't Hooft and Wilson loop ratios in the QCD plasma

The spatial 't Hooft loop measuring the electric flux and the spatial Wilsonloop measuring the magnetic flux are analyzed in hot SU(N) gauge theory. Both display area laws. On one hand the tension of the 't Hooft loop is perturbatively calculable, in the same sense as the pressure. We show that the O(g^3) contribution is absent. The ratio of multi-charged 't Hooft loops have a remarkably simple dependence on the charge, true up to, but not including, O(g^4). This dependence follows also from a simple model of free screened colour charges. On the other hand the surface tension of the Wilsonloop is non-perturbative. But in a model of screened free monopoles at very high temperature the known area law follows. The density of these monopoles starts to contribute to O(g^6) to the pressure. The ratio of the multicharged Wilson loops is calculable and identical to that of the 't Hooft loops.Comment: 28 pages, 8 figure

Non-Abelian Monopoles as the Origin of Dark Matter

We suggest that dark matter may be partially constituted by a dilute 't Hooft-Polyakov monopoles gas. We reach this conclusion by using the Georgi-Glashow model coupled to a dual kinetic mixing term $F{\tilde {\cal G}}$ where $F$ is the electromagnetic field and ${\cal G}$ the 't Hooft tensor. We show that these monopoles carry both (Maxwell) electric and (Georgi-Glashow) magnetic charges and the electric charge quantization condition is modified in terms of a dimensionless real parameter. This parameter could be determined from milli-charged particle experiments.Comment: 5 pp, no figure

Quantum 't Hooft operators and S-duality in N=4 super Yang-Mills

We provide a quantum path integral definition of an 't Hooft loop operator, which inserts a pointlike monopole in a four dimensional gauge theory. We explicitly compute the expectation value of the circular 't Hooft operators in N=4 super Yang-Mills with arbitrary gauge group G up to next to leading order in perturbation theory. We also compute in the strong coupling expansion the expectation value of the circular Wilson loop operators. The result of the computation of an 't Hooft loop operator in the weak coupling expansion exactly reproduces the strong coupling result of the conjectured dual Wilson loop operator under the action of S-duality. This paper demonstrates - for the first time - that correlation functions in N=4 super Yang-Mills admit the action of S-duality.Comment: 38 pages; v2: references added, typos fixe

Low-lying meson spectrum of large NCN_C strongly coupled lattice QCD

We compute the low energy mass spectrum of lattice QCD in the large $N_C$ limit. Expanding around a gauge-invariant ground state, which spontaneously breaks the discrete chiral symmetry, we derive an improved strong-coupling expansion and evaluate, for any value of $N_C$, the masses of the low-lying states in the unflavored meson spectrum. We then take the 't Hooft limit by rescaling $g^2 N_C\to g^2$; the 't Hooft limit is smooth and no arbitrary parameters are needed. We find, already at the fourth order of the strong coupling perturbation theory, a very good agreement between the results of our lattice computation and the known continuum values.Comment: 43 pages, 1 figure. Minor corrections. One reference added in section

The Intermediate Coupling Regime in the AdS/CFT Correspondence

The correspondence between the 't Hooft limit of N=4 super Yang-Mills theory and tree-level IIB superstring theory on AdS(5)xS(5) in a Ramond-Ramond background at values of lambda=g^2 N ranging from infinity to zero is examined in the context of unitarity. A squaring relation for the imaginary part of the holographic scattering of identical string fields in the two-particle channels is found, and a mismatch between weak and strong 't Hooft coupling is pointed out within the correspondence. Several interpretations and implications are proposed.Comment: 10 pages, LaTeX, reference adde

TransPlanckian Particles and the Quantization of Time

Trans-Planckian particles are elementary particles accelerated such that their energies surpass the Planck value. There are several reasons to believe that trans-Planckian particles do not represent independent degrees of freedom in Hilbert space, but they are controlled by the cis-Planckian particles. A way to learn more about the mechanisms at work here, is to study black hole horizons, starting from the scattering matrix Ansatz. By compactifying one of the three physical spacial dimensions, the scattering matrix Ansatz can be exploited more efficiently than before. The algebra of operators on a black hole horizon allows for a few distinct representations. It is found that this horizon can be seen as being built up from string bits with unit lengths, each of which being described by a representation of the SO(2,1) Lorentz group. We then demonstrate how the holographic principle works for this case, by constructing the operators corresponding to a field in space-time. The parameter t turns out to be quantized in Planckian units, divided by the period R of the compactified dimension.Comment: 12 pages plain tex, 1 figur

Positivity of hexagon perturbation theory

The hexagon-form-factor program was proposed as a way to compute three- and higher-point correlation functions in $\mathcal{N}=4$ super-symmetric Yang-Mills theory and in the dual AdS$_5\times$S$^5$ superstring theory, by exploiting the integrability of the theory in the 't Hooft limit. This approach is reminiscent of the asymptotic Bethe ansatz in that it applies to a large-volume expansion. Finite-volume corrections can be incorporated through L\"uscher-like formulae, though the systematics of this expansion is largely unexplored so far. Strikingly, finite-volume corrections may feature negative powers of the 't Hooft coupling $g$ in the small-$g$ expansion, potentially leading to a breakdown of the formalism. In this work we show that the finite-volume perturbation theory for the hexagon is positive and thereby compatible with the weak-coupling expansion for arbitrary $n$-point functions.Comment: v2: misprints corrected, further details on physical magnons adde