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Antti J. Niemi

Publications and source records attributed to Antti J. Niemi.

88 records · Page 5Linked to original sources
arXiv1999

(Meta)stable closed vortices in 3+1 dimensional gauge theories with an extended Higgs sector

In gauge theories with an extended Higgs sector the classical equations of motion can have solutions that describe stable, closed finite energy vortices. Such vortices separate two disjoint Higgs vacua, with one of the vacua embedded in the other in a manner that forms a topologically nontrivial knot. The knottedness stabilizes the vortex against shrinkage in 3+1 dimensional space-time. But in a world with extra large dimensions we expect the configuration to decay by unknotting. As an example we consider the semilocal $θ_W \to \fracπ{2}$ limit of the Weinberg-Salam model. We present numerical evidence for the existence of a stable closed vortex, twisted into a toroidal configuration around a circular Higgs vacuum at its core.

hep-th↗
arXiv1999

Aspects of Duality and Confining Strings

We inspect the excitation energy spectrum of a confining string in terms of solitons in an effective field theory model. The spectrum can be characterized by a spectral function, and twisting and bending of the string is manifested by the invariance of this function under a duality transformation. Both general considerations and numerical simulations reveal that the spectral function can be approximated by a simple rational form, which we propose becomes exact in the Yang-Mills theory.

hep-th↗
arXiv1999

On the Arnold Conjecture and the Atiyah-Patodi-Singer Index Theorem

The Arnold conjecture yields a lower bound to the number of periodic classical trajectories in a Hamiltonian system. Here we count these trajectories with the help of a path integral, which we inspect using properties of the spectral flow of a Dirac operator in the background of a $\Sp(2N)$ valued gauge field. We compute the spectral flow from the Atiyah-Patodi-Singer index theorem, and apply the results to evaluate the path integral using localization methods. In this manner we find a lower bound to the number of periodic classical trajectories which is consistent with the Arnold conjecture.

hep-th↗
arXiv1999

Decomposing the Yang-Mills Field

Recently we have proposed a set of variables for describing the physical parameters of SU(N) Yang--Mills field. Here we propose an off-shell generalization of our Ansatz. For this we envoke the Darboux theorem to decompose arbitrary one-form with respect to some basis of one-forms. After a partial gauge fixing we identify these forms with the preimages of holomorphic and antiholomorphic forms on the coset space $ SU(N)/U(1)^{N-1}$, identified as a particular coadjoint orbit. This yields an off-shell gauge fixed decomposition of the Yang-Mills connection that contains our original variables in a natural fashion.

hep-th↗
arXiv1999

Towards a string representation of infrared SU(2) Yang-Mills theory

We employ a heat kernel expansion to derive an effective action that describes four dimensional SU(2) Yang-Mills theory in the infrared limit. Our result supports the proposal that at large distances the theory is approximated by the dynamics of knotted string-like fluxtubes which appear as solitons in the effective theory.

hep-th↗
arXiv1999

Knots in interaction

We study the geometry of interacting knotted solitons. The interaction is local and advances either as a three-body or as a four-body process, depending on the relative orientation and a degeneracy of the solitons involved. The splitting and adjoining is governed by a four-point vertex in combination with duality transformations. The total linking number is preserved during the interaction. It receives contributions both from the twist and the writhe, which are variable. Therefore solitons can twine and coil and links can be formed.

hep-th↗
arXiv1999

Partial duality in SU(N) Yang-Mills theory

Recently we have proposed a set of variables for describing the infrared limit of four dimensional SU(2) Yang-Mills theory. here we extend these variables to the general case of four dimensional SU(N) Yang-Mills theory. We find that the SU(N) connection A decomposes according to irreducible representations of SO(N-1) and the curvature two-form F is related to the symplectic Kirillov two forms that characterize irreducible representations of SU(N). We propose a general class of nonlinear chiral models that may describe stable, soliton-like configurations with nontrivial topological numbers.

hep-th↗
arXiv1998

Partially Dual variables in SU(2) Yang-Mills Theory

We propose a reformulation of SU(2) Yang-Mills theory in terms of new variables. These variables are appropriate for describing the theory in its infrared limit, and indicate that it admits knotlike configurations as stable solitons. As a consequence we arrive at a dual picture of the Yang-Mills theory where the short distance limit describes asymptotically free, massless point gluons and the large distance limit describes extended, massive knotlike solitons.

hep-th↗
arXiv1996

Knots and Particles

Using methods of high performance computing, we have found indications that knotlike structures appear as stable finite energy solitons in a realistic 3+1 dimensional model. We have explicitly simulated the unknot and trefoil configurations, and our results suggest that all torus knots appear as solitons. Our observations open new theoretical possibilities in scenarios where stringlike structures appear, including physics of fundamental interactions and early universe cosmology. In nematic liquid crystals and 3He superfluids such knotted solitons might actually be observed.

hep-th↗
arXiv1996

Topological Sigma-model, Hamiltonian Dynamics and Loop Space Lefschetz Number

We use path integral methods and topological quantum field theory techniques to investigate a generic classical Hamiltonian system. In particular, we show that Floer's instanton equation is related to a functional Euler character in the quantum cohomology defined by the topological nonlinear $σ$--model. This relation is an infinite dimensional analog of the relation between Poincaré--Hopf and Gauss--Bonnet--Chern formulæ$~$ in classical Morse theory, and can also be viewed as a loop space generalization of the Lefschetz fixed point theorem. By applying localization techniques to path integrals we then show that for a Kähler manifold our functional Euler character coincides with the Euler character determined by the finite dimensional de Rham cohomology of the phase space. Our results are consistent with the Arnold conjecture which estimates periodic solutions to classical Hamilton's equations in terms of de Rham cohomology of the phase space.

hep-th↗
arXiv1996

Aspects of mass gap, confinement and N=2 structure in 4-D Yang-Mills theory

We introduce new variables in four dimensional SU(N) Yang-Mills theory. These variables emerge when we sum the path integral over classical solutions and represent the summation as an integral over appropriate degrees of freedom. In this way we get an effective field theory with SU(N)$\times$SU(N) gauge symmetry. In the instanton approximation our effective theory has in addition a N=2 supersymmetry, and when we sum over all possible solutions we find a Parisi-Sourlas supersymmetry. These extra symmetries can then be broken explicitly by a SU(N) invariant and power counting renormalizable mass term. Our results suggest that the confinement mechanism which has been recently identified in the N=2 supersymmetric Yang-Mills theory might also help to understand color confinement in ordinary, pure Yang-Mills theory. In particular, there appears to be an intimate relationship between the N=2 supersymmetry approach to confinement and the Parisi-Sourlas dimensional reduction.

hep-th↗
arXiv1995

Quantum Mechanical Anomalies and the De Witt Effective Action

We study the partition function of N=1 supersymmetric De Rham quantum mechanics on a Riemannian manifold, with a nontrivial chemical potential $μ$ for the fermions. General arguments suggest that when $μ\to \infty$ we should get the partition function of a free point particle. We investigate this limit by exact evaluation of the fermionic path integral. In even dimensions we find the De Witt term with a definite numerical factor. However, in odd dimensions our result is pestered by a quantum mechanical anomaly and the numerical factor in the De Witt term remains ambiquous.

hep-th↗
arXiv1995

Gauge Vector Masses from Flat Connections?

We suggest that four dimensional massive gauge vectors could be described by coupling ordinary Yang-Mills theory to a topological gauge theory. For this the coupling should excite a nontrivial degree of freedom from the topological theory, corresponding to the longitudinal polarization of a massive gauge vector. If the coupling can be selected so that further degrees of freedom are not excited, one may entirely avoid particles such as the Higgs. Here we discuss a simple example of this idea, obtained by coupling standard Yang-Mills theory to the topological gauge theory of flat connections. We propose that our example might describe a renormalizable theory of massive gauge vectors with no additional physical degrees of freedom.

hep-ph↗
arXiv1995

On the number of periodic classical trajectories in a Hamiltonian dynamical system

Periodic classical trajectories are of fundamental importance both in classical and quantum physics. Here we develop path integral techniques to investigate such trajectories in an arbitrary, not necessarily energy conserving hamiltonian system. In particular, we present a simple derivation of a lower bound for the number of periodic classical trajectories.

hep-th↗
arXiv1994

Equivariance, BRST and Superspace

The structure of equivariant cohomology in non-abelian localization formulas and topological field theories is discussed. Equivariance is formulated in terms of a nilpotent BRST symmetry, and another nilpotent operator which restricts the BRST cohomology onto the equivariant, or basic sector. A superfield formulation is presented and connections to reducible (BFV) quantization of topological Yang-Mills theory are discussed.

hep-th↗