Nonlocal nonlinear sigma models
Abstract
We study nonlocal nonlinear 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 bilocal integral of the square of the arc length between points on the target manifold. Oneloop divergences can be canceled by introducing an additional bilocal 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 twoderivative nonlinear sigma model is absent in the nonlocal 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 nonlinear sigma models and speculate on a possible application to the dynamics of M2branes.
 Authors:

 Princeton Univ., NJ (United States)
 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:
 FG0291ER40671; 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 10298479
 Publisher:
 Springer Berlin
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Physics; Renormalization Group; Sigma Models; MTheory
Citation Formats
Gubser, Steven S., Jepsen, Christian B., Ji, Ziming, Trundy, Brian, and Yarom, Amos. Nonlocal nonlinear sigma models. United States: N. p., 2019.
Web. doi:10.1007/jhep09(2019)005.
Gubser, Steven S., Jepsen, Christian B., Ji, Ziming, Trundy, Brian, & Yarom, Amos. Nonlocal nonlinear 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 .
"Nonlocal nonlinear sigma models". United States. https://doi.org/10.1007/jhep09(2019)005. https://www.osti.gov/servlets/purl/1610173.
@article{osti_1610173,
title = {Nonlocal nonlinear sigma models},
author = {Gubser, Steven S. and Jepsen, Christian B. and Ji, Ziming and Trundy, Brian and Yarom, Amos},
abstractNote = {We study nonlocal nonlinear 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 bilocal integral of the square of the arc length between points on the target manifold. Oneloop divergences can be canceled by introducing an additional bilocal 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 twoderivative nonlinear sigma model is absent in the nonlocal 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 nonlinear sigma models and speculate on a possible application to the dynamics of M2branes.},
doi = {10.1007/jhep09(2019)005},
journal = {Journal of High Energy Physics (Online)},
number = 9,
volume = 2019,
place = {United States},
year = {2019},
month = {9}
}
Web of Science
Works referenced in this record:
A fourdimensional nonlinear σmodel
journal, August 1978
 Gava, E.; Jengo, R.
 Nuclear Physics B, Vol. 140, Issue 3
Conformal invariance in the longrange Ising model
journal, January 2016
 Paulos, Miguel F.; Rychkov, Slava; van Rees, Balt C.
 Nuclear Physics B, Vol. 902
The supermembrane is unstable
journal, June 1989
 De Wit, B.; Lüscher, M.; Nicolai, H.
 Nuclear Physics B, Vol. 320, Issue 1
O(N) and O(N) and O(N)
journal, November 2017
 Gubser, Steven S.; Jepsen, Christian; Parikh, Sarthak
 Journal of High Energy Physics, Vol. 2017, Issue 11
Riemann normal coordinate expansions using Cadabra
journal, August 2009
 Brewin, Leo
 Classical and Quantum Gravity, Vol. 26, Issue 17
A scaling theory for the longrange to shortrange crossover and an infrared duality
journal, August 2017
 Behan, Connor; Rastelli, Leonardo; Rychkov, Slava
 Journal of Physics A: Mathematical and Theoretical, Vol. 50, Issue 35
Nonlinear models in 2 + ε dimensions
journal, September 1985
 Friedan, Daniel Harry
 Annals of Physics, Vol. 163, Issue 2
Critical Exponents for LongRange Interactions
journal, October 1972
 Fisher, Michael E.; Ma, Shangkeng; Nickel, B. G.
 Physical Review Letters, Vol. 29, Issue 14
On the quantum mechanics of supermembranes
journal, December 1988
 de Wit, B.; Hoppe, J.; Nicolai, H.
 Nuclear Physics B, Vol. 305, Issue 4
Existence of a phasetransition in a onedimensional Ising ferromagnet
journal, June 1969
 Dyson, Freeman J.
 Communications in Mathematical Physics, Vol. 12, Issue 2
pAdic AdS/CFT
journal, January 2017
 Gubser, Steven S.; Knaute, Johannes; Parikh, Sarthak
 Communications in Mathematical Physics, Vol. 352, Issue 3
Scalar models of padic quantum field theory and hierarchical models
journal, February 1989
 Lerner, �. Yu.; Missarov, M. D.
 Theoretical and Mathematical Physics, Vol. 78, Issue 2
Tensor networks, $p$adic fields, and algebraic curves: arithmetic and the $\mathrm{AdS}_3 / \mathrm{CFT}_2$ correspondence
journal, January 2018
 Heydeman, Matthew; Marcolli, Matilde; Saberi, Ingmar A.
 Advances in Theoretical and Mathematical Physics, Vol. 22, Issue 1
Recursion Relations and Fixed Points for Ferromagnets with LongRange Interactions
journal, July 1973
 Sak, J.
 Physical Review B, Vol. 8, Issue 1
Crossover between field theories with shortrange and longrange exchange or correlations
journal, March 1989
 Honkonen, J.; Nalimov, M. Y.
 Journal of Physics A: Mathematical and General, Vol. 22, Issue 6