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Register a new userFrom center-vortex ensembles to the confining flux tube
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In this review, we discuss the present status of the description of confining flux tubes in SU(N) pure Yang-Mills theory in terms of ensembles of percolating center vortices. This is based on three main pillars: modelling in the continuum the ensemble components detected in the lattice, the derivation of effective field representations, and contrasting the associated properties with Monte Carlo lattice results. The integration of the present knowledge about these points is essential to get closer to a unified physical picture for confinement. Here, we shall emphasize the last advances, which point to the importance of including the nonoriented center-vortex component and non-Abelian degrees when modelling the center-vortex ensemble measure. These inputs are responsible for the emergence of topological solitons and the possibility of accommodating the asymptotic scaling properties of the confining string tension.
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We bootstrap the S-matrix of massless particles in unitary, relativistic two dimensional quantum field theories. We find that the low energy expansion of such S-matrices is strongly constrained by the existence of a UV completion. In the context of flux tube physics, this allows us to constrain several terms in the S-matrix low energy expansion or -- equivalently -- on Wilson coefficients of several irrelevant operators showing up in the flux tube effective action. These bounds have direct implications for other physical quantities; for instance, they allow us to further bound the ground state energy as well as the level splitting of degenerate energy levels of large flux tubes. We find that the S-matrices living at the boundary of the allowed space exhibit an intricate pattern of resonances with one sharper resonance whose quantum numbers, mass and width are precisely those of the world-sheet axion proposed in [1,2]. The general method proposed here should be extendable to massless S-matrices in higher dimensions and should lead to new quantitative bounds on irrelevant operators in theories of Goldstones and also in gauge and gravity theories.
We review the current knowledge about the theoretical foundations of the effective string theory for confining flux tubes and the comparison of the predictions to pure gauge lattice data. A concise presentation of the effective string theory is provided, incorporating recent developments. We summarize the predictions for the spectrum and the profile/width of the flux tube and their comparison to lattice data. The review closes with a short summary of open questions for future research.
We consider correlator of two concentric Wilson loops, a small and large ones related to the problem of flux-tube formation. There are three mechanisms which can contribute to the connected correlator and yield different dependences on the radius of the small loop. The first one is quite standard and concerns exchange by supergravity modes. We also consider a novel mechanism when the flux-tube formation is described by a barrier transition in the string language, dual to the field-theoretic formulation of Yang-Mills theories. The most interesting possibility within this approach is resonant tunneling which would enhance the correlator of the Wilson loops for particular geometries. The third possibility involves exchange by a dyonic string supplied with the string junction. We introduce also tHooft and composite dyonic loops as probes of the flux tube. Implications for lattice measurements are briefly discussed.
We consider coarse-graining applied to nonselfintersecting planar center-vortex loops as they emerge in the confining phase of an SU(2) Yang-Mills theory. Well-established properties of planar curve-shrinking predict that a suitably defined, geometric effective action exhibits (mean-field) critical behavior when the conformal limit of circular points is reached. This suggests the existence of an asymptotic mass gap. We demonstrate that the initially sharp mean center-of-mass position in a given ensemble of curves develops a variance under the flow as is the case for a position eigenstate in free-particle quantum mechanics under unitary time evolution. A possible application of these concepts is an approach to high-$T_c$ superconductivity based (a) on the nonlocal nature of the electron (1-fold selfintersecting center-vortex loop) and (b) on planar curve-shrinking flow representing the decrease in thermal noise in a cooling cuprate.
We perform $SU(2)$ Yang-Mills lattice simulation of the electric field distribution in the Coulomb gauge for different values of $beta$ to further investigate the nature of the Coulomb flux tube.
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