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Title: IR dynamics from UV divergences: UV/IR mixing, NCFT, and the hierarchy problem

Abstract

The persistence of the hierarchy problem points to a violation of effective field theory expectations. A compelling possibility is that this results from a physical breakdown of EFT, which may arise from correlations between ultraviolet (UV) and infrared (IR) physics. To this end, we study noncommutative field theory (NCFT) as a toy model of UV/IR mixing which generates an emergent infrared scale from ultraviolet dynamics. We explore the range of such theories where ultraviolet divergences are transmogrified into infrared scales, focusing particularly on the properties of Yukawa theory, where we identify a new infrared pole accessible in the s-channel of the Lorentzian theory. We further investigate the interplay between UV-finiteness and UV/IR mixing by studying properties of the softly-broken noncommutative Wess-Zumino model as soft terms are varied relative to the cutoff. While the Lorentz violation inherent to noncommutative theories may limit their direct application to the hierarchy problem, these toy models provide general lessons to guide the realization of UV/IR mixing in more realistic theories.

Authors:
 [1]; ORCiD logo [1]
  1. University of California, Santa Barbara, CA (United States)
Publication Date:
Research Org.:
Univ. of California, Santa Barbara, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), High Energy Physics (HEP)
OSTI Identifier:
1673185
Grant/Contract Number:  
SC0014129
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: 2020; Journal Issue: 3; Journal ID: ISSN 1029-8479
Publisher:
Springer Berlin
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Effective Field Theories; Non-Commutative Geometry; Nonperturbative Effects; Space-Time Symmetries

Citation Formats

Craig, Nathaniel, and Koren, Seth. IR dynamics from UV divergences: UV/IR mixing, NCFT, and the hierarchy problem. United States: N. p., 2020. Web. doi:10.1007/jhep03(2020)037.
Craig, Nathaniel, & Koren, Seth. IR dynamics from UV divergences: UV/IR mixing, NCFT, and the hierarchy problem. United States. https://doi.org/10.1007/jhep03(2020)037
Craig, Nathaniel, and Koren, Seth. Fri . "IR dynamics from UV divergences: UV/IR mixing, NCFT, and the hierarchy problem". United States. https://doi.org/10.1007/jhep03(2020)037. https://www.osti.gov/servlets/purl/1673185.
@article{osti_1673185,
title = {IR dynamics from UV divergences: UV/IR mixing, NCFT, and the hierarchy problem},
author = {Craig, Nathaniel and Koren, Seth},
abstractNote = {The persistence of the hierarchy problem points to a violation of effective field theory expectations. A compelling possibility is that this results from a physical breakdown of EFT, which may arise from correlations between ultraviolet (UV) and infrared (IR) physics. To this end, we study noncommutative field theory (NCFT) as a toy model of UV/IR mixing which generates an emergent infrared scale from ultraviolet dynamics. We explore the range of such theories where ultraviolet divergences are transmogrified into infrared scales, focusing particularly on the properties of Yukawa theory, where we identify a new infrared pole accessible in the s-channel of the Lorentzian theory. We further investigate the interplay between UV-finiteness and UV/IR mixing by studying properties of the softly-broken noncommutative Wess-Zumino model as soft terms are varied relative to the cutoff. While the Lorentz violation inherent to noncommutative theories may limit their direct application to the hierarchy problem, these toy models provide general lessons to guide the realization of UV/IR mixing in more realistic theories.},
doi = {10.1007/jhep03(2020)037},
journal = {Journal of High Energy Physics (Online)},
number = 3,
volume = 2020,
place = {United States},
year = {2020},
month = {3}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Figures / Tables:

Figure 1 Figure 1: Representative leading nonplanar corrections to the self-energies in the noncommutative Yukawa theory of [107]. Fermion lines have arrows and dashing denotes nonintersection.

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Works referenced in this record:

On the Newtonian limit of emergent NC gravity and long-distance corrections
journal, December 2009


Emergent gravity, matrix models and UV/IR mixing
journal, April 2008

  • Grosse, Harald; Steinacker, Harold; Wohlgenannt, Michael
  • Journal of High Energy Physics, Vol. 2008, Issue 04
  • DOI: 10.1088/1126-6708/2008/04/023

Noncommutative gauge field theories: a no-go theorem
journal, January 2002


Hamiltonian formalism for space-time noncommutative theories
journal, January 2001


Noncommutative field theory
journal, November 2001


On evaluation of nonplanar diagrams in noncommutative field theory
journal, May 2005


UV/IR mixing for noncommutative complex scalar field theory interacting with gauge fields
journal, September 2001


Circumventing the no-go theorem in noncommutative gauge field theory
journal, March 2008


The fundamental need for a SM Higgs and the weak gravity conjecture
journal, November 2018


Minimal Length Scale Scenarios for Quantum Gravity
journal, January 2013


A Translation-Invariant Renormalizable Non-Commutative Scalar Model
journal, October 2008

  • Gurau, R.; Magnen, J.; Rivasseau, V.
  • Communications in Mathematical Physics, Vol. 287, Issue 1
  • DOI: 10.1007/s00220-008-0658-3

Strings in background electric field, space/time noncommutativity and a new noncritical string theory
journal, May 2000


On the Correspondence Between Noncommutative Field Theory and Gravity
journal, May 2007


Renormalisation of ?4-Theory on Noncommutative ?4 in the Matrix Base
journal, February 2005

  • Grosse, Harald; Wulkenhaar, Raimar
  • Communications in Mathematical Physics, Vol. 256, Issue 2
  • DOI: 10.1007/s00220-004-1285-2

On the unitarity problem in space/time noncommutative theories
journal, May 2002


The Lee-Wick standard model
journal, January 2008


Remarks on noncommutative phenomenology
journal, April 2002


Time-ordered perturbation theory on non-commutative spacetime II: Unitarity
journal, October 2002


Noncommutative perturbative dynamics
journal, February 2000


A review of the generalized uncertainty principle
journal, October 2015


A new derivation of the CPT and spin-statistics theorems in noncommutative field theories
journal, August 2005

  • Franco, Daniel H. T.; Polito, Caio M. M.
  • Journal of Mathematical Physics, Vol. 46, Issue 8
  • DOI: 10.1063/1.1982769

Untwisting noncommutative and the equivalence of quantum field theories
journal, August 2000


Deformation Quantization of Poisson Manifolds
journal, December 2003


Space–time noncommutative field theories and unitarity
journal, December 2000


On the IR/UV mixing and experimental limits on the parameters of canonical noncommutative spacetimes
journal, January 2004

  • Amelino-Camelia, Giovanni; Mandanici, Gianluca; Yoshida, Kensuke
  • Journal of High Energy Physics, Vol. 2004, Issue 01
  • DOI: 10.1088/1126-6708/2004/01/037

The IR/UV connection in the non-commutative gauge theories
journal, December 2000


A generalized uncertainty principle in quantum gravity
journal, April 1993


The quantum structure of spacetime at the Planck scale and quantum fields
journal, August 1995

  • Doplicher, Sergio; Fredenhagen, Klaus; Roberts, John E.
  • Communications in Mathematical Physics, Vol. 172, Issue 1
  • DOI: 10.1007/BF02104515

Dielectric-branes
journal, December 1999


The Low Energy Limit of the Noncommutative Wess-Zumino Model
journal, May 2002

  • Girotti, Horacio O.; Gomes, Marcelo; Rivelles, Victor O.
  • Journal of High Energy Physics, Vol. 2002, Issue 05
  • DOI: 10.1088/1126-6708/2002/05/040

Non-supersymmetric AdS and the swampland
journal, January 2017


Space/time non-commutativity and causality
journal, May 2000


4D Conformal Field Theories and Strings on Orbifolds
journal, June 1998


Noncommutative gauge theory, divergences and closed strings
journal, March 2000


Axiomatic formulations of nonlocal and noncommutative field theories
journal, May 2006


Three-dimensional noncommutative Yukawa theory: Induced effective action and propagating modes
journal, February 2017


Translational-invariant noncommutative gauge theory
journal, January 2011


Closed strings tachyons and non-commutative instabilities
journal, February 2003


Noncommutative geometry and Matrix theory
journal, February 1998


String theory and noncommutative geometry
journal, September 1999


Duality in scalar field theory on noncommutative phase spaces
journal, May 2002


Two-component spinor techniques and Feynman rules for quantum field theory and supersymmetry
journal, September 2010


The meaning of infrared singularities in noncommutative gauge theories
journal, November 2001


S-duality and noncommutative gauge theory
journal, May 2000


Non-commutative standard model: model building
journal, July 2003

  • Chaichian, M.; Presnajder, P.; Sheikh-Jabbari, M. M.
  • The European Physical Journal C, Vol. 29, Issue 3
  • DOI: 10.1140/epjc/s2003-01204-7

D-branes and the noncommutative torus
journal, February 1998


Time ordered perturbation theory for non-local interactions; applications to NCQFT
journal, September 2003


On the stringy nature of winding modes in noncommutative thermal field theories
journal, May 2000


From UV/IR mixing to closed strings
journal, September 2003


Negative metric and the unitarity of the S-matrix
journal, February 1969


Spin-statistics and CPT theorems in noncommutative field theory
journal, August 2003


Divergencies in a field theory on quantum space
journal, May 1996


Open strings in a B-field background as electric dipoles
journal, May 1999


Nonlocal vertices and analyticity: Landau equations and general Cutkosky rule
journal, June 2018


Naturalness and the Weak Gravity Conjecture
journal, July 2014


Unitarity in space–time noncommutative field theories
journal, November 2003


Gravitational observables and local symmetries
journal, September 1993


On the unitarity of quantum gauge theories on non-commutative spaces
journal, July 2001


UV/IR mixing and the Goldstone theorem in noncommutative field theory
journal, August 2002


Evidence for winding states in noncommutative quantum field theory
journal, May 2000


Discrete gauge symmetries and the weak gravity conjecture
journal, May 2019

  • Craig, Nathaniel; Garcia, Isabel Garcia; Koren, Seth
  • Journal of High Energy Physics, Vol. 2019, Issue 5
  • DOI: 10.1007/JHEP05(2019)140

Lorentz-Invariant Non-Commutative Space-Time Based on DFR Algebra
journal, April 2003

  • Kase, H.; Morita, K.; Okumura, Y.
  • Progress of Theoretical Physics, Vol. 109, Issue 4
  • DOI: 10.1143/PTP.109.663

Duality of nonsupersymmetric large N gauge theories
journal, April 1999


A consistent noncommutative field theory: the Wess–Zumino model
journal, October 2000


The weak scale from weak gravity
journal, September 2019

  • Craig, Nathaniel; Garcia Garcia, Isabel; Koren, Seth
  • Journal of High Energy Physics, Vol. 2019, Issue 9
  • DOI: 10.1007/JHEP09(2019)081

Space/time non-commutative field theories and causality
journal, July 2003


Fermions and emergent noncommutative gravity
journal, August 2008


Weak gravity conjecture, multiple point principle and the standard model landscape
journal, November 2017


One loop radiative corrections to the translation-invariant noncommutative Yukawa Theory
journal, August 2015


A Poincaré covariant noncommutative spacetime
journal, August 2018

  • Much, Albert; David Vergara, J.
  • International Journal of Geometric Methods in Modern Physics, Vol. 15, Issue 09
  • DOI: 10.1142/S0219887818501591

Quantum field theory on noncommutative spaces
journal, May 2003


UV / IR mixing in noncommutative field theory via open string loops
journal, October 2000


Translation invariance, commutation relations and ultraviolet/infrared mixing
journal, September 2009


Phase structure of non-commutative scalar field theories
journal, July 2001


Covariant field equations, gauge fields and conservation laws from Yang-Mills matrix models
journal, February 2009


Renormalization group equations and the Lifshitz point in noncommutative Landau–Ginsburg theory
journal, February 2002


Noncommutative time in quantum field theory
journal, July 2011


Minimum physical length and the generalized uncertainty principle in string theory
journal, January 1990


Nonlocal and quasilocal field theories
journal, December 2015


Light-like noncommutativity, light-front quantization and new light on UV/IR mixing
journal, February 2011


On a Lorentz-invariant interpretation of noncommutative space–time and its implications on noncommutative QFT
journal, December 2004


Noncommutative field theories and gravity
journal, April 2003


Covariant non-commutative space–time
journal, May 2015


Comments on noncommutative perturbative dynamics
journal, March 2000


A note on non-commutative orbifold field theories
journal, March 2000


Emergent gravity and noncommutative branes from Yang–Mills matrix models
journal, March 2009


AdS-phobia, the WGC, the Standard Model and Supersymmetry
journal, June 2018

  • Gonzalo, Eduardo; Herráez, Alvaro; Ibáñez, Luis E.
  • Journal of High Energy Physics, Vol. 2018, Issue 6
  • DOI: 10.1007/JHEP06(2018)051

Gauge-invariant observables, gravitational dressings, and holography in AdS
journal, November 2018

  • Giddings, Steven B.; Kinsella, Alex
  • Journal of High Energy Physics, Vol. 2018, Issue 11
  • DOI: 10.1007/JHEP11(2018)074

Magnetic fields, branes, and noncommutative geometry
journal, August 2000


Scalar fields, hierarchical UV/IR mixing and the Weak Gravity Conjecture
journal, February 2018


On theories with light-like noncommutativity
journal, September 2000


New Concept of Relativistic Invariance in Noncommutative Space-Time: Twisted Poincaré Symmetry and Its Implications
journal, April 2005


Instantons and emergent geometry
journal, November 2009


Spontaneous reduction of noncommutative gauge symmetry and model building
journal, April 2006


A non-perturbative approach to non-commutative scalar field theory
journal, March 2005


Comments on perturbative dynamics of non-commutative Yang–Mills theory
journal, January 2001


Paramagnetic dominance, the sign of the beta function and UV/IR mixing in non-commutative
journal, March 2001


Constraining neutrino masses, the cosmological constant and BSM physics from the weak gravity conjecture
journal, November 2017

  • Ibáñez, Luis E.; Martín-Lozano, Víctor; Valenzuela, Irene
  • Journal of High Energy Physics, Vol. 2017, Issue 11
  • DOI: 10.1007/JHEP11(2017)066

Remarks on time-space noncommutative field theories
journal, May 2001

  • Alvarez-Gaumé, Luis; Barbón, José L. F.; Zwicky, Roman
  • Journal of High Energy Physics, Vol. 2001, Issue 05
  • DOI: 10.1088/1126-6708/2001/05/057

Towards LHC physics with nonlocal Standard Model
journal, September 2015


Self-Dual Noncommutative $${\phi^4}$$ ϕ 4 -Theory in Four Dimensions is a Non-Perturbatively Solvable and Non-Trivial Quantum Field Theory
journal, March 2014

  • Grosse, Harald; Wulkenhaar, Raimar
  • Communications in Mathematical Physics, Vol. 329, Issue 3
  • DOI: 10.1007/s00220-014-1906-3

Observables in effective gravity
journal, September 2006


Dynamics with infinitely many derivatives: the initial value problem
journal, February 2008


Nonlocal quantum field theory without acausality and nonunitarity at quantum level: Is SUSY the key?
journal, May 2015

  • Addazi, Andrea; Esposito, Giampiero
  • International Journal of Modern Physics A, Vol. 30, Issue 15
  • DOI: 10.1142/S0217751X15501031

Emergent geometry and gravity from matrix models: an introduction
journal, May 2010


Two-loop diagrams in noncommutative ϕ44 theory
journal, March 2000


No UV/IR mixing in unitary space-time non-commutative field theory
journal, January 2004


Nonuniform symmetry breaking in noncommutative λ Φ 4 theory
journal, September 2003


Lorentz Invariance and Quantum Gravity: An Additional Fine-Tuning Problem?
journal, November 2004


C , P , and T Invariance of Noncommutative Gauge Theories
journal, June 2000


Small Lorentz violations in quantum gravity: do they lead to unacceptably large effects?
journal, June 2011


Exact Seiberg–Witten map and Induced Gravity from Noncommutativity
journal, November 2006


UV/IR mixing via closed strings and tachyonic instabilities
journal, June 2002


Particle creation by black holes
journal, August 1975

  • Hawking, S. W.
  • Communications In Mathematical Physics, Vol. 43, Issue 3
  • DOI: 10.1007/BF02345020

Quantized Space-Time
journal, January 1947


Emergent gravity from noncommutative gauge theory
journal, December 2007


Renormalization of quantum field theories on noncommutative Bbb R d , 1. Scalars
journal, May 2000


Noncommutative Standard Modelling
journal, September 2004


Noncommutative gauge theory without Lorentz violation
journal, October 2002


Towards LHC physics with nonlocal Standard Model
journal, September 2015


On a Lorentz-invariant interpretation of noncommutative space–time and its implications on noncommutative QFT
journal, December 2004


The fundamental need for a SM Higgs and the weak gravity conjecture
journal, November 2018


General properties of non-commutative field theories
journal, September 2003


Large N limit of orbifold field theories
journal, December 1998


Evidence for winding states in noncommutative quantum field theory
journal, May 2000


The IR/UV connection in the non-commutative gauge theories
journal, December 2000


Remarks on time-space noncommutative field theories
journal, May 2001

  • Alvarez-Gaumé, Luis; Barbón, José L. F.; Zwicky, Roman
  • Journal of High Energy Physics, Vol. 2001, Issue 05
  • DOI: 10.1088/1126-6708/2001/05/057

Time ordered perturbation theory for non-local interactions; applications to NCQFT
journal, September 2003


On the IR/UV mixing and experimental limits on the parameters of canonical noncommutative spacetimes
journal, January 2004

  • Amelino-Camelia, Giovanni; Mandanici, Gianluca; Yoshida, Kensuke
  • Journal of High Energy Physics, Vol. 2004, Issue 01
  • DOI: 10.1088/1126-6708/2004/01/037

Noncommutative Standard Modelling
journal, September 2004


One loop radiative corrections to the translation-invariant noncommutative Yukawa Theory
journal, August 2015


Canonical quantization of noncommutative field theory
journal, February 2003


String Theory and the Space-Time Uncertainty Principle
journal, June 2000


Minimal Length Scale Scenarios for Quantum Gravity
journal, January 2013


Gauge-invariant observables, gravitational dressings, and holography in AdS
text, January 2018


On the unitarity problem in space/time noncommutative theories
text, January 2002


Noncommutative Field Theories and Gravity
text, January 2002


Magnetic fields, branes and noncommutative geometry
text, January 1999


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