Caloron Solutions Research Articles

SYNCYCLONS OR SOLITONIC SIGNALS FROM EXTRA DIMENSIONS

In theories where space-time is a direct product of Minkowski space (M4) and a d-dimensional compact space (Kd), there can exist topological solitons that simultaneously wind around ℝ3 (or ℝ2 or ℝ1) in M4 and the compact dimensions. A paradigmatic non-gravitational example of such "co-winding" solitons is furnished by Yang-Mills theory defined on M4 × S1. Point-like, string-like and sheet-like solitons can be identified by transcribing and generalizing the procedure used to construct the periodic instanton (caloron) solutions. Asymptotically the classical point-like objects have non-Abelian magnetic dipole fields together with a non-Abelian scalar potential while the "color" electric charge is zero. However quantization of collective coordinates associated with zero modes and coupling to fermions can radically change these quantum numbers due to fermion number fractionalization and its non-Abelian generalization. Interpreting the YM group as color (or the electroweak SU(2) group) and assuming that an extra circular dimension exists thus implies the existence of topologically stable solitonic objects which carry baryon(lepton) number and a mass O(1/g2R), where R is the radius of the compact dimension.

Self dual solutions of the temperature SU(2) Yang-Mills theory

Continuing previous work we elaborate on the method of “heating” the self-dual axially symmetric fields of the SU(2) Yang-Mills theory to finite temperature. Heating consists of performing—in certain Ansatz functions which are two-dimensional (2D) conformally invariant—a 2D conformal transformation x = x 0 + i ∥ x∥ → y(x), where the analytic function y( x) is periodic in the Euclidean time variable x 0. Solutions are preserved by this manipulation, which automatically changes zero-temperature fields into finite temperature ones. One can exploit this simple fact in various ways. The Harrington-Shepard caloron solution of the temperature Yang-Mills theory can be gotten from the T = 0 instanton by the transformation y( x) = ( πT) −1 tan πTx. One can generate a multicaloron solution from the T = 0 one instanton solution by a conformal transformation. Generally, self-dual axially symmetric Yang-Mills fields can be heated without spoiling self duality. The caloron and three other temperature solutions are studied in some detail. One of the new solutions is a generalized caloron with interesting properties. Our study reveals a remarkable property of the self-dual sector of the temperature Yang-Mills theory: it is full of Wu-Yang (color) monopoles at high temperature. At low temperature these monopoles disappear.

Semiclassical probability distribution function for finite-temperature field theory

Semiclassical methods for evaluating the canonical probability distribution function rho(phi) = in field theory for systems in thermodynamic equilibrium is studied. Field configurations which dominate the semiclassical distribution function are interpretable as finite-temperature most-probable escape paths (FTMPEP's) in field space and are related to the recently discovered caloron solutions, which are known to partially dominate the semiclassical partition function Z = ..integral..Dphi rho(phi). Presented is a semiclassical path-integral approximation for the distribution function and also discuss a Hartree self-consistent field approximation.