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Effective string theory revisited

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Abstract

We revisit the effective field theory of long relativistic strings such as confining flux tubes in QCD. We derive the Polchinski-Strominger interaction by a calculation in static gauge. This interaction implies that a non-critical string which initially oscillates in one direction gets excited in orthogonal directions as well. In static gauge no additional term in the effective action is needed to obtain this effect. It results from a one-loop calculation using the Nambu-Goto action. Non-linearly realized Lorentz symmetry is manifest at all stages in dimensional regularization. We also explain that independent of the number of dimensions non-covariant counterterms have to be added to the action in the commonly used zeta-function regularization.

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References

  1. M. Teper, Large-N and confining flux tubes as strings — a view from the lattice, Acta Phys. Polon. B 40 (2009) 3249 [arXiv:0912.3339] [INSPIRE].

    Google Scholar 

  2. J. Kuti, Lattice QCD and string theory, PoS(LAT2005)001 [hep-lat/0511023] [INSPIRE].

  3. I. Low and A.V. Manohar, Spontaneously broken space-time symmetries and Goldstone’s theorem, Phys. Rev. Lett. 88 (2002) 101602 [hep-th/0110285] [INSPIRE].

    Article  ADS  Google Scholar 

  4. S.R. Coleman, J. Wess and B. Zumino, Structure of phenomenological Lagrangians. 1, Phys. Rev. 177 (1969) 2239 [INSPIRE].

    Article  ADS  Google Scholar 

  5. C.G. Callan Jr., S.R. Coleman, J. Wess and B. Zumino, Structure of phenomenological Lagrangians. 2, Phys. Rev. 177 (1969) 2247 [INSPIRE].

    Article  ADS  Google Scholar 

  6. C. Isham, A. Salam and J. Strathdee, Nonlinear realizations of space-time symmetries. Scalar and tensor gravity, Annals Phys. 62 (1971) 98 [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  7. D.V. Volkov, Phenomenological Lagrangians, Fiz. Elem. Chast. Atom. Yadra 4 (1973) 3 [INSPIRE].

    Google Scholar 

  8. A.M. Polyakov, Fine structure of strings, Nucl. Phys. B 268 (1986) 406 [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  9. H. Kleinert, The membrane properties of condensing strings, Phys. Lett. B 174 (1986) 335 [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  10. O. Aharony and N. Klinghoffer, Corrections to Nambu-Goto energy levels from the effective string action, JHEP 12 (2010) 058 [arXiv:1008.2648] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  11. O. Aharony and M. Field, On the effective theory of long open strings, JHEP 01 (2011) 065 [arXiv:1008.2636] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  12. M. Billó, M. Caselle, F. Gliozzi, M. Meineri and R. Pellegrini, The Lorentz-invariant boundary action of the confining string and its universal contribution to the inter-quark potential, JHEP 05 (2012) 130 [arXiv:1202.1984] [INSPIRE].

    Article  ADS  Google Scholar 

  13. H. Georgi, Effective field theory, Ann. Rev. Nucl. Part. Sci. 43 (1993) 209 [INSPIRE].

    Article  ADS  Google Scholar 

  14. J. Polchinski and A. Strominger, Effective string theory, Phys. Rev. Lett. 67 (1991) 1681 [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  15. J. Polchinski, Strings and QCD?, hep-th/9210045 [INSPIRE].

  16. A.M. Polyakov, Quantum geometry of bosonic strings, Phys. Lett. B 103 (1981) 207 [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  17. M. Natsuume, Nonlinear σ-model for string solitons, Phys. Rev. D 48 (1993) 835 [hep-th/9206062] [INSPIRE].

    ADS  Google Scholar 

  18. M. Lüscher, Symmetry breaking aspects of the roughening transition in gauge theories, Nucl. Phys. B 180 (1981) 317 [INSPIRE].

    Article  ADS  Google Scholar 

  19. M. Lüscher and P. Weisz, String excitation energies in SU(N) gauge theories beyond the free-string approximation, JHEP 07 (2004) 014 [hep-th/0406205] [INSPIRE].

    Article  Google Scholar 

  20. O. Aharony and E. Karzbrun, On the effective action of confining strings, JHEP 06 (2009) 012 [arXiv:0903.1927] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  21. O. Aharony and M. Dodelson, Effective string theory and nonlinear Lorentz invariance, JHEP 02 (2012) 008 [arXiv:1111.5758] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  22. I. Gerstein, R. Jackiw, S. Weinberg and B. Lee, Chiral loops, Phys. Rev. D 3 (1971) 2486 [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  23. W. Cai, T.C. Lubensky, P. Nelson and T. Powers, Measure factors, tension and correlations of fluid membranes, J. Phys. France II 4 (1994) 931 [cond-mat/9401020].

    Article  Google Scholar 

  24. S. Dubovsky, R. Flauger and V. Gorbenko, Solving the simplest theory of quantum gravity, arXiv:1205.6805 [INSPIRE].

  25. J. Polchinski, String theory. Volume 1: an introduction to the bosonic string, Cambridge University Press, Cambridge U.K. (1998) [INSPIRE].

    Google Scholar 

  26. A. Adams, N. Arkani-Hamed, S. Dubovsky, A. Nicolis and R. Rattazzi, Causality, analyticity and an IR obstruction to UV completion, JHEP 10 (2006) 014 [hep-th/0602178] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  27. O. Aharony, M. Field and N. Klinghoffer, The effective string spectrum in the orthogonal gauge, JHEP 04 (2012) 048 [arXiv:1111.5757] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  28. M.J. Dugan and B. Grinstein, On the vanishing of evanescent operators, Phys. Lett. B 256 (1991) 239 [INSPIRE].

    ADS  Google Scholar 

  29. H.-C. Cheng, K.T. Matchev and M. Schmaltz, Radiative corrections to Kaluza-Klein masses, Phys. Rev. D 66 (2002) 036005 [hep-ph/0204342] [INSPIRE].

    ADS  Google Scholar 

  30. M. Lüscher, Volume dependence of the energy spectrum in massive quantum field theories. 2. Scattering states, Commun. Math. Phys. 105 (1986) 153 [INSPIRE].

    Article  ADS  Google Scholar 

  31. M. Lüscher and U. Wolff, How to calculate the elastic scattering matrix in two-dimensional quantum field theories by numerical simulation, Nucl. Phys. B 339 (1990) 222 [INSPIRE].

    Article  ADS  Google Scholar 

  32. A. Zamolodchikov, From tricritical Ising to critical Ising by thermodynamic Bethe ansatz, Nucl. Phys. B 358 (1991) 524 [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

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Authors and Affiliations

  1. Center for Cosmology and Particle Physics, Department of Physics, New York University, New York, NY, 10003, USA

    Sergei Dubovsky, Raphael Flauger & Victor Gorbenko

  2. School of Natural Sciences, Institute for Advanced Study, Princeton, NJ, 08540, USA

    Raphael Flauger

Authors
  1. Sergei Dubovsky
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  2. Raphael Flauger
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  3. Victor Gorbenko
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Correspondence to Raphael Flauger.

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Dubovsky, S., Flauger, R. & Gorbenko, V. Effective string theory revisited. J. High Energ. Phys. 2012, 44 (2012). https://doi.org/10.1007/JHEP09(2012)044

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  • DOI: https://doi.org/10.1007/JHEP09(2012)044

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