Papers
Topics
Authors
Recent
Detailed Answer
Quick Answer
Concise responses based on abstracts only
Detailed Answer
Well-researched responses based on abstracts and relevant paper content.
Custom Instructions Pro
Preferences or requirements that you'd like Emergent Mind to consider when generating responses
Gemini 2.5 Flash
Gemini 2.5 Flash 84 tok/s
Gemini 2.5 Pro 48 tok/s Pro
GPT-5 Medium 21 tok/s Pro
GPT-5 High 28 tok/s Pro
GPT-4o 96 tok/s Pro
GPT OSS 120B 462 tok/s Pro
Kimi K2 189 tok/s Pro
2000 character limit reached

On the UV/IR mixing of Lie algebra-type noncommutatitive $φ^4$-theories (2309.08917v4)

Published 16 Sep 2023 in hep-th, math-ph, and math.MP

Abstract: We show that a UV divergence of the propagator integral implies the divergences of the UV/IR mixing in the two-point function at one-loop for a $\phi4$-theory on a generic Lie algebra-type noncommutative space-time. The UV/IR mixing is defined as a UV divergence of the planar contribution and an IR singularity of the non-planar contribution, the latter being due to the former UV divergence, and the UV finiteness of the non-planar contribution. Some properties of this general treatment are discussed. The UV finiteness of the non-planar contribution and the renormalizability of the theory are not treated but commented. Applications are performed for the Moyal space, having a UV/IR mixing, and the $\kappa$-Minkowski space for which the two-point function at one-loop is finite.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (35)
  1. S. Doplicher, K. Fredenhagen, J.E. Roberts, “The quantum structure of space-time at the Planck scale and quantum fields”, Commun. Math. Phys. 172 (1995) 187, doi:10.1007/BF02104515, arXiv:hep-th/0303037.
  2. H. S. Snyder, “Quantized Space-Time”, Phys. Rev. 71 (1947) 38, doi:10.1103/PhysRev.71.38.
  3. S. Minwalla, M. Van Raamsdonk, N. Seiberg, “Noncommutative perturbative dynamics”, JHEP 02 (2000) 020, doi:10.1088/1126-6708/2000/02/020, arXiv:hep-th/9912072.
  4. A. Micu and M. M. Sheikh-Jabbari, “Noncommutative Φ4superscriptnormal-Φ4\Phi^{4}roman_Φ start_POSTSUPERSCRIPT 4 end_POSTSUPERSCRIPT theory at two loops”, JHEP 01 (2001) 025, doi:10.1088/1126-6708/2001/01/025, arXiv:hep-th/0008057.
  5. A. Matusis, L. Susskind, N. Toumbas, “The IR/UV Connection in the Non-Commutative Gauge Theories”, JHEP 12 (2000) 002, doi:10.1088/1126-6708/2000/12/002, arXiv:hep-th/0002075.
  6. D. N. Blaschke, E. Kronberger, A. Rofner, M. Schweda, R. I. P. Sedmik, M.Wohlgenannt, “On the Problem of Renormalizability in Non-Commutative Gauge Field Models - A Critical Review”, Fortschr. Phys. 58 (2010) 364, doi:10.1002/prop.200900102, arXiv:0908.0467.
  7. H. Grosse and M. Wohlgenannt, “On κ𝜅\kappaitalic_κ-deformation and UV/IR mixing”, Nuc. Phys. B 748 (2006) 473-484, doi:10.1016/j.nuclphysb.2006.05.004, arXiv:hep-th/0507030.
  8. T. Poulain and J.-C. Wallet, “κ𝜅\kappaitalic_κ-Poincaré invariant orientable field theories at one-loop”, JHEP 2019 (2019), doi:10.1007/jhep01(2019)064, arXiv:1808.00350.
  9. M. Dimitrijević Ćirić, N. Konjik, M. A. Kurkov, F. Lizzi and P. Vitale, “Noncommutative field theory from angular twist”, Phys. Rev. D 98 (2018), doi:10.1103/physrevd.98.085011, arXiv:1806.06678.
  10. K. Hersent and J.-C. Wallet, “Field theories on ρ𝜌\rhoitalic_ρ-deformed Minkowski space-time”, arXiv (2023), arXiv:2304.05787.
  11. D. Robbins and S. Sethi, “The UV/IR interplay in theories with space-time varying non-commutativity”, JHEP 07 (2003) 034, doi:10.1088/1126-6708/2003/07/034, arXiv:hep-th/0306193.
  12. R. Gurau, J. Magnen, V. Rivasseau and A. Tanasa, “A translation-invariant renormalizable non-commutative scalar model”, Commun. Math. Phys. 287 (2009) 275, doi:10.1007/s00220-008-0658-3, arXiv:0802.0791.
  13. B. Mirza and M. Zarei, “Cancellation of soft and collinear divergences in noncommutative QED”, Phys. Rev. D 74 (2006), doi:10.1103/physrevd.74.065019, arXiv:hep-th/0609181.
  14. A. Jafar Salim and N. Sadooghi, “Dynamics of the O⁢(N)𝑂𝑁O(N)italic_O ( italic_N ) model in a strong magnetic background field as a modified noncommutative field theory”, Phys. Rev. D 73 (2006), doi:10.1103/physrevd.73.065023, arXiv:hep-th/0602023.
  15. A. Schenkel and C. F. Uhlemann, “High energy improved scalar quantum field theory from noncommutative geometry without UV/IR-mixing”, Phys. Lett. B 694 (2010) 258-260, doi:10.1016/j.physletb.2010.09.066, arXiv:1002.4191.
  16. H. C. Steinacker, “String states, loops and effective actions in noncommutative field theory and matrix models”, Nuc. Phys. B 910 (2016) 346-373, doi:10.1016/j.nuclphysb.2016.06.029, arXiv:1606.00646.
  17. A. Van-Brunt and M. Visser, “Special-case closed form of the Baker-Campbell-Hausdorff formula”, Jour. Phys. A 48 (2015) 225207, doi:10.1088/1751-8113/48/22/225207, arXiv:1501.02506.
  18. A. Van-Brunt and M. Visser, “Explicit Baker-Campbell-Hausdorff Expansions”, Mathematics 6 (2018) 135, doi:10.3390/math6080135, arXiv:1505.04505
  19. F. Mercati and M. Sergola, “Pauli-Jordan function and scalar field quantization in κ𝜅\kappaitalic_κ-Minkowski noncommutative spacetime”, Phys. Rev. D 98 (2018), doi:10.1103/physrevd.98.045017, arXiv:1801.01765
  20. S. Galluccio, F. Lizzi and P. Vitale, “Translation invariance, commutation relations and ultraviolet/infrared mixing”, JHEP 2009 (2009) 054-054, doi:10.1088/1126-6708/2009/09/054, arXiv:0907.3640.
  21. A. Dietmar and S. Echterhoff, “Principles of harmonic analysis”, Springer (2014), doi:10.1007/978-3-319-05792-7.
  22. A. H. Fatollahi and M. Khorrami, “Field theories on spaces with linear fuzziness”, Europhysics Letters 80 (2007) 20003, doi:10.1209/0295-5075/80/20003, arXiv:hep-th/0612013.
  23. H. Komaie-Moghaddam, A. H. Fatollahi and M. Khorrami, “Field theory amplitudes in a space with S⁢U⁢(2)𝑆𝑈2SU(2)italic_S italic_U ( 2 ) fuzziness”, European Physical Journal C 53 (2007) 679-688, doi:10.1140/epjc/s10052-007-0484-3, arXiv:0712.1670.
  24. H. Komaie-Moghaddam, A. H. Fatollahi and M. Khorrami, “Loop diagrams in space with S⁢U⁢(2)𝑆𝑈2SU(2)italic_S italic_U ( 2 ) fuzziness”, Phys. Lett. B 661 (2008) 226-232, doi:10.1016/j.physletb.2008.02.002, arXiv:0712.2216.
  25. T. Flik, “Divergences in a field theory on quantum space”, Phys. Let. B 376 (1996) 53-58, doi:10.1016/0370-2693(96)00024-X.
  26. P. Vitale and J.-C. Wallet, “Noncommutative field theories on ℝλ3subscriptsuperscriptℝ3𝜆\mathbb{R}^{3}_{\lambda}blackboard_R start_POSTSUPERSCRIPT 3 end_POSTSUPERSCRIPT start_POSTSUBSCRIPT italic_λ end_POSTSUBSCRIPT: towards UV/IR mixing freedom”, JHEP 2013 (2013), doi:10.1007/jhep04(2013)115, arXiv:1212.5131.
  27. N. Craig and S. Koren, “IR dynamics from UV divergences: UV/IR mixing, NCFT, and the hierarchy problem”, JHEP 2020 (2020), doi:10.1007/jhep03(2020)037, arXiv:1909.01365.
  28. H. Steinacker, “Emergent gravity from noncommutative gauge theory”, JHEP 2007 (2007) 049, doi:10.1088/1126-6708/2007/12/049, arXiv:0708.2426.
  29. A. Addazi et al, “Quantum gravity phenomenology at the dawn of the multi-messenger era - A review”, Prog. Part. Nuc. Phys. 125 (2022) 103948, DOI:10.1016/j.ppnp.2022.103948, arXiv:2111.05659.
  30. J. Lukierski, “κ𝜅\kappaitalic_κ-deformations: historical developments and recent results”, Jour. Phys. Conf. Ser. 804 (2017) 012028, DOI:10.1088/1742-6596/804/1/012028, arXiv:1611.10213.
  31. T. Poulain and J.-C. Wallet, “κ𝜅\kappaitalic_κ-Poincaré invariant quantum field theories with Kubo-Martin-Schwinger weight”, Phys. Rev. D 98 (2018), DOI:10.1103/PhysRevD.98.025002, arXiv:1801.02715.
  32. P. Kosiński, J. Lukierski and P. Maślanka, “Local D=4 Field Theory on κ𝜅\kappaitalic_κ-Deformed Minkowski Space”, Phys. Rev. D 62 (2000), doi:10.1103/physrevd.62.025004, arXiv:hep-th/9902037.
  33. G. Amelino-Camelia and M. Arzano, “Coproduct and star product in field theories on Lie-algebra noncommutative space-times”, Phys. Rev. D 65 (2002), doi:10.1103/physrevd.65.084044, arXiv:hep-th/0105120.
  34. F. Buscemi, M. Dall’Arno, M. Ozawa and V. Vedral, “Direct observation of any two-point quantum correlation function”, arXiv (2013), arXiv:1312.4240. B. Bertúlio de Lima, S. Azevedo and A. Rosas, “On the measurability of quantum correlation functions”, Annals of Physics 356 (2015) 336-345, doi:10.1016/j.aop.2015.03.012. J. de Ramón, L. J. Garay and E. Martín-Martínez, “Direct measurement of the two-point function in quantum fields”, Phys. Rev. D 98 (2018), doi:10.1103/physrevd.98.105011, arXiv:1807.00013. P. Guilmin, P. Rouchon and A. Tilloy, “Correlation functions for realistic continuous quantum measurement”, arXiv (2023), arXiv:2212.00176.
  35. P. Mathieu and J.-C. Wallet, “Gauge theories on κ𝜅\kappaitalic_κ-Minkowski spaces: Twist and modular operators”, JHEP 2020 (2020) 112 doi:10.1007/JHEP05(2020)112, arXiv:2002.02309.
Citations (1)
View on Semantic Scholar
List To Do Tasks Checklist Streamline Icon: https://streamlinehq.com

Collections

Sign up for free to add this paper to one or more collections.

User Circle Single Streamline Icon: https://streamlinehq.com Sign Up

Summary

We haven't generated a summary for this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Summarize Now
Ai Generate Text Spark Streamline Icon: https://streamlinehq.com

Paper Prompts

Sign up for free to create and run prompts on this paper using GPT-5.

List Streamline Icon: https://streamlinehq.com Explore 10 Community Prompts
Dice Question Streamline Icon: https://streamlinehq.com

Follow-up Questions

We haven't generated follow-up questions for this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Generate Now

Authors (1)

  1. Kilian Hersent
X Twitter Logo Streamline Icon: https://streamlinehq.com

Tweets