Loop expansion in Yang-Mills thermodynamics

We argue that a selfconsistent spatial coarse-graining, which involves interacting (anti)calorons of unit topological charge modulus, implies that real-time loop expansions of thermodynamical quantities in the deconfining phase of SU(2) and SU(3) Yang-Mills thermodynamics are, modulo 1PI resummations, determined by a finite number of connected bubble diagrams.Comment: 15 pages, 2 figures, v5: discussion of much more severely constrained nonplanar situation included in Sec.

One Monopole with k Singularities

We present all charge one monopole solutions of the Bogomolny equation with k prescribed Dirac singularities for the gauge groups U(2), SO(3), or SU(2). We analyze these solutions comparing them to the previously known expressions for the cases of one or two singularities.Comment: 12 pages, LaTe

Constraints on dark matter particles charged under a hidden gauge group from primordial black holes

In order to accommodate increasingly tighter observational constraints on dark matter, several models have been proposed recently in which dark matter particles are charged under some hidden gauge group. Hidden gauge charges are invisible for the standard model particles, hence such scenarios are very difficult to constrain directly. However black holes are sensitive to all gauge charges, whether they belong to the standard model or not. Here, we examine the constraints on the possible values of the dark matter particle mass and hidden gauge charge from the evolution of primordial black holes. We find that the existence of the primordial black holes with reasonable mass is incompatible with dark matter particles whose charge to mass ratio is of the order of one. For dark matter particles whose charge to mass ratio is much less than one, we are able to exclude only heavy dark matter in the mass range of 10^(11) GeV - 10^(16) GeV. Finally, for dark matter particles whose charge to mass ratio is much greater than one, there are no useful limits coming from primordial black holes.Comment: accepted for publication in JCA

Rectangular Wilson Loops at Large N

This work is about pure Yang-Mills theory in four Euclidean dimensions with gauge group SU(N). We study rectangular smeared Wilson loops on the lattice at large N and relatively close to the large-N transition point in their eigenvalue density. We show that the string tension can be extracted from these loops but their dependence on shape differs from the asymptotic prediction of effective string theory.Comment: 47 pages, 21 figures, 8 table

Diagonal deformations of thin center vortices and their stability in Yang-Mills theories

The importance of center vortices for the understanding of the confining properties of SU(N) Yang-Mills theories is well established in the lattice. However, in the continuum, there is a problem concerning the relevance of center vortex backgrounds. They display the so called Savvidy-Nielsen-Olesen instability, associated with a gyromagnetic ratio $g^{(b)}_m=2$ for the off-diagonal gluons. In this work, we initially consider the usual definition of a {\it thin} center vortex and rewrite it in terms of a local color frame in SU(N) Yang-Mills theories. Then, we define a thick center vortex as a diagonal deformation of the thin object. Besides the usual thick background profile, this deformation also contains a frame defect coupled with gyromagnetic ratio $g^{(d)}_m=1$, originated from the charged sector. As a consequence, the analysis of stability is modified. In particular, we point out that the defect should stabilize a vortex configuration formed by a pair of straight components separated by an appropriate finite distance.Comment: 20 pages, LaTe

Holographic Phase Transition to Topological Dyons

The dynamical stability of a Julia-Zee solution in the AdS background in a four dimensional Einstein-Yang-Mills-Higgs theory is studied. We find that the model with a vanishing scalar field develops a non-zero value for the field at a certain critical temperature which corresponds to a topological dyon in the bulk and a topological phase transition at the boundary.Comment: 18 pages, 2 figures, 2 tables, sections 2 and 4 are shortened, an error in the last part of section 5 is corrected and equations are modified. This version to be published in JHE

Wilson loops stability in the gauge/string correspondence

We study the stability of some classical string worldsheet solutions employed for computing the potential energy between two static fundamental quarks in confining and non-confining gravity duals. We discuss the fixing of the diffeomorphism invariance of the string action, its relation with the fluctuation orientation and the interpretation of the quark mass substraction worldsheet needed for computing the potential energy in smooth (confining) gravity background. We consider various dual gravity backgrounds and show by a numerical analysis the existence of instabilities under linear fluctuations for classical string embedding solutions having positive length function derivative $L'(r_0)>0$. Finally we make a brief discussion of 't Hooft loops in non-conformal backgrounds.Comment: 34 pages, 36 figures. Reference added. Final version JHEP accepte

The semi-classical expansion and resurgence in gauge theories: new perturbative, instanton, bion, and renormalon effects

We study the dynamics of four dimensional gauge theories with adjoint fermions for all gauge groups, both in perturbation theory and non-perturbatively, by using circle compactification with periodic boundary conditions for the fermions. There are new gauge phenomena. We show that, to all orders in perturbation theory, many gauge groups are Higgsed by the gauge holonomy around the circle to a product of both abelian and nonabelian gauge group factors. Non-perturbatively there are monopole-instantons with fermion zero modes and two types of monopole-anti-monopole molecules, called bions. One type are "magnetic bions" which carry net magnetic charge and induce a mass gap for gauge fluctuations. Another type are "neutral bions" which are magnetically neutral, and their understanding requires a generalization of multi-instanton techniques in quantum mechanics - which we refer to as the Bogomolny-Zinn-Justin (BZJ) prescription - to compactified field theory. The BZJ prescription applied to bion-anti-bion topological molecules predicts a singularity on the positive real axis of the Borel plane (i.e., a divergence from summing large orders in peturbation theory) which is of order N times closer to the origin than the leading 4-d BPST instanton-anti-instanton singularity, where N is the rank of the gauge group. The position of the bion--anti-bion singularity is thus qualitatively similar to that of the 4-d IR renormalon singularity, and we conjecture that they are continuously related as the compactification radius is changed. By making use of transseries and Ecalle's resurgence theory we argue that a non-perturbative continuum definition of a class of field theories which admit semi-classical expansions may be possible.Comment: 112 pages, 7 figures; v2: typos corrected, discussion of supersymmetric models added at the end of section 8.1, reference adde

Matrix Models for the Black Hole Information Paradox

We study various matrix models with a charge-charge interaction as toy models of the gauge dual of the AdS black hole. These models show a continuous spectrum and power-law decay of correlators at late time and infinite N, implying information loss in this limit. At finite N, the spectrum is discrete and correlators have recurrences, so there is no information loss. We study these models by a variety of techniques, such as Feynman graph expansion, loop equations, and sum over Young tableaux, and we obtain explicitly the leading 1/N^2 corrections for the spectrum and correlators. These techniques are suggestive of possible dual bulk descriptions. At fixed order in 1/N^2 the spectrum remains continuous and no recurrence occurs, so information loss persists. However, the interchange of the long-time and large-N limits is subtle and requires further study.Comment: 35 pages, 11 eps figures; v.2 minor typos fixe

Soliton pair creation in classical wave scattering

We study classical production of soliton-antisoliton pairs from colliding wave packets in (1+1)-dimensional scalar field model. Wave packets represent multiparticle states in quantum theory; we characterize them by energy E and particle number N. Sampling stochastically over the forms of wave packets, we find the entire region in (E,N) plane which corresponds to classical creation of soliton pairs. Particle number is parametrically large within this region meaning that the probability of soliton-antisoliton pair production in few-particle collisions is exponentially suppressed.Comment: 16 pages, 8 figures, journal version; misprint correcte