electric fields is formulated and solved in the large $N$ limit. The explicit solution exhibits a first order confinement-deconfinement phase transition with computable properties and describes two dimensional adjoint QCD in the limit where matter field masses are large.Comment: 8 pages, late

Interaction potential in compact three-dimensional QED with mixed action

We use a variational wave function to calculate the energy of the interaction between external charges in the compact Abelian gauge theory in 2+1 dimensions with mixed action. Our variational wave functions preserve the compact gauge invariance of the theory both in the vacuum and in the charged sectors. We find that a good estimate of the interaction energy is obtained only when we allow more variational parameters in the charged sector than in the vacuum sector. These extra parameters are the profile of an induced electric field. We find that the theory has a two-phase structure: When the charge-2 coupling is large and negative there is no mass gap in the theory and no confinement, while otherwise a mass gap is generated dynamically and the theory confines charges. The pure Wilson theory is in the confining phase.Comment: 22 pages, Latex -- final version, minor changes from first versio

Nonabelian D-branes and Noncommutative Geometry

We discuss the nonabelian world-volume action which governs the dynamics of N coincident Dp-branes. In this theory, the branes' transverse displacements are described by matrix-valued scalar fields, and so this is a natural physical framework for the appearance of noncommutative geometry. One example is the dielectric effect by which Dp-branes may be polarized into a noncommutative geometry by external fields. Another example is the appearance of noncommutative geometries in the description of intersecting D-branes of differing dimensions, such as D-strings ending on a D3- or D5-brane. We also describe the related physics of giant gravitons.Comment: 21 pages, Latex, ref. adde

Ladders for Wilson Loops Beyond Leading Order

We set up a general scheme to resum ladder diagrams for the quark-anti-quark potential in N=4 super-Yang-Mills theory, and do explicit calculations at the next-to-leading order. The results perfectly agree with string theory in AdS(5)xS(5) when continued to strong coupling, in spite of a potential order-of-limits problem.Comment: 18 pages, 5 figure

AdS/CFT duality at strong coupling

We study the strong coupling limit of AdS/CFT correspondence in the framework of a recently proposed fermionic formulation of the Bethe Ansatz equations governing the gauge theory anomalous dimensions. We provide examples of states that do not follow the Gubser-Klebanov-Polyakov law at large 't Hooft coupling $\lambda$, in contrast with recent results on the quantum string Bethe equations valid in that regime. This result indicates that the fermionic construction cannot be trusted at large $\lambda$, although it remains an efficient tool to compute the weak coupling expansion of anomalous dimensions.Comment: Presented at Nonlinear Physics. Theory and Experiment. IV Gallipoli, June 22 - July 1, 2006. To appear in the proceeding

Variational calculations with improved energy functionals in gauge theories

For a SU(N) Yang-Mills theory, we present variational calculations using gaussian wave functionals combined with an approximate projection on gauge invariant states. The projection amounts to correcting the energy of the gaussian states by substracting the spurious energy associated with gauge rotations. Based on this improved energy functional, we perform variational calculations of the interaction energy in the presence of external electric and magnetic fields. We verify that the ultraviolet behaviour of our approximation scheme is consistent, as it should, with that expected from perturbation theory. In particular, we recover in this variational framework the standard one-loop beta function, with a transparent interpretation of the screening and anti-screening contributions.Comment: 40 pages, no figure

Possible Pseudogap Phase in QCD

Thermal pion fluctuations, in principle, can completely disorder the phase of the quark condensate and thus restore chiral symmetry. If this happens before the quark condensate melts, strongly-interacting matter will be in the pseudogap state just above the chiral phase transition. The quark condensate does not vanish locally and quarks acquire constituent masses in the pseudogap phase, despite chiral symmetry is restored.Comment: 8 pages, 1 figure; v2: references added; v3: argumerts modified; v4: minor changes; v5: a misprint correcte

Static Potential in N=4 Supersymmetric Yang-Mills Theory

We compute the leading order perturbative correction to the static potential in ${\cal N}=4$ supersymmetric Yang-Mills theory. We show that the perturbative expansion contains infrared logarithms which, when resummed, become logarithms of the coupling constant. The resulting correction goes in the right direction to match the strong coupling behavior obtained from the AdS/CFT correspondence. We find that the strong coupling extrapolation of the sum of ladder diagrams goes as $\sqrt{g^2N}$, as in the supergravity approach.Comment: 8 pages, four figures using feynm

Correlation functions, null polygonal Wilson loops, and local operators

We consider the ratio of the correlation function of n+1 local operators over the correlator of the first n of these operators in planar N=4 super-Yang-Mills theory, and consider the limit where the first n operators become pairwise null separated. By studying the problem in twistor space, we prove that this is equivalent to the correlator of a n-cusp null polygonal Wilson loop with the remaining operator in general position, normalized by the expectation value of the Wilson loop itself, as recently conjectured by Alday, Buchbinder and Tseytlin. Twistor methods also provide a BCFW-like recursion relation for such correlators. Finally, we study the natural extension where n operators become pairwise null separated with k operators in general position. As an example, we perform an analysis of the resulting correlator for k=2 and discuss some of the difficulties associated to fixing the correlator completely in the strong coupling regime.Comment: 34 pages, 6 figures. v2: typos corrected and references added; v3: published versio