Non-local non-linear sigma models

Gubser, Steven S.; Jepsen, Christian B.; Ji, Ziming; Trundy, Brian; Yarom, Amos

doi:10.1007/jhep09(2019)005

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:

Gubser, Steven S. ^[1]; Jepsen, Christian B. ^[1];

^[1]; Trundy, Brian ^[1]; Yarom, Amos ^[2]

Princeton Univ., NJ (United States)
Princeton Univ., NJ (United States); Technion, Haifa (Israel)

Publication Date:: 2019-09-02

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.  doi:10.1007/jhep09(2019)005.

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                    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

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                    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.

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@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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Title: Non-local non-linear sigma models

Abstract

Citation Formats

A four-dimensional non-linear σ-model journal, August 1978

Conformal invariance in the long-range Ising model journal, January 2016

The supermembrane is unstable journal, June 1989

O(N) and O(N) and O(N) journal, November 2017

Riemann normal coordinate expansions using Cadabra journal, August 2009

A scaling theory for the long-range to short-range crossover and an infrared duality journal, August 2017

Nonlinear models in 2 + ε dimensions journal, September 1985

Critical Exponents for Long-Range Interactions journal, October 1972

On the quantum mechanics of supermembranes journal, December 1988

Existence of a phase-transition in a one-dimensional Ising ferromagnet journal, June 1969

p-Adic AdS/CFT journal, January 2017

Scalar models of p-adic quantum field theory and hierarchical models journal, February 1989

Tensor networks, $p$-adic fields, and algebraic curves: arithmetic and the $\mathrm{AdS}_3 / \mathrm{CFT}_2$ correspondence journal, January 2018

Recursion Relations and Fixed Points for Ferromagnets with Long-Range Interactions journal, July 1973

Crossover between field theories with short-range and long-range exchange or correlations journal, March 1989

A four-dimensional non-linear σ-model
journal, August 1978

Conformal invariance in the long-range Ising model
journal, January 2016

The supermembrane is unstable
journal, June 1989

O(N) and O(N) and O(N)
journal, November 2017

Riemann normal coordinate expansions using Cadabra
journal, August 2009

A scaling theory for the long-range to short-range crossover and an infrared duality
journal, August 2017

Nonlinear models in 2 + ε dimensions
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Critical Exponents for Long-Range Interactions
journal, October 1972

On the quantum mechanics of supermembranes
journal, December 1988

Existence of a phase-transition in a one-dimensional Ising ferromagnet
journal, June 1969

p-Adic AdS/CFT
journal, January 2017

Scalar models of p-adic quantum field theory and hierarchical models
journal, February 1989

Tensor networks, $p$-adic fields, and algebraic curves: arithmetic and the $\mathrm{AdS}_3 / \mathrm{CFT}_2$ correspondence
journal, January 2018

Recursion Relations and Fixed Points for Ferromagnets with Long-Range Interactions
journal, July 1973

Crossover between field theories with short-range and long-range exchange or correlations
journal, March 1989