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 finite-energy dyon-type Yang-Mills solutions. The special case of G=SU(2)xSU(2) may be used in heterotic flux compactifications.
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.
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…
We study the one-instanton sector of 5d U(N) maximal SYM theory. By using the moduli space approximation we obtain all the 1/4-BPS bound states of one dyonic instanton when a vev is given to one of the SYM scalar fields that breaks U(N) maximally. We compute the corresponding 1/4-BPS index and partition function and find agreement with arXiv:1110.2175.
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.
This paper contains the results of our investigations of BPS instantons and of our work on N=2 supersymmetric gauge theories. The BPS instantons we study appear in type II string theory compactifications on Calabi-Yau threefolds. In the corresponding four-dimensional effective supergravity actions the BPS instantons arise as finite action solutions to the Euclidean equations of motion. For N=2 supersymmetric gauge theories we construct general Lagrangians involving gauge groups with (non-abelian) electric and magnetic (dyonic) charges. In this work a coupling to hypermultiplets is included.
We calculate exactly the functional determinant for fermions in fundamental representation of SU(2) in the background of periodic instanton with non-trivial value of the Polyakov line at spatial infinity. The determinant depends on the value of the holonomy v, the temperature, and the parameter r_12, which at large values can be treated as separation between the Bogomolny--Prasad--Sommerfeld monopoles (or dyons) which constitute the periodic instanton. We find a compact expression for small and large r_12 and compute the determinant numerically for arbitrary r_12 and v.
We explore the correspondence between Yang-Mills instantons and algebraic curves. The curve is defined by Higgs zero locus of dyonic instantons in 1+4 dimensional Yang-Mills-Higgs theory, and it is identified in string theory with the cross-section of supertubes connecting parallel D4-branes. To present evidence for the identification, we show that with total charges fixed, the supertube angular momentum computed from the Higgs zero locus is maximized when the locus is circular, which has been proven for the cross-section of the supertubes. This leads to a consistent dictionary between the cha…
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.
Calorons of the SU(N) gauge group with non-trivial holonomy, i.e. periodic instantons with arbitrary eigenvalues of the Polyakov line at spatial infinity, can be viewed as composed of N Bogomolnyi--Prasad--Sommerfeld (BPS) monopoles or dyons. Using the metric of the caloron moduli space found previously we compute the integration measure over caloron collective coordinates in terms of the constituent monopole positions and their U(1) phases. In the limit of small separations between dyons and/or trivial holonomy, calorons reduce locally to the standard instantons whose traditional collective c…
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…
Non-abelian gauge theories can be cast into abelian gauge theories with monopoles. We ask what becomes of the instantons after abelian projection. Instantons are found to consist of closed dyon loops. It is shown that the electric charge of the dyons is quantized. The implication of this result for the dynamics of the Yang-Mills vacuum is briefly discussed.
We revisit the instanton-dyon liquid model in the confined phase by using a non-linear Debye-Huckel (DH) resummation for the Coulomb interactions induced by the moduli, followed by a cluster expansion. The organization is shown to rapidly converge and yields center symmetry at high density. The dependence of these results on a finite vacuum angle are also discussed. We also formulate the hypernetted chain (HCN) resummation for the dense instanton-dyon liquid and use it to estimate the liquid pair correlation functions in the DH limit. At very low temperature, the dense limit interpolates betwe…
We calculate exactly functional determinants for quantum oscillations about periodic instantons with non-trivial value of the Polyakov line at spatial infinity. Hence, we find the weight or the probability with which calorons with non-trivial holonomy occur in the Yang--Mills partition function. The weight depends on the value of the holonomy, the temperature, Lambda_QCD, and the separation between the BPS monopoles (or dyons) which constitute the periodic instanton. At large separation between constituent dyons, the quantum measure factorizes into a product of individual dyon measures, times …
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.
Three-dimensional string models with half-maximal supersymmetry are believed to be invariant under a large U-duality group which unifies the S and T dualities in four dimensions. We propose an exact, U-duality invariant formula for four-derivative scalar couplings of the form $F(Φ) (\nablaΦ)^4$ in a class of string vacua known as CHL $\mathbb{Z}_N$ heterotic orbifolds with $N$ prime, generalizing our previous work which dealt with the case of heterotic string on $T^6$. We derive the Ward identities that $F(Φ)$ must satisfy, and check that our formula obeys them. We analyze the weak coupling ex…
We discuss an extension of the instanton-dyon liquid model that includes light quarks at finite chemical potential in the center symmetric phase. We develop the model in details for the case of SU_c(2)\times SU_f(2) by mapping the theory on a 3-dimensional quantum effective theory. We analyze the different phases in the mean-field approximation. We extend this analysis to the general case of SU_c(N_c)\times SU_f(N_f) and note that the chiral and diquark pairings are always comparable.
N=1^* gauge theories are believed to have fractional instanton contributions in the confining vacua. D3 brane probe computations in gravitation dual of large-N N=2^* gauge theories point to the absence of such contributions in the low energy gauge dynamics. We study fractional instantons in N=2 SU(2) Yang-Mills theory from the field theoretical perspective. We present new solutions to the Seiberg-Witten SU(2) monodromy problem with the same perturbative asymptotic, a massless monopole and a dyon singularity on the moduli space, and fractional instanton corrections to N=2 prepotential in the se…
Recent work has shown the existence of a unique nonlinear extension of electromagnetism which preserves conformal symmetry and allows for the freedom of duality rotations. Moreover, black holes and gravitational waves have been found to exist in this nonlinearly extended electrovacuum. We generalise these dyonic black holes in two major ways: with the relaxation of their horizon topology and with the inclusion of magnetic mass. Motivated by recent attention to traversable wormholes, we use this new family of Taub-NUT spaces to construct AdS wormholes. We explore some thermodynamic features by …
We discuss an extension of the instanton-dyon liquid model that includes twisted light quarks in the fundamental representation with explicit $Z_{N_c}$ symmetry for the case with equal number of colors $N_c$ and flavors $N_f$. We map the model on a 3-dimensional quantum effective theory, and analyze it in the mean-field approximation. The effective potential and the vacuum chiral condensates are made explicit for $N_f=N_c=2, 3$. The low temperature phase is center symmetric but breaks spontaneously flavor symmetry with $N_f-1$ massless pions. The high temperature phase breaks center symmetry b…
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…
Motivated by precision counting of BPS black holes, we analyze six-derivative couplings in the low energy effective action of three-dimensional string vacua with 16 supercharges. Based on perturbative computations up to two-loop, supersymmetry and duality arguments, we conjecture that the exact coefficient of the $\nabla^2(\nablaϕ)^4$ effective interaction is given by a genus-two modular integral of a Siegel theta series for the non-perturbative Narain lattice times a specific meromorphic Siegel modular form. The latter is familiar from the Dijkgraaf-Verlinde-Verlinde (DVV) conjecture on exact…
We discuss the instanton-dyon liquid model with $N_f$ Majorana quark flavors in the adjoint representation of color $SU_c(2)$ at finite temperature. We briefly recall the index theorem on $S^1\times R^3$ for twisted adjoint fermions in a BPS dyon background of arbitrary holonomy, and use the ADHM construction to explicit the adjoint anti-periodic zero modes. We use these results to derive the partition function of an interacting instanton-dyon ensemble with $N_f$ light and anti-periodic adjoint quarks. We develop the model in details by mapping the theory on a 3-dimensional quantum effective t…
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.
Instantons at finite temperature consist of dyons, with their masses depending on the asymptotic Polyakov loop. It is shown that the suppression of heavy dyons can explain qualitatively the behavior of the periodic and antiperiodic chiral condensate and the topological susceptibility above the phase transition.
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 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 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 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 b…
The functional determinant is computed exactly for quantum oscillations about periodic instantons with non-trivial values of the Polyakov line at spatial infinity (or holonomy). Such instantons can be viewed as composed of the Bogomolnyi--Prasad--Sommerfeld (BPS) monopoles or dyons. We find the weight or the probability with which dyons occur in the pure Yang--Mills partition function. It turns out that dyons experience quantum interactions having the familiar "linear plus Coulomb" form but with the "string tension'' depending on the holonomy. We present an argument that at temperatures below …
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 present a semiclassical calculation of instanton effects in N=4 supersymmetric Yang-Mills theory formulated on R^{3}XS^{1} and also in the N=1 theory obtained by introducing chiral multiplet masses. In the N=4 case, these instanton effects are related to the bulk contribution to the index which counts BPS dyons in the corresponding four dimensional theory. In both cases, the calculations provide semiclassical tests of recently proposed exact results for the lowest non-trivial terms in the derivative expansion of the Wilsonian effective action.
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…
Self-dual instantons and gravitating dyons in non-Abelian ModMax theory
Centro de Estudios Científicos (CECs)（科学研究中心）；Facultad de Ingeniería, Arquitectura y Diseño, Universidad San Sebastian（圣塞巴斯蒂安大学工程、建筑与设计学院）；Departamento de Ciencias, Facultad de Artes Liberales, Universidad Adolfo Ibáñez（阿道夫·伊巴涅斯大学自由艺术学院科学系）；Instituto de Matemáticas (INSTMAT), Universidad de Talca（塔尔卡大学数学研究所）；Departamento de Física, Universidad de Concepción（孔塞普西翁大学物理系）
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 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 …
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 present a relatively simple argument showing that the H-dyon states required by S-duality of the heterotic string on $T^6$ are present provided that the BPS dyons required by S-duality of N=4 supersymmetric Yang-Mills theory are present. We also conjecture and provide evidence that H-dyons at singularities where the nonperturbative gauge symmetry is completely broken are actually BPS dyons.
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 …
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 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.
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.
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.
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.
The one-instanton contributions to various correlation functions of supercurrents in four-dimensional N=4 supersymmetric SU(2) Yang-Mills theory are evaluated to the lowest order in perturbation theory.Expressions of the same form are obtained from the leading effects of a single D-instanton extracted from the IIB superstring effective action around the AdS5*S5 background. This is in line with the suggested AdS/Yang-Mills correspondence. The relation between Yang--Mills instantons and D-instantons is further confirmed by the explicit form of the classical D-instanton solution in the AdS5*S5 ba…
We consider the Yang-Mills flow equations on a reductive coset space G/H and the Yang-Mills equations on the manifold R x G/H. On nonsymmetric coset spaces G/H one can introduce geometric fluxes identified with the torsion of the spin connection. The condition of G-equivariance imposed on the gauge fields reduces the Yang-Mills equations to phi^4-kink equations on R. Depending on the boundary conditions and torsion, we obtain solutions to the Yang-Mills equations describing instantons, chains of instanton-anti-instanton pairs or modifications of gauge bundles. For Lorentzian signature on R x G…
When instantons are put into the Higgs phase, vortices are attached to instantons. We construct such composite solitons as 1/4 BPS states in five-dimensional supersymmetric U(Nc) gauge theory with Nf(>=Nc) fundamental hypermultiplets. We solve the hypermultiplet BPS equation and show that all 1/4 BPS solutions are generated by an Nc x Nf matrix which is holomorphic in two complex variables, assuming the vector multiplet BPS equation does not give additional moduli. We determine the total moduli space formed by topological sectors patched together and work out the multi-instanton solution insid…
We construct a four-parameter class of self-dual instanton solutions of the classical SU(2)-Yang-Mills equations in a closed Euclidean Robertson-Walker space-time.
We investigate Yang-Mills instantons on a 7-dimensional manifold of G_2 holonomy. By proposing a spherically symmetric ansatz for the Yang-Mills connection, we have ordinary differential equations as the reduced instanton equation, and give some explicit and numerical solutions.
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.
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…
The analysis in previous publications of the instanton constraints required to produce a finite action of the theory is carried out also for N=2 supersymmetric Yang-Mills theory.
In the finite-temperature Yang-Mills theory we calculate the functional determinant for fermions in the fundamental representation of the SU(N) in the background of an instanton with non-trivial values of the Polyakov line at spatial infinity. This object, called the Kraan--van Baal -- Lee--Lu caloron, can be viewed as composed of N Bogomolny--Prasad--Sommerfeld monopoles (or dyons). We compute analytically two leading terms of the fermionic determinant at large separations between dyons.
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.
