We consider SU(N) Yang-Mills theory on the space R^1\times S^3 with Minkowski signature (-+++). The condition of SO(4)-invariance imposed on gauge fields yields a bosonic matrix model which is a consistent truncation of the plane wave matrix model. For matrices parametrized by a scalar ϕ, the Yang-Mills equations are reduced to the equation of a particle moving in the double-well potential. The classical solution is a bounce, i.e. a particle which begins at the saddle point ϕ=0 of the potential, bounces off the potential wall and returns to ϕ=0. The gauge field tensor components parametrized by ϕare smooth and for finite time both electric and magnetic fields are nonvanishing. The energy density of this non-Abelian dyon configuration does not depend on coordinates of R^1\times S^3 and the total energy is proportional to the inverse radius of S^3. We also describe similar bounce dyon solutions in SU(N) Yang-Mills theory on the space R^1\times S^2 with signature (-++). Their energy is proportional to the square of the inverse radius of S^2. From the viewpoint of Yang-Mills theory on R^{1,1}\times S^2 these solutions describe non-Abelian (dyonic) flux tubes extended along the x^3-axis.
In the previous paper, we have shown the existence of magnetic monopoles in the pure $SU(2)$ Yang--Mills theory with a gauge-invariant mass term for the gluon field being introduced. In this paper, we extend our previous construction of magnetic monopoles to obtain dyons with both magnetic and electric charges. In fact, we solve under the static and spherically symmetric ansatz the field equations of the $SU(2)$ "complementary" gauge-scalar model, which is the $SU(2)$ Yang--Mills theory coupled to a single adjoint scalar field whose radial degree of freedom is eliminated. We show that the nove…
We construct non-BPS dyon solutions of N=4 SU(n) supersymmetric Yang-Mills theory. These solutions are the worldvolume solitons which describe non-BPS Type IIB non-planar string junctions connecting n parallel D3-branes. The solutions are smooth deformations of the 1/4 BPS states which describe planar string junctions.
We consider the BPS dyonic instantons in the 5-dim supersymmetric Yang-Mills Chern-Simons theories. Its field theoretic structures and the moduli space dynamics in term of the ADHM data have been explored in detail. We find that the field theoretic Chern-Simons term leads to an effective magnetic field on instanton moduli space.
We study the dyon spectrum in $N=2$ Super Yang-Mills theory with gauge group $SU(2)$ coupled to $N_f$ matter multiplets in the fundamental representation. For magnetic charge one and two we determine the spectrum explicitly and show that it is in agreement with the duality predictions of Seiberg and Witten. We briefly discuss the extension to higher charge monopoles for the self-dual $N_f=4$ case and argue that the conjectured spectrum of dyons predicts the existence of certain harmonic spinors on the moduli space of higher charge monopoles.
We show that dyon and magnetic monopole can be constructed in the gauge-independent way for the $SU(2)$ Yang--Mills theory even in the absence of the scalar field. This result is derived from the recent proposal for obtaining non-trivial topological configurations responsible for quark confinement in the Yang-Mills theory based on the Confinement-Higgs complementary relationship between the pure Yang-Mills theory and the gauge-scalar model with an adjoint scalar field of the fixed length. We discuss how such configurations have the implications for quark confinement.
We investigate finite energy solutions of Yang-Mills--Chern-Simons systems in odd spacetime dimensions, d=2n+1, with n>2. This can be carried out systematically for all n, but the cases n=3,4 corresponding to a 7,8 dimensional spacetime are treated concretely. These are static and spherically symmetric configurations, defined in a flat Minkowski background. The value of the electric charge is fixed by the Chern-Simons coupling constant.
We consider Euclidean SU(N) Yang-Mills theory on the space GxR, where G is a compact semisimple Lie group, and introduce first-order BPS-type equations which imply the full Yang-Mills equations. For gauge fields invariant under the adjoint G-action these BPS equations reduce to first-order matrix equations, to which we give instanton solutions. In the case of G=SU(2)=S^3, our matrix equations are recast as Nahm equations, and a further algebraic reduction to the Toda chain equations is presented and solved for the SU(3) example. Finally, we change the metric on GxR to Minkowski and construct f…
We use the low energy effective $U(1)^r$ action on the Coulomb branch of ${\cal N}=4$ super Yang-Mills theory to construct approximate field configurations for solitonic dyons in these theories, building on the brane prong description developed in hep-th/0101114. This dovetails closely with the corresponding description of these dyons as string webs stretched between D-branes in the transverse space. The resulting picture within these approximations shows the internal structure of these dyons (for fixed asymptotic charges) to be molecule-like, with multiple charge cores held together at equili…
We show that in a certain region of a negative coordinate axis, the U(1amaharia) sector of the static dyonic solutions to the noncommutative U(4) N=4 Super Yang-Mills (SYM) can be consistently decoupled from the SU(4) to {\it all orders in the noncommutativity parameter}. We show the above decoupling in two ways. First, we show the noncommutative dyon being the same as the commutative dyon, is a consistent solution to noncommutative equations of motion in that region of noncommutative space. Second, as an example of decoupling of a non-null U(1) sector, we also obtain a family of solutions wit…
We review work on construction of Monopoles in higher dimensions. These are solutions to a particular class of models descending from Yang--Mills systems on even dimensional bulk, with Spheres as codimensions. The topological lower bounds on the Yang-Mills action translate to Bogomol'nyi lower bounds on the residual Yang-Mills-Higgs systems. Mostly, consideration is restricted to 8 dimensional bulk systems, but extension to the arbitrary case follows systematically. After presenting the monopoles, the corresponding dyons are also constructed. Finally, new Chern-Simons densities expressed in te…
We have studied a modified Yang-Mills-Higgs system coupled to Einstein gravity. The modification of the Einstein-Hilbert action involves a direct coupling of the Higgs field to the scalar curvature. In this modified system we are able to write a Bogomol'nyi type condition in curved space and demonstrate that the positive static energy functional is bounded from below. We then investigate non-Abelian sperically symmetric static solutions in a similar fashion to the `t Hooft-Polyakov monopole. After reviewing previously studied monopole solutions of this type, we extend the formalism to included…
We investigate the stability of four-dimensional dyonic soliton and black hole solutions of ${\mathfrak {su}}(2)$ Einstein-Yang-Mills theory in anti-de Sitter space. We prove that, in a neighbourhood of the embedded trivial (Schwarzschild-)anti-de Sitter solution, there exist non-trivial dyonic soliton and black hole solutions of the field equations which are stable under linear, spherically symmetric, perturbations of the metric and non-Abelian gauge field.
We study dyonic soliton and black hole solutions of the ${\mathfrak {su}}(2)$ Einstein-Yang-Mills equations in asymptotically anti-de Sitter space. We prove the existence of non-trivial dyonic soliton and black hole solutions in a neighbourhood of the trivial solution. For these solutions the magnetic gauge field function has no zeros and we conjecture that at least some of these non-trivial solutions will be stable. The global existence proof uses local existence results and a non-linear perturbation argument based on the (Banach space) implicit function theorem.
We apply the BPS Lagrangian method~\cite{Atmaja:2015umo} to derive BPS equations of monopole and dyon in the $SU(2)$ Yang-Mills-Higgs model, Nakamula-Shiraishi models, and their Generalized versions. We argue that by identifying the effective fields of scalar field, $f$, and of time-component gauge field, $j$, explicitly by $j=βf$ with $β$ is a real constant, the usual BPS equations for dyon can be obtained naturally. We validate this identification by showing that both Euler-Lagrange equations for $f$ and $j$ are identical in the BPS limit. The value of $β$ is bounded to $|β|<1$ due to realit…
The static Yang-Mills-Higgs dyonic instanton is shown to have a non-vanishing, but anti-self-dual, angular momentum 2-form with skew eigenvalues equal to the electric charge; for large charge the angular momentum causes the instanton to expand into a hyper-spherical shell. A class of exact multi dyonic instantons is then found and then generalized to a new class of 1/4 supersymmetric, non-singular, stationary, exact solutions of the ten-dimensional supergravity/Yang-Mills theory. These self-gravitating dyonic instantons yield new heterotic string solitons, to leading order in the inverse strin…
Here we study the global existence of `hairy' dyonic black hole and dyon solutions to four dimensional, anti-de Sitter Einstein-Yang-Mills theories for a general simply-connected and semisimple gauge group $G$, for so-called topologically symmetric systems, concentrating here on the regular case. We generalise here cases in the literature which considered purely magnetic spherically symmetric solutions for a general gauge group and topological dyonic solutions for $\mathfrak{su}(N)$. We are able to establish the global existence of non-trivial solutions to all such systems, both near existing …
We construct axially symmetric dyons in SU(2) Yang-Mills-Higgs theory. In the Prasad-Sommerfield limit, they are obtained via scaling relations from axially symmetric multimonopole solutions. For finite Higgs self-coupling they are constructed numerically.
We count the supersymmetric bound states of many distinct BPS monopoles in N=4 Yang-Mills theories and in pure N=2 Yang-Mills theories. The novelty here is that we work in generic Coulombic vacua where more than one adjoint Higgs fields are turned on. The number of purely magnetic bound states is again found to be consistent with the electromagnetic duality of the N=4 SU(n) theory, as expected. We also count dyons of generic electric charges, which correspond to 1/4 BPS dyons in N=4 theories and 1/2 BPS dyons in N=2 theories. Surprisingly, the degeneracy of dyons is typically much larger than …
Dyonic classical solutions of Yang-Mills theory are considered and the complete set of fermionic zero modes of these solutions are studied. Representing the QCD vacuum as a gas of dyons, one obtains chiral symmetry breaking due to zero modes similarly to the case of instantonic vacuum.
We determine the low energy dynamics of monopoles in pure N=2 Yang-Mills theories for points in the vacuum moduli space where the two Higgs fields are not aligned. The dynamics is governed by a supersymmetric quantum mechanics with potential terms and four real supercharges. The corresponding superalgebra contains a central charge but nevertheless supersymmetric states preserve all four supercharges. The central charge depends on the sign of the electric charges and consequently so does the BPS spectrum. We focus on the SU(3) case where certain BPS states are realised as zero-modes of a Dirac …
We construct new axially symmetric solutions of SU(2) Yang-Mills theory in a four dimensional anti-de Sitter spacetime. Possessing nonvanishing nonabelian charges, these regular configurations have also a nonzero angular momentum. Numerical arguments are also presented for the existence of rotating solutions of Einstein-Yang-Mills equations in an asymptotically anti-de Sitter spacetime.
We study dyonic instantons in (4+1) dimensional Yang-Mills theory. Especially we consider the most general two instanton solution given by the Jackiw-Nohl-Rebbi ansatz and find its dyonic version. By exploring the zeros of the Higgs field, we rederive the porism structure of triangles in this solution and also find the magnetic monopole string loop. This leads to the identification of dyonic instanton with the supertube inserted between D4 branes.
A continuum of new monopole and dyon solutions in the Einstein-Yang-Mills theory in asymptotically anti-de Sitter space are found. They are regular everywhere and specified with their mass, and non-Abelian electric and magnetic charges. A class of monopole solutions which have no node in non-Abelian magnetic fields are shown to be stable against spherically symmetric linear perturbations.
Scaling behavior in the moduli space of monopole and dyon solutions in the Einstein-Yang-Mills theory in the asymptotically anti-de Sitter space is derived. The mass of monopoles and dyons scales with respect to their magnetic and electric charges, independent of the values of the cosmological constant and gauge coupling constant. The stable monopole and dyon solutions are approximated by solutions in the fixed anti-de Sitter spacetime. Unstable solutions can be viewed as the Bartnik-McKinnon solutions dressed with monopole and dyon solutions in the fixed anti-de Sitter space.
We study the profile functions of two overlapped dyons at infinity. We assume that the superposition of two dyons satisfies Yang-Mills (Y-M) equation and then we find new equations of motion for individual dyons which do not satisfy the original Y-M equation, anymore. By solving these new equations, we find out that the profile functions of two overlapped dyons of the same type at infinity, looks like the profile functions of one dyon. However, the superposition of two dyons of different types gives trivial holonomy and therefore no contribution in the confinement phase is observed.
Three dyon solutions to the SU(2) Yang-Mills-Higgs system are presented. These solutions are obtained from the BPS dyon by allowing the gauge fields to be complex, or by letting the free parameter of the BPS solution become imaginary. In all cases however the physically measurable quantities connected with these new solutions are entirely real. Although the new solutions are mathematically simple variations of the BPS solution, they have one or more physically distinct characteristics.
In the pure Einstein-Yang-Mills theory in four dimensions there exist monopole and dyon solutions. The spectrum of the solutions is discrete in asymptotically flat or de Sitter space, whereas it is continuous in asymptotically anti-de Sitter space. The solutions are regular everywhere and specified with their mass, and non-Abelian electric and magnetic charges. In asymptotically anti-de Sitter space a class of monopole solutions have no node in non-Abelian magnetic fields, and are stable against spherically symmetric perturbations.
Regular monopole and dyon solutions to the SU(2) Einstein Yang-Mills equations in asymptotically anti-de Sitter space are discussed. A class of monopole solutions are shown to be stable against spherically symmetric linear perturbations.
We consider vortex-type solutions in $d=5$ dimensions of the Einstein gravity coupled to a nonabelian SU(2) field posessing a nonzero electric part. After the dimensional reduction, this corresponds to a $d=4$ Einstein-Yang-Mills-Higgs-U(1)-dilaton model. A general axially symmetric ansatz is presented, and the properties of the spherically symmetric solutions are analysed.
A continuum of monopole, dyon and black hole solutions exist in the Einstein-Yang-Mills theory in asymptotically anti-de Sitter space. Their structure is studied in detail. The solutions are classified by non-Abelian electric and magnetic charges and the ADM mass. The stability of the solutions which have no node in non-Abelian magnetic fields is established. There exist critical spacetime solutions which terminate at a finite radius, and have universal behavior. The moduli space of the solutions exhibits a fractal structure as the cosmological constant approaches zero.
We study three-dimensional Yang-Mills-Higgs theories with and without a Chern-Simons interaction. We find that these theories admit a rich spectrum of vortex solitons carrying both a topological charge and a global flavour charge. We further derive a low-energy description of the vortex dynamics from a gauged linear sigma model on the vortex worldline.
We present an explicit classical dyon solution for the noncommutative version of the Yang-Mills-Higgs model (in the Prasad-Sommerfield limit) with a tehta term. We show that the relation between classical electric and magnetic charges also holds in noncommutative space. Extending the Noether approach to the case of a noncommutative gauge theory, we analyze the effect of CP violation at the quantum level, induced both by the theta term and by noncommutativity and we prove that the Witten effect formula for the dyon charge remains the same as in ordinary space.
Based on a detailed analysis of nonlinear field equations of the SU(2) Yang-Mills-Higgs system, we obtain the effective field theory describing low-energy interaction of BPS dyons and massless particles (i.e., photons and Higgs particles). Our effective theory manifests electromagnetic duality and spontaneously broken scale symmetry, and reproduces the multimonopole moduli space dynamics of Manton in a suitable limit. Also given is a generalization of our approach to the case of BPS dyons in a gauge theory with an arbitrary gauge group that is maximally broken.
Einstein- Schroedinger (ES) non-symmetric theory has been extended to accommodate the Abelian and non-Abelian gauge theories of dyons in terms of the quaternion-octonion metric realization. Corresponding covariant derivatives for complex, quaternion and octonion spaces in internal gauge groups are shown to describe the consistent field equations and generalized Dirac equation of dyons. It is also shown that quaternion and octonion representations extend the so-called unified theory of gravitation and electromagnetism to the Yang-Mill's fields leading to two SU(2) gauge theories of internal spa…
A quarter-BPS dyon in $\mathcal{N}=4$ super Yang-Mills theory is generically `decadent' in that it is stable only in some regions of the moduli space and decays on submanifolds in the moduli space. Using this fact, and from the degeneracy of the system close to the decay, a new derivation for the degeneracy of such dyons is given. The degeneracy obtained from these very simple physical considerations is in precise agreement with the results obtained from index computations in all known cases. Similar considerations apply to dyons in $\mathcal{N}=2$ gauge theories. The relation between the $\ma…
The spacetime dependent lagrangian formalism of references [1-2] is used to obtain is used to obtain a classical solution of Yang-Mills theory. This is then used to obtain an estimate of the vacuum expectation value of the Higgs field,{\it viz.} $ϕ_{a}=A/e$, where $A$ is a constant and $e$ is the Yang-Mills coupling (related to the usual electric charge).The solution can also accommodate non-commuting coordinates on the boundary of the theory which may be used to construct $D$-brane actions. The formalism is also used to obtain the Deser-Gomberoff-Henneaux-Teitelboim results [10] for dyon char…
We study the existence of monopole bound states saturating the BPS bound in N=2 supersymmetric Yang-Mills theories. We describe how the existence of such bound states relates to the topology of index bundles over the moduli space of BPS solutions. Using an $L^2$ index theorem, we prove the existence of certain BPS states predicted by Seiberg and Witten based on their study of the vacuum structure of N=2 Yang-Mills theories.
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.
We systematically construct and study smooth supersymmetric solutions in 5 dimensional N=1 Yang-Mills-Einstein supergravity. Our solution is based on the ADHM construction of (dyonic) multi-instantons in Yang-Mills theory, which extends to the gravity-coupled system. In a simple supergravity model obtained from N=2 theory, our solutions are regular ring-like configurations, which can also be interpreted as supertubes. By studying the SU(2) 2-instanton example in detail, we find that angular momentum is maximized, with fixed electric charge, for circular rings. This feature is qualitatively sam…
We use the well-known Bogomolny's equations, in general coordinate system, for BPS monopoles and dyons in the $SU(2)$ Yang-Mills-Higgs model to obtain an explicit form of BPS Lagrangian density under the BPS Lagrangian method. We then generalize this BPS Lagrangian density and use it to derive several possible generalized Bogomolny's equations, with(out) additional constraint equations, for BPS monopoles and dyons in the generalized $SU(2)$ Yang-Mills-Higgs model. We also compute the stress-energy-momentum tensor of the generalized model, and argue that the BPS monopole and dyon solutions are …
We present solutions of the Yang-Mills equation on cylinders $\mathbb R\times G/H$ over coset spaces with Sasakian structure and odd dimension $2m+1$. The gauge potential is assumed to be $SU(m)$-equivariant, parametrized by two real, scalar-valued functions. Yang-Mills theory with torsion in this setup reduces to the Newtonian mechanics of a point particle moving in $\mathbb R^2$ under the influence of an inverted potential. We analyze the critical points of this potential and present an analytic as well as several numerical finite-action solutions. Apart from the Yang-Mills solutions that co…
We present a self-gravitating dyon solution of the Einstein-Yang-Mills-Higgs equations of motion in asymptotically AdS space. The back reaction of gauge and Higgs fields on the space-time geometry leads to the metric of an asymptotically AdS black hole. Using the gauge/gravity correspondence we analyze relevant properties of the finite temperature quantum field theory defined on the boundary. In particular we identify an order operator, characterize a phase transition of the dual theory on the border and also compute the expectation value of the finite temperature Wilson loop.
We study a system of external particles of various charges in N =4 super Yang-Mills in the large N limit at finite temperature. We demonstrate that at high enough temperature partial or complete screening of the particles can occur. At zero temperature the total electric or magnetic charge cannot be screened, while higher multipole moments of these charges can be screened. The specific case of a quark, a monopole and a dyon is worked out and the above properties are verified. We also discuss the free energy of isolated particles and show that their entropy is independent of the temperature.
In this paper, making use of the 't Hooft-Polyakov-Julia-Zee ansatz for the SU(2) Yang-Mills-Higgs gauge field theory, we present the straightforward generalization of the Bogomoln'yi equations and its several consequences. Particularly, this is shown that this idea is able to generate new types of non-abelian both dyons and magnetic monopoles and, moreover, that within the new model the scalar field can be described through the Coulomb potential, whereas, up to a constant, the non-abelian gauge field becomes the Wu-Yang monopole.
Using the low energy effective action of the N=2 supersymmetric SU(2) Yang-Mills theory we calculate the free energy at finite temperature, both in the semiclassical region and in the dual monopole/dyon theory. In all regions the free energy depends on both the temperature T and the appropriate moduli parameter, and is thus minimized only for specific values of the moduli parameter, in contrast to the T=0 case where the energy vanishes all over the moduli space. Within the validity of perturbation theory, we find that the finite temperature Yang-Mills theory is stable only at definite points i…
Classical 1/4 BPS configurations consist of 1/2 BPS dyons which are positioned by competing static forces from electromagnetic and Higgs sectors. These forces do not follow the simple inverse square law, but can be encoded in some low energy effective potential between fundamental monopoles of distinct types. In this paper, we find this potential, by comparing the exact 1/4 BPS bound from a Yang-Mills field theory with its counterpart derived from low energy effective dynamics of monopoles. Our method is generalized to arbitrary gauge groups and to arbitrary BPS monopole/dyon configurations. T…
We consider Lie G-valued Yang-Mills fields on the space R x G/H, where G/H is a compact nearly K"ahler six-dimensional homogeneous space, and the manifold R x G/H carries a G_2-structure. After imposing a general G-invariance condition, Yang-Mills theory with torsion on R x G/H is reduced to Newtonian mechanics of a particle moving in R^6, R^4 or R^2 under the influence of an inverted double-well-type potential for the cases G/H = SU(3)/U(1)xU(1), Sp(2)/Sp(1)xU(1) or G_2/SU(3), respectively. We analyze all critical points and present analytical and numerical kink- and bounce-type solutions, wh…
We explore the low energy dynamics of charge two instantons and dyonic instantons in SU(2) 5-dimensional Yang-Mills. We make use of the moduli space approximation and first calculate the moduli space metric for two instantons. For dyonic instantons the effective action of the moduli space approximation also includes a potential term which we calculate. Using the ADHM construction we are able to understand some aspects of the topology and structure of the moduli space. We find that instantons undergo right angled scattering after a head on collision and we are able to give an analytic descripti…
We consider monopole and dyon classical solutions of the Yang-Mills-Higgs system coupled to gravity in asymptotically anti-de Sitter space. We discuss both singular and regular solutions to the second order equations of motion showing that singular Wu-Yang like dyons can be found, the resulting metric being of the Reissner-Nördstrom type (with cosmological constant). Concerning regular solutions, we analyze the conditions under which they can be constructed discussing, for vanishing coupling constant, the main distinctive features related to the anti-de Sitter asymptotic condition; in particul…
In this paper, we investigate some electrically charged magnetic solutions of the SU(2) Yang-Mills-Higgs field theory in the net zero topological charge sector. We only examine the case when the Higgs field vanishes at two points along the z-axis and when the Higgs field vanishes along a ring with the z-axis as its symmetry axis. We study the possible electric charges the dyons can carry in relation to the electric-magnetic charge separations and calculate for the finite total energy and magnet dipole moment of these dyons. These stationary dyon solutions do not satisfy the first order Bogomol…
Taking advantage of the equivalence between supersymmetric Yang-Mills theory on non-commutative spaces and the field theory limit of D3-branes in the background of NSNS 2-form field, we investigate the static properties of magnetic monopoles and dyons using brane construction techniques. When parallel D3-branes are separated by turning on a Higgs vacuum expectation value, D-strings will stretch between them at an angle which depends on the value of the background 2-form potential. These states preserve half of the supersymmetries and have the same masses as their commutative counterparts in th…
We propose a new nonabelian Kaluza-Klein dyon solution in the seven-dimensional spacetimes. This is a Wu-Yang-like Kaluza-Klein dyon. The dyonic metric is spherically symmetric, two spherical coordinate systems are used, and the metric admits SO(3) Killing vectors. It can be verified that the Einstein equation is satisfied in seven-dimensional spacetimes. The stress-energy tensor of the Yang-Mills field in Einstein equation is derived from Ricci tensor automatically, not put by hand from outside. The Ricci scalar curvature \bar{R} vanishes. The four-dimensional part of the dyonic metric is jus…
We evaluate the gauge invariant, dynamically conserved charges, recently obtained from the integral form of the Yang-Mills equations, for the BPS multi-dyon solutions of a Yang-Mills-Higgs theory associated to any compact semi-simple gauge group G. Those charges are shown to correspond to the eigenvalues of the next-to-leading term of the asymptotic form of the Higgs field at spatial infinity, and so coinciding with the usual topological charges of those solutions. Such results show that many of the topological charges considered in the literature are in fact dynamical charges, which conservat…
We argue that the Einstein-Yang-Mills-Higgs theory presents nontrivial solutions with a NUT charge. These solutions approach asymptotically the Taub-NUT spacetime and generalize the known dyon black hole configurations. The main properties of the solutions and the differences with respect to the asymptotically flat case are discussed. We find that a nonabelian magnetic monopole placed in the field of gravitational dyon necessarily acquires an electric field, while the magnetic charge may take arbitrary values.
In this review, we consider the case where electrons, magnetic monopoles, and dyons become massless. Here we consider the ${\cal N} = 2$ supersymmetric Yang-Mills (SYM) theories with classical gauge groups with a rank r, SU(r+1), SO(2r), Sp(2r), and SO(2r+1). which are studied by Riemann surfaces called Seiberg-Witten curves. We discuss physical singularity associated with massless particles, which can be studied by geometric singularity of vanishing 1-cycles in Riemann surfaces in hyperelliptic form. We pay particular attention to the cases where mutually non-local states become massless (Arg…
Basing on a semiclassical picture of dyons, we present a nonperturbative model of a pure Yang--Mills theory at any temperatures, for an arbitrary simple gauge group. We argue that at low temperatures dyons drive the Yang--Mills system for all groups to a phase where the `eigenphases' of the Polyakov line are, as a vector, proportional to the Weyl vector being the half sum of positive roots. For most gauge groups it means confinement, in particular for `quarks' in any N-ality nonzero representation of the SU(N) gauge group. At a critical temperature there is a 1st order phase transition for all…
These lectures contain an introduction to instantons, calorons and dyons of the Yang--Mills gauge theory. Since we are interested in the mechanism of confinement and of the deconfinement phase transition at some critical temperature, the Yang--Mills theory is formulated and studied at nonzero temperatures. We introduce ``calorons with a nontrivial holonomy'' that are generalizations of instantons and can be viewed as ``made of'' constituent dyons. The quantum weight with which these calorons contribute to the Yang--Mills partition function is considered, and the ensuing statistical mechanics o…
We construct a dyon solution for a Yang-Mills-Higgs theory in a 4 dimensional Schwarzschild-anti-de Sitter black hole background with temperature T. We then apply the AdS/CFT correspondence to describe the strong coupling regime of a 2+1 quantum field theory which undergoes a phase transition exhibiting the condensation of a composite charge operator below a critical temperature $T_c$.
