Abstract:We investigate the properties of the twist line defect in the critical 3d Ising model using Monte Carlo simulations. In this model the twist line defect is the boundary of a surface of frustrated links or, in a dual description, the Wilson line of the Z 2 gauge theory. We test the hypothesis that the twist line defect flows to a conformal line defect at criticality and evaluate numerically the low-lying spectrum of anomalous dimensions of the local operators which live on the defect as well as mixed correlation functions of local operators in the bulk and on the defect.

In U(1) lattice gauge theory in three spacetime dimensions, the problem of confinement can be studied analytically in a semi-classical approach, in terms of a gas of monopoles with Coulomb-like interactions. In addition, this theory can be mapped to a spin model via an exact duality transformation, which allows one to perform highprecision numerical studies of the confining potential. Taking advantage of these properties, we carried out an accurate investigation of the effective string describing the low-energy properties of flux tubes in this confining gauge theory. We found striking deviations from the expected Nambu-Goto-like behavior, and, for the first time, evidence for contributions that can be described by a term proportional to the extrinsic curvature of the effective string worldsheet. Such term is allowed by Lorentz invariance, and its presence in the infrared regime of the U(1) model was indeed predicted by Polyakov several years ago. Our results show that this term scales as expected according to Polyakov's solution, and becomes the dominant contribution to the effective string action in the continuum limit. We also demonstrate analytically that the corrections to the confining potential induced by the extrinsic curvature term can be related to the partition function of the massive perturbation of a c = 1 bosonic conformal field theory. The implications of our results for SU(N ) Yang-Mills theories in three and in four spacetime dimensions are discussed.

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Observed advantages of autoplanning were clinically relevant and larger than reported in the literature. The latter is likely related to the multi-criterial nature of the applied autoplanning algorithm, with for each center a dedicated configuration that aims at plan improvements relative to its (clinical) training plans. Large variations among patients in differences between manVMAT and autoVMAT point at inconsistencies in manual planning.

Abstract:We study the boundary contribution to the low energy effective action of the open string describing the confining flux tube in gauge theories. The form of the boundary terms is strongly constrained by the requirement of Lorentz symmetry, which is spontaneously broken by the formation of a long confining flux tube in the vacuum. Writing the boundary action as an expansion in the derivatives of the Nambu-Goldstone modes describing the transverse fluctuations of the string, we single out and put in a closed form the first few Lorentz invariant boundary terms. We also evaluate the leading deviation from the Nambu-Goto string produced by the boundary action on the vacuum expectation value of the Wilson loop and we test this prediction in the 3d Ising gauge model. Our simulation attains a level of precision which is sufficient to test the contribution of this term.