Non-local non-linear sigma models
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Publication:2332175
DOI10.1007/JHEP09(2019)005zbMATH Open1423.83082arXiv1906.10281WikidataQ127320568 ScholiaQ127320568MaRDI QIDQ2332175
Author name not available (Why is that?)
Publication date: 1 November 2019
Published in: (Search for Journal in Brave)
Abstract: We study non-local non-linear sigma models in arbitrary dimension, focusing on the scale invariant limit in which the scalar fields naturally have scaling dimension zero, so that the free propagator is logarithmic. The classical action is a bi-local integral of the square of the arc length between points on the target manifold. One-loop divergences can be canceled by introducing an additional bi-local term in the action, proportional to the target space laplacian of the square of the arc length. The metric renormalization that one encounters in the two-derivative non-linear sigma model is absent in the non-local case. In our analysis, the target space manifold is assumed to be smooth and Archimedean; however, the base space may be either Archimedean or ultrametric. We comment on the relation to higher derivative non-linear sigma models and speculate on a possible application to the dynamics of M2-branes.
Full work available at URL: https://arxiv.org/abs/1906.10281
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