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Locality in theory space

Journal of High Energy Physics volume 2012, Article number: 7 (2012) Cite this article

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Abstract

Locality is a guiding principle for constructing realistic quantum field theories. Compactified theories offer an interesting context in which to think about locality, since interactions can be nonlocal in the compact directions while still being local in the extended ones. In this paper, we study locality in “theory space”, four-dimensional Lagrangians which are dimensional deconstructions of five-dimensional Yang-Mills. In explicit ultraviolet (UV) completions, one can understand the origin of theory space locality by the irrelevance of nonlocal operators. From an infrared (IR) point of view, though, theory space locality does not appear to be a special property, since the lowest-lying Kaluza- Klein (KK) modes are simply described by a gauged nonlinear sigma model, and locality imposes seemingly arbitrary constraints on the KK spectrum and interactions. We argue that these constraints are nevertheless important from an IR perspective, since they affect the four-dimensional cutoff of the theory where high energy scattering hits strong coupling. Intriguingly, we find that maximizing this cutoff scale implies five-dimensional locality. In this way, theory space locality is correlated with weak coupling in the IR, independent of UV considerations. We briefly comment on other scenarios where maximizing the cutoff scale yields interesting physics, including theory space descriptions of QCD and deconstructions of anti-de Sitter space.

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References

  1. N. Arkani-Hamed, A.G. Cohen and H. Georgi, (De)constructing dimensions, Phys. Rev. Lett. 86 (2001) 4757 [hep-th/0104005] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  2. J.M. Maldacena, The Large-N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys. 2 (1998) 231 [hep-th/9711200] [INSPIRE].

    MathSciNet  ADS  MATH  Google Scholar 

  3. S. Gubser, I.R. Klebanov and A.M. Polyakov, Gauge theory correlators from noncritical string theory, Phys. Lett. B 428 (1998) 105 [hep-th/9802109] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  4. E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].

    MathSciNet  ADS  MATH  Google Scholar 

  5. I. Heemskerk, J. Penedones, J. Polchinski and J. Sully, Holography from Conformal Field Theory, JHEP 10 (2009) 079 [arXiv:0907.0151] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  6. I. Heemskerk and J. Sully, More Holography from Conformal Field Theory, JHEP 09 (2010) 099 [arXiv:1006.0976] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  7. A.L. Fitzpatrick, E. Katz, D. Poland and D. Simmons-Duffin, Effective Conformal Theory and the Flat-Space Limit of AdS, JHEP 07 (2011) 023 [arXiv:1007.2412] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  8. R. Sundrum, From Fixed Points to the Fifth Dimension, arXiv:1106.4501 [INSPIRE].

  9. A.L. Fitzpatrick and J. Kaplan, Analyticity and the Holographic S-matrix, arXiv:1111.6972 [INSPIRE].

  10. R.S. Chivukula, D.A. Dicus and H.-J. He, Unitarity of compactified five-dimensional Yang-Mills theory, Phys. Lett. B 525 (2002) 175 [hep-ph/0111016] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  11. R.S. Chivukula and H.-J. He, Unitarity of deconstructed five-dimensional Yang-Mills theory, Phys. Lett. B 532 (2002) 121 [hep-ph/0201164] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  12. S. De Curtis, D. Dominici and J.R. Pelaez, Strong tree level unitarity violations in the extra dimensional standard model with scalars in the bulk, Phys. Rev. D 67 (2003) 076010 [hep-ph/0301059] [INSPIRE].

    ADS  Google Scholar 

  13. M.D. Schwartz, Constructing gravitational dimensions, Phys. Rev. D 68 (2003) 024029 [hep-th/0303114] [INSPIRE].

    ADS  Google Scholar 

  14. H. Georgi, Vector Realization of Chiral Symmetry, Nucl. Phys. B 331 (1990) 311 [INSPIRE].

    Article  ADS  Google Scholar 

  15. L. Randall and R. Sundrum, A Large mass hierarchy from a small extra dimension, Phys. Rev. Lett. 83 (1999) 3370 [hep-ph/9905221] [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  16. L. Randall and R. Sundrum, An Alternative to compactification, Phys. Rev. Lett. 83 (1999) 4690 [hep-th/9906064] [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  17. H. Abe, T. Kobayashi, N. Maru and K. Yoshioka, Field localization in warped gauge theories, Phys. Rev. D 67 (2003) 045019 [hep-ph/0205344] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  18. R.S. Chivukula, E.H. Simmons, H.-J. He, M. Kurachi and M. Tanabashi, Deconstruction and Elastic pi pi Scattering in Higgsless Models, Phys. Rev. D 75 (2007) 035005 [hep-ph/0612070] [INSPIRE].

    ADS  Google Scholar 

  19. L. Randall, Y. Shadmi and N. Weiner, Deconstruction and gauge theories in AdS 5, JHEP 01 (2003) 055 [hep-th/0208120] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  20. A. Falkowski and H.D. Kim, Running of gauge couplings in AdS 5 via deconstruction, JHEP 08 (2002) 052 [hep-ph/0208058] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  21. A. Manohar and H. Georgi, Chiral Quarks and the Nonrelativistic Quark Model, Nucl. Phys. B 234 (1984) 189 [INSPIRE].

    Article  ADS  Google Scholar 

  22. S. Weinberg, Phenomenological Lagrangians, Physica A 96 (1979) 327 [INSPIRE].

    ADS  Google Scholar 

  23. J.M. Cornwall, D.N. Levin and G. Tiktopoulos, Derivation of Gauge Invariance from High-Energy Unitarity Bounds on the s Matrix, Phys. Rev. D 10 (1974) 1145 [Erratum ibid. D 11 (1975) 972] [INSPIRE].

    ADS  Google Scholar 

  24. C. Vayonakis, Born Helicity Amplitudes and Cross-Sections in Nonabelian Gauge Theories, Lett. Nuovo Cim. 17 (1976) 383 [INSPIRE].

    Article  Google Scholar 

  25. B.W. Lee, C. Quigg and H. Thacker, The Strength of Weak Interactions at Very High-Energies and the Higgs Boson Mass, Phys. Rev. Lett. 38 (1977) 883 [INSPIRE].

    Article  ADS  Google Scholar 

  26. S. Chang and H.-J. He, Unitarity of little Higgs models signals new physics of UV completion, Phys. Lett. B 586 (2004) 95 [hep-ph/0311177] [INSPIRE].

    ADS  Google Scholar 

  27. R.N. Cahn and M. Suzuki, The Scalar bound state in nonminimal technicolor: A Surrogate Higgs boson, Phys. Rev. Lett. 67 (1991) 169 [INSPIRE].

    Article  ADS  Google Scholar 

  28. D. Son and M. Stephanov, QCD and dimensional deconstruction, Phys. Rev. D 69 (2004) 065020 [hep-ph/0304182] [INSPIRE].

    ADS  Google Scholar 

  29. R.S. Chivukula, M. Kurachi and M. Tanabashi, Generalized Weinberg sum rules in deconstructed QCD, JHEP 06 (2004) 004 [hep-ph/0403112] [INSPIRE].

    Article  ADS  Google Scholar 

  30. M. Piai, A. Pierce and J.G. Wacker, Composite vector mesons from QCD to the little Higgs, hep-ph/0405242 [INSPIRE].

  31. C. Csáki, C. Grojean, H. Murayama, L. Pilo and J. Terning, Gauge theories on an interval: Unitarity without a Higgs, Phys. Rev. D 69 (2004) 055006 [hep-ph/0305237] [INSPIRE].

    ADS  Google Scholar 

  32. N. Arkani-Hamed, A.G. Cohen and H. Georgi, Electroweak symmetry breaking from dimensional deconstruction, Phys. Lett. B 513 (2001) 232 [hep-ph/0105239] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  33. N. Arkani-Hamed, A.G. Cohen, T. Gregoire and J.G. Wacker, Phenomenology of electroweak symmetry breaking from theory space, JHEP 08 (2002) 020 [hep-ph/0202089] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  34. N. Arkani-Hamed, A. Cohen, E. Katz and A. Nelson, The Littlest Higgs, JHEP 07 (2002) 034 [hep-ph/0206021] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  35. M. Bando, T. Kugo and K. Yamawaki, Nonlinear Realization and Hidden Local Symmetries, Phys. Rept. 164 (1988) 217 [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  36. G. Brown and M. Rho, Chiral symmetry restoration and the Georgi vector limit, Phys. Lett. B 338 (1994) 301 [hep-ph/9408223] [INSPIRE].

    ADS  Google Scholar 

  37. A. Falkowski, C. Grojean, A. Kaminska, S. Pokorski and A. Weiler, If no Higgs then what?, JHEP 11 (2011) 028 [arXiv:1108.1183] [INSPIRE].

    Article  ADS  Google Scholar 

  38. K. Kawarabayashi and M. Suzuki, Partially conserved axial vector current and the decays of vector mesons, Phys. Rev. Lett. 16 (1966) 255 [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  39. Riazuddin and Fayyazuddin, Algebra of current components and decay widths of ρ and \(K *\) mesons, Phys. Rev. 147 (1966) 1071 [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  40. N. Arkani-Hamed, H. Georgi and M.D. Schwartz, Effective field theory for massive gravitons and gravity in theory space, Annals Phys. 305 (2003) 96 [hep-th/0210184] [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  41. N. Arkani-Hamed and M.D. Schwartz, Discrete gravitational dimensions, Phys. Rev. D 69 (2004) 104001 [hep-th/0302110] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  42. L. Randall, M.D. Schwartz and S. Thambyahpillai, Discretizing gravity in warped spacetime, JHEP 10 (2005) 110 [hep-th/0507102] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  43. J. Gallicchio and I. Yavin, Curvature as a remedy or discretizing gravity in warped dimensions, JHEP 05 (2006) 079 [hep-th/0507105] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  44. R.S. Chivukula, M.J. Dugan and M. Golden, Analyticity, crossing symmetry and the limits of chiral perturbation theory, Phys. Rev. D 47 (1993) 2930 [hep-ph/9206222] [INSPIRE].

    ADS  Google Scholar 

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Authors and Affiliations

  1. Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, MA, 02139, U.S.A.

    Yonatan Kahn & Jesse Thaler

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  1. Yonatan Kahn
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  2. Jesse Thaler
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Correspondence to Yonatan Kahn.

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ArXiv ePrint: 1202.5491

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Kahn, Y., Thaler, J. Locality in theory space. J. High Energ. Phys. 2012, 7 (2012). https://doi.org/10.1007/JHEP07(2012)007

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  • DOI: https://doi.org/10.1007/JHEP07(2012)007

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