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Title: Non-local non-linear sigma models

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.

Authors:
 [1];  [1]; ORCiD logo [1];  [1];  [2]
  1. Princeton Univ., NJ (United States)
  2. Princeton Univ., NJ (United States); Technion, Haifa (Israel)
Publication Date:
Research Org.:
Princeton Univ., NJ (United States)
Sponsoring Org.:
USDOE Office of Science (SC); Simons Foundation; Israeli Science Foundation; Binational Science Foundation
OSTI Identifier:
1610173
Grant/Contract Number:  
FG02-91ER40671; 511167; 2289/18; 2016324
Resource Type:
Accepted Manuscript
Journal Name:
Journal of High Energy Physics (Online)
Additional Journal Information:
Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2019; Journal Issue: 9; Journal ID: ISSN 1029-8479
Publisher:
Springer Berlin
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Physics; Renormalization Group; Sigma Models; M-Theory

Citation Formats

Gubser, Steven S., Jepsen, Christian B., Ji, Ziming, Trundy, Brian, and Yarom, Amos. Non-local non-linear sigma models. United States: N. p., 2019. Web. https://doi.org/10.1007/jhep09(2019)005.
Gubser, Steven S., Jepsen, Christian B., Ji, Ziming, Trundy, Brian, & Yarom, Amos. Non-local non-linear sigma models. United States. https://doi.org/10.1007/jhep09(2019)005
Gubser, Steven S., Jepsen, Christian B., Ji, Ziming, Trundy, Brian, and Yarom, Amos. Mon . "Non-local non-linear sigma models". United States. https://doi.org/10.1007/jhep09(2019)005. https://www.osti.gov/servlets/purl/1610173.
@article{osti_1610173,
title = {Non-local non-linear sigma models},
author = {Gubser, Steven S. and Jepsen, Christian B. and Ji, Ziming and Trundy, Brian and Yarom, Amos},
abstractNote = {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.},
doi = {10.1007/jhep09(2019)005},
journal = {Journal of High Energy Physics (Online)},
number = 9,
volume = 2019,
place = {United States},
year = {2019},
month = {9}
}

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