non-Abelian Hair Research Articles

Universal formula for the density of states with continuous symmetry

We consider a $d$-dimensional unitary conformal field theory with a compact Lie group global symmetry $G$ and show that, at high temperature $T$ and on a compact Cauchy surface, the probability of a randomly chosen state being in an irreducible unitary representation $R$ of $G$ is proportional to $(\mathrm{dim}\text{ }R{)}^{2}\mathrm{exp}[\ensuremath{-}{c}_{2}(R)/(b{T}^{d\ensuremath{-}1})]$. We use the spurion analysis to derive this formula and relate the constant $b$ to a domain wall tension. We also verify it for free field theories and holographic conformal field theories and compute $b$ in these cases. This generalizes the result in 2109.03838 that the probability is proportional to $(\mathrm{dim}R{)}^{2}$ when $G$ is a finite group. As a byproduct of this analysis, we clarify thermodynamical properties of black holes with non-Abelian hair in anti--de Sitter space.

Consequences of thermal fluctuations of well-known black holes in modified gravity

Quantum fluctuation consequences have significant role in high-energy physics. These fluctuation often regarded as a correction of the infrared (IR) limit. Such correction contribute to the high-energy limit of thermodynamical quantities and the stability conditions of black holes. In this work, we analyze the thermal stability of black holes in the presence of thermal fluctuations. We consider AdS black hole in Born–Infeld massive gravity with non-abelian hair and the charged AdS black hole with a global monopole. We develop many thermodynamical quantities such as entropy, temperature, pressure, heat capacity of a system at constant volume and pressure, ratio between the heat capacities at constant pressure and volume, Gibbs free energy and Helmholtz free energy for both black holes. The critical behavior and phase transitions of black holes are also presented. We also observe the local and global stability of black holes in the grand canonical ensemble and canonical ensemble for the specific values of different parameters, such as, symmetry breaking parameter η, massive parameter m and non-abelian hair ν.

Thermodynamic description and quasinormal modes of adS black holes in Born-lnfeld massive gravity with a non-abelian hair

We construct a new class of asymptotically (a)dS black hole solutions of Einstein-Yang-Mills massive gravity in the presence of Born-Infeld nonlinear electrody­ namics. The obtained solutions possess a Coulomb electric charge, massive term and a non-abelian hair as well. We calculate the conserved and thermodynamic quantities, and investigate the validity of the first law of thermodynamics. Also, we investigate thermal stability conditions by using the sign of heat capacity through canonical ensemble. Next, we consider the cosmological constant as a thermodynamical pressure and study the van der Waals like phase transition of black holes in the extended phase space thermodynamics. Our results indicate the existence of a phase transition which is affected by the parameters of theory. Finally, we consider a massless scalar perturbation in the background of asymptotically adS solutions and calculate the quasinormal modes by employing the pseu­ dospectral method. The imaginary part of quasinormal frequencies is the time scale of a thermal state (in the conformal field theory) for the approach to thermal equilibrium.

Non-perturbative decay of non-Abelian hair

We construct a solution of Heterotic supergravity which interpolates between two different AdS3 × S3 × T4 geometries corresponding to the near-horizon limits of two 5-dimensional black holes, only one of which has non-Abelian hair. This solution can be used to estimate the amplitude of probability of the non-perturbative decay of the gauge 5-brane responsible for the non-Abelian hair into eight solitonic 5-branes by evaluating its Euclidean action. The Wick rotation of this solution poses several problems which we argue can be overcome by using a non-extremal off-shell (NEOS) deformation of the solution. This NEOS field configuration can be Wick rotated straight away and its Euclidean action can be computed for any value of the deformation parameter. The Euclidean result can then be anti-Wick-rotated and its extremal limit gives the Euclidean action of the original solution, which turns out to be one half of the difference between the entropies of the 5-dimensional black holes.

Dyonic black holes at arbitrary locations

We construct and study stationary, asymptotically flat multicenter solutions describing regular black holes with non-Abelian hair (colored magnetic-monopole and dyon fields) in two models of mathcal{N}=2 , d = 4 Super-Einstein-Yang-Mills theories: the quadratic model {overline{mathrm{mathbb{C}}mathrm{mathbb{P}}}}^3 and the cubic model ST[2, 6], which can be embedded in 10-dimensional Heterotic Supergravity. These solutions are based on the multicenter dyon recently discovered by one of us, which solves the SU(2) Bogomol’nyi and dyon equations on {mathbb{E}}^3 . In contrast to the well-known Abelian multicenter solutions, the relative positions of the non-Abelian black-hole centers are unconstrained.We study necessary conditions on the parameters of the solutions that ensure the regularity of the metric. In the case of the {overline{mathrm{mathbb{C}}mathrm{mathbb{P}}}}^3 model we show that it is enough to require the positivity of the “masses” of the individual black holes, the finiteness of each of their entropies and their superadditivity. In the case of the ST[2, 6] model we have not been able to show that analogous conditions are sufficient, but we give an explicit example of a regular solution describing thousands of non-Abelian dyonic black holes in equilibrium at arbitrary relative positions.We also construct non-Abelian solutions that interpolate smoothly between just two aDS2×S2 vacua with different radii (dumbbell solutions).

Reissner–Nordström black holes with non-Abelian hair

We consider d⩾4 Einstein–(extended-)Yang–Mills theory, where the gauge sector is augmented by higher order terms. Linearising the (extended) Yang–Mills equations on the background of the electric Reissner–Nordström (RN) black hole, we show the existence of normalisable zero modes, dubbed non-Abelian magnetic stationary clouds. The non-linear realisation of these clouds bifurcates the RN family into a branch of static, spherically symmetric, electrically charged and asymptotically flat black holes with non-Abelian hair. Generically, the hairy black holes are thermodynamically preferred over the RN solution, which, in this model, becomes unstable against the formation of non-Abelian hair, for sufficiently large values of the electric charge.

Rotating black holes with non-Abelian hair

We here review asymptotically flat rotating black holes in the presence of non-Abelian gauge fields. Like their static counterparts these black holes are no longer uniquely determined by their global charges. In the case of pure SU(2) Yang–Mills fields, the rotation generically induces an electric charge, while the black holes do not carry a magnetic charge. When a Higgs field is coupled, rotating black holes with monopole hair arise in the case of a Higgs triplet, while in the presence of a complex Higgs doublet the black holes carry sphaleron hair. The inclusion of a dilaton allows for Smarr type mass formulae.

Thermodynamic properties of asymptotically anti-de Sitter black holes in d = 4 Einstein–Yang–Mills theory

We investigate the thermodynamics of spherically symmetric black hole solutions in a four-dimensional Einstein–Yang–Mills-SU(2) theory with a negative cosmological constant. Special attention is paid to configurations with a unit magnetic charge. We find that a set of Reissner–Nordström–Anti-de Sitter black holes can become unstable to forming non-Abelian hair. However, the hairy black holes are never thermodynamically favoured over the full set of abelian monopole solutions. The thermodynamics of the generic configurations possessing a noninteger magnetic charge is also discussed.

Electrically charged black branes in [formula omitted], [formula omitted] gauged supergravity

We analyze the properties of asymptotically AdS electrically charged black brane solutions in a consistent truncation of the N=4+, D=5 Romansʼ gauged supergravity which contains gravity, SU(2) and U(1) gauge fields, and a dilaton possessing a nontrivial potential approaching a constant negative value at infinity. We find that the U(1)×U(1) solutions become unstable to forming non-Abelian hair. These configurations emerge as zero modes of the Abelian solutions at critical temperature and a critical (non-vanishing) ratio of the electric charges and can be viewed as holographic p-wave superfluids.

Stable black hole solutions with non-Abelian fields

We construct finite mass, asymptotically flat black hole solutions in $d=4$ Einstein---Yang-Mills theory augmented with higher order curvature terms of the gauge field. They possess non-Abelian hair in addition to Coulomb electric charge, and, below some nonzero critical temperature, they are thermodynamically preferred over the Reissner-Nordstr\"om solution. Our results indicate the existence of hairy non-Abelian black holes which are stable under linear, spherically symmetric perturbations.

Einstein–Yang-Mills–Chern-Simons solutions inD=2n+1dimensions

We investigate finite energy solutions of the Einstein--Yang-Mills--Chern-Simons system in odd spacetime dimensions, $D=2n+1$, with $n>1$. Our configurations are static and spherically symmetric, approaching at infinity a Minkowski spacetime background. In contrast with the Abelian case, the contribution of the Chern-Simons term is nontrivial already in the static, spherically symmetric limit. Both globally regular, particlelike solutions and black holes are constructed numerically for several values of $D$. These solutions carry a nonzero electric charge and have finite mass. For globally regular solutions, the value of the electric charge is fixed by the Chern-Simons coupling constant. The black holes can be thought of as nonlinear superpositions of Reissner-Nordstr\"om and non-Abelian configurations. A systematic discussion of the solutions is given for $D=5$, in which case the Reissner-Nordstr\"om black hole becomes unstable and develops non-Abelian hair. We show that some of these non-Abelian configurations are stable under linear, spherically symmetric perturbations. A detailed discussion of an exact $D=5$ solution describing extremal black holes and solitons is also provided.

N= 2 Einstein-Yang-Mills's BPS solutions

We find the general form of all the supersymmetric configurations and solutions of N=2,d=4 Einstein-Yang-Mills theories. In the timelike case, which we study in great detail, giving many examples, the solutions to the full supergravity equations can be constructed from known flat spacetime solutions of the Bogomol'nyi equations. This allows the regular supersymmetric embedding in supergravity of regular monopole solutions ('t Hooft-Poyakov's, Weinberg's, Wilkinson and Bais's) but also embeddings of irregular solutions to the Bogomol'nyi equations which turn out to be regular black holes with different forms of non-Abelian hair once the non-triviality of the spacetime metric is taken into account. The attractor mechanism is realized in a gauge-covariant way. In the null case we determine the general equations that supersymmetric configurations and solutions must satisfy but we do not find relevant new supersymmetric solutions.

Magnetic monopoles near the black hole threshold

We present new analytic and numerical results for self-gravitating SU(2)-Higgs magnetic monopoles approaching the black hole threshold. Our investigation extends to large Higgs self-coupling, lambda, a regime heretofore unexplored. When lambda is small, the critical solution where a horizon first appears is extremal Reissner-Nordstrom outside the horizon but has a nonsingular interior. When lambda is large, the critical solution is an extremal black hole with non-Abelian hair and a mass less than the extremal Reissner-Nordstrom value. The transition between these two regimes is reminiscent of a first-order phase transition. We analyze in detail the approach to these critical solutions as the Higgs expectation value is varied, and compare this analysis with the numerical results.

Exotic solutions in Einstein-antisymmetric tensor theory

Classical solutions of the self-interacting, non-abelian antisymmetric tensor gauge theory of Freedman and Townsend coupled to Einstein gravity are discussed. Particularly, it is demonstrated that the theory admits a classical metric solution which, depending on the value of the gauge coupling parameter of the theory, exhibits a black hole with an exotic non-abelian hair or a spacetime showing the “violation of the cosmic censorship hypothesis” which should be distinguished from white holes.

NON-ABELIAN TOPOLOGICAL SOLUTIONS IN STRINGY GRAVITY

Non-Abelian solutions of the low-energy heterotic string effective action are discussed. Three types of solutions are shown to exist: regular uncharged shaleron-like solutions, uncharged non-Abelian black holes and charged black holes with non-Abelian hair. In the extremal limit charged non-Abelian black holes generate regular throat structure in the string frame similar to that of the Gibbons-Maeda-Horowitz-Strominger solution.

Black holes with non-Abelian hair and their thermodynamical properties.

We present some black-hole solutions of the Einstein-Yang-Mills-dilaton system and calculate their Hawking temperatures. We find that if the coupling constant of the dilation is smaller than some critical value, the thermodynamical behavior of these black holes includes two phase transitions at points determined by the value of the mass parameter. The black holes with masses between those two critical values have a positive specific heat. This is also true for the known colored black-hole solutions. We also reanalyze Skyrme black holes and find that there exist two types of solutions (a stable type and an unstable excited type) and these two types converge to a bifurcation point at some critical horizon radius, beyond which there is no Skyrme black hole. The stable black holes have two possible fates: they can evaporate via the Hawking process, and so evolve into a particlelike (Skyrmion) solution, or they can accrete matter and evolve into the Schwarzschild solution. When a Skyrme black hole evolves into a Schwarzschild black hole, its area changes discontinuously, so that we may regard this evolution as a kind of first-order phase transition. The specific heat of stable Skyrme black holes is always negative, while there are either one or three transition points for unstable Skyrme black holes.

Charged stringy black holes with non-abelian hair

Static spherically symmetric asymptotically flat charged black hole solutioons are constructed within the magnetic SU (3) sector of the four-dimensional heterotic string effective action. They posesss non-abelian hair in addition to the Coulomb magnetic field and are qualitatively similar to the Einstein-Yang-Mills colored SU (3) black holes except for the extremal case. In the extremality limit the horizon shrinks and the resulting geometry around the origin coincides with that of an extremal abelian dilatonic black hole with magnetic charge. Non-abelian hair exhibits then typical sphaleron structure.

Curved-space magnetic monopoles.

Explicit solutions of the coupled Einstein-Yang-Mills-Higgs field equations representing a 't Hooft--Polyakov--type magnetic monopole are constructed, both in and away from the Bogomolny-Prasad-Sommerfield limit. The solutions are seen to tend towards black-hole solutions as the strength of the gravitational coupling is increased, as might be expected. A careful analysis of solutions near the transition to a black hole shows that the monopole loses its non-Abelian hair as it develops a horizon. In certain cases, solutions without a horizon are seen to be unstable to gravitational collapse.