We compute semi-classical corrections to the energy of rotating closed Nambu-Goto strings. We confirm the results obtained by means of the Polchinski-Strominger action. We also show that in this semi-classical approximation, the spectrum of physical excitations contains modes that are unphysical non-perturbatively, i.e., to which no physical excitations of the covariantly quantized Nambu-Goto string correspond. 24 − 26 − D 48
Time-distance inversions usually provide tomographic maps of the interesting plasma properties (we will focus on flows) at various depths. These maps however do not correspond directly to the flow field, but rather to the true flow field smoothed by the averaging kernels. We introduce a method to derive a regularly gridded estimate of the true velocity field from the set of tomographic maps. We aim mainly to reconstruct the flow on a uniform grid in the vertical domain. We derive the algorithm, implement it and validate using synthetic data. The use of the synthetic data allows us to investigate the influence of random noise and to develop the methodology to deal with it properly.Key words. techniques: miscellaneous -Sun: helioseismology -Sun: interior SOLA helioseismic inversions in a nutshellThe solar interior is filled with waves travelling between various places. In the convective envelope, the pressure (p) modes largely dominate the spectrum. The propagation of the waves is affected by perturbations in the plasma state parameters, by magnetic fields, and last but not least by plasma streaming. The time-distance helioseismology comprises a set of tools used to measure and analyse the wave travel times. In this study we focus on difference travel times, i.e. the difference of the measured travel time of waves travelling in the opposite directions. The difference travel times in the quiet Sun regions are mostly sensitive to flows (Burston et al. 2015).The standard time-distance helioseismic pipeline consists of the following consecutive steps: first the spatio-temporal datacube is prepared using the tracking and mapping pipeline, this datacube is spatio-temporarily filtered to retain only waves of interest and subsequently the travel times are measured from crosscorrelations of the filtered signal at two places. These travel times are finally inverted for flows assuming the linear relation between flow vector v true and the measured difference travel time δτ via the sensitivity kernel K a (coming usually from forward modelling, e.g. Birch & Gizon 2007;Burston et al. 2015)where the position vector splits into the horizontal r and the vertical z domains. Index a uniquely refers to the selection of the measurement geometry (there is a free choice of spatio-temporal filters, distance of the measurement points, and/or additional spatial averaging). The realisation of the random noise n a is not known, however its covariance matrix may be measured from the data and used in the estimate of the random-noise level in the inverted flow velocities. Equation (1) describes the forward problem which gives the recipe how to compute the (forward-modelled) travel times when the vector velocity field v is known. The usual need is an inverse modelling, hence the derivation of the velocity field in the Sun from the measured set of travel-time maps. To do so, various classes of methods were employed, where two of them are used most often: the regularised least squares (RLS) and optimally localised averaging (OLA). The RLS ...
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