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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.
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The discrete nature of the solar magnetic field as it emerges into the corona through the photosphere indicates that it exists as isolated flux tubes in the convection zone, and will remain as discrete flux tubes in the corona until it collides and reconnects with other coronal fields. Collisions of these flux tubes will in general be three dimensional, and will often lead to reconnection, both rearranging the magnetic field topology in fundamental ways, and releasing magnetic energy. With the goal of better understanding these dynamics, we carry out a set of numerical experiments exploring fundamental characteristics of three dimensional magnetic flux tube reconnection. We first show that reconnecting flux tubes at opposite extremes of twist behave very differently: in some configurations, low twist tubes slingshot while high twist tubes tunnel. We then discuss a theory explaining these differences: by assuming helicity conservation during the reconnection one can show that at high twist, tunneled tubes reach a lower magnetic energy state than slingshot tubes, whereas at low twist the opposite holds. We test three predictions made by this theory. 1) We find that the level of twist at which the transition from slingshot to tunnel occurs is about two to three times higher than predicted on the basis of energetics and helicity conservation alone, probably because the dynamics of the reconnection play a large role as well. 2) We find that the tunnel occurs at all flux tube collision angles predicted by the theory. 3) We find that the amount of magnetic energy a slingshot or a tunnel reconnection releases agrees reasonably well with the theory, though at the high resistivities we have to use for numerical stability, a significant amount of magnetic energy is lost to diffusion, independent of reconnection.
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 study the time evolution of early universe which is developed by a cosmological constant $Lambda_4$ and supersymmetric Yang-Mills (SYM) fields in the Friedmann-Robertson-Walker (FRW) space-time. The renormalized vacuum expectation value of energy-momentum tensor of the SYM theory is obtained in a holographic way. It includes a radiation of the SYM field, parametrized as $C$. The evolution is controlled by this radiation $C$ and the cosmological constant $Lambda_4$. For positive $Lambda_4$, an inflationary solution is obtained at late time. When $C$ is added, the quantum mechanical situation at early time is fairly changed. Here we perform the early time analysis in terms of two different approaches, (i) the Wheeler-DeWitt equation and (ii) Lorentzian path-integral with the Picard-Lefschetz method by introducing an effective action. The results of two methods are compared.
We identify instantons representing vacuum decay in a 6-dimensional toy model for string theory flux compactifications, with the two extra dimensions compactified on a sphere. We evaluate the instanton action for tunneling between different flux vacua, as well as for the decompactification decay channel. The bubbles resulting from flux tunneling have an unusual structure. They are bounded by two-dimensional branes, which are localized in the extra dimensions. This has important implications for bubble collisions.
We propose gauge theories in which the unstable branes and the fundamental string are realized as classical solutions. While the former are represented by domain wall like configurations of a scalar field coupled to the gauge field, the latter is by a confined flux tube in the bulk. It is shown that the confined flux tube is really a source of the bulk B-field. Our model also provides a natural scenario of the confinement on the brane in the context of the open string tachyon condensation. It is also argued that the fundamental string can be realized as a classical solution in a certain IIB matrix model as in our model.
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