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In search of QCD-strings

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Abstract

In this article I describe the work done with Pushan Majumdar that provided a significant push towards identifying Yang–Mills flux tubes(our works only deal with flux tubes of pure gauge theory, i.e. without dynamical quarks) as the hadronic strings of early days. The main finding was that the static potential V(R) for large \(Q\) \({{\bar{Q}}}\) separations R has the form (D is the space-time dimensionality) \(\begin{aligned} V(R)=\sigma R-\frac{(D-2)\pi }{24R}-\frac{(D-2)^2\pi ^2}{1152\sigma R^3} \cdots \end{aligned}\) for SU(3) in \(D=4\) and SU(2) in \(D=3\). Remarkably this is also the \(\tfrac{1}{R}\) expansion of the ground state energy of the bosonic string theory as given by Arvis. While that derivation is supposed to be valid only in \(D=26\), the measured potentials are for QCD which is a consistent field theory in \(D=3,4\). In subsequent works with Peter Matlock and Yashas Bharadwaj, I resolved this issue within the framework of Polchinski–Strominger effective string theories. I conclude with a brief account of recent and related works.

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Notes

  1. It is important to emphasize that LGT was independently discovered by Wegner, Polyakov and Jan Smit. I quote in verbatim the historical note in Wilson’s talk [10] at the Lepton-Photon symposium of 1983 held at Cornell. " the first studies of lattice gauge theories were carried out independently by Wegner [11], Smit [12], Polyakov [13], and finally myself [8]. The original feature of my paper is its discussion of quark confinement in the lattice theory for strong coupling."

  2. We learnt of the Polchinski–Strominger approach from Prof. Julius Kuti.

  3. I thank one of the referees of this paper for providing me with a concise and accurate account of them which has enabled me to add this very important post-script!

References

  1. C F Weizsäcker, Physik. Zeits. 36 779 (1935); Zeits. f. Physik 96 431 (1935)

  2. G Gamow, Mass defect curve and nuclear constitution, Proc. R. Soc. A 123 386 (1929); Proc. R. Soc. a 126 803 (1930)

  3. Y Nambu Proceedings of International Conference on Symmetries and Quark Models, Wayne State University, 1969; H.B. Nielsen, 15th Conference on High Energy Physics, Kiev Conference, 1970; L.Susskind, Nuovo Cim. A69 (1970) 457

  4. M Gell-Mann Phys. Lett. B8 214 (1964); G Zweig, CERN Reports 8182/TH401, 8419/TH412

  5. M Y Han and Y Nambu Phys. Rev. 139 B1006 (1965)

  6. H Fritzsch, M Gell-Mann and H Leutwyler Phys. Lett. B47 4 (1973).

    Google Scholar 

  7. J C Pati and A Salam Phys. Rev. D8 1240 (1973)

  8. K G Wilson Phys. Rev. D10 2445 (1974)

  9. S Mandelstam Phys. Rep. C23 (1976)

  10. K G Wilson Future Directions in Particle Theory, 1983 Lepton-Photon Symposium - Cornell University

  11. F Wegner J. Math. Phys. 12 2259 (1971)

  12. J Smit, unpublished, 1972–73, Private communication to K.G. Wilson from R.J. Finkelstein, with unpublished documentation, of J. Smit’s studies of lattice gauge theory while he was a graduate student at UCLA

  13. A M Polyakov unpublished; see also Phys. Lett. B59 82 (1975)

  14. M Creutz Phys. Rev. D21 2308 (1980)

  15. J Ambjorn, P Olesen and C Petersen Phys. Lett. B 142 410 (1984)

  16. RW Haymaker, V Singh, Y Peng and J Wosiek Phys. Rev. D53 389 (1996)

  17. GS Bali, C Schlichter and K Schilling Phys. Rev. D51 5165 (1995)

  18. GS Bali Quark Forces and Heavy quark bound states, Phys. Rep. 343 (2001)

  19. M Lüscher and P Weisz JHEP 0207 049 (2002)

  20. M Lüscher and P Weisz JHEP 0407 014 (2004)

  21. M Lüscher and P Weisz JHEP 09 010 (2001)

  22. B B Brandt and P Majumdar Phys.Lett. B 682 253 (2009); B B Brandt, JHEP 029 040 (2011); B B Brandt Revisiting the fluxtube spectrum of 3d SU(2) LGT. arXiv: 2102.06413 (hep-lat)

  23. N D Hari Dass, Lattice Gauge Theory and KABRU—The Teraflop Linux Cluster at IMSc, p. 107, Recent Trends in Practice and Theory of Information Technology, Proceedings of the NRB Seminar, NPOL Kochi, 10-11 January 2005. Ed: S.N. Maheshwari

  24. N D Hari Dass and P Majumdar JHEP 0610 020 (2006)

  25. N D Hari Dass and P Majumdar PoS LATTICE 2007 316 (2007)

  26. N D Hari Dass and P Majumdar Phys. Lett. B 658 273 (2008)

  27. J F Arvis Phys. Lett. B 127 106 (1983)

  28. Y Nambu Phys. Lett. B 80 372 (1979)

  29. J Polchinski and A Strominger Phys. Rev. Lett. 67 1681 (1991)

  30. O Aharony and E Karzbrun JHEP 0906 012 (2009)

  31. K J Juge, J Kuti and C J Morningstar Phys. Rev. Lett. 90 161601 (2003)

  32. M Caselle, M Pepe and A Rago JHEP 0410 005 (2004)

  33. J Kuti Proceedings of Lattice 2005, PoS(Lat2005), 1

  34. A M Polyakov Phys. Lett. B 103 207 (1981)

  35. N D Hari Dass and P Matlock, Covariant Calculus for Effective String Theories, Ind. J. Phys. 88 965 (2014), hep-th 0709.1765

  36. N D Hari Dass and P Matlock, hep-th/0606265; arXiv:0709.1765 [hep-th]

  37. J M Drummond, hep-th/0411017

  38. N D Hari Dass, P Matlock and Y Bharadwaj, Spectrum to all orders of Polchinski–Strominger Effective String Theory of Polyakov–Liouville Type, hep-th arXiv:0910.5615

  39. N D Hari Dass and Y Bharadwaj, Spectrum to all orders of Polchinski–Strominger Effective String Theories of Drummond Type, hep-th arXiv:0910.5620

  40. N D Hari Dass, All Conformal Effective String Theories are Isospectral to Nambu–Goto Theory, hep-th arXiv:0911.3236

  41. E Braten, R D Pisarski and S H Tse Phys. Rev. Lett. 58 93 (1987)

  42. N D Hari Dass AIP Conference (IX QCHS, Madrid 2010) Proceedings No 1343 p. 230–232(2010)

  43. O Aharony and Z Komargodski, Effective Theory of Long Strings, JHEP 05 (2013)

  44. O Aharony, M Field and N Klinghofer JHEP 04 048 (2012)

  45. M Teper, Large N and confining flux tubes as strings—a view from the lattice, Acta Phys. Pol. B 40 3249 (2009)

  46. A Athenodorou, B Bringholtz and M Teper, Closed flux tubes and their string description in D = 3 + 1 SU(N) gauge theories, JHEP 02 030 (2011)

  47. M Bilio, M Caselle, F Gliozzi, M Meiner and R Pellegrini, The Lorentz invariant boundary action of the confining string and its universal contribution to the inter-quark potential, JHEP 05 130 (2012)

  48. M Bilio, M Caselle and R Pellegrini, New numerical results and novel effective string predictions for Wilson loops, JHEP 12 01 (2011)

  49. S Dubovsky, R Flauger and V Gorbenko, Effective String Theory revisited. arXiv:1203.1054v2 (hep-th)

  50. M Bilio et al, Recent progress in effective string description of lattice gauge theories, PoS Lattice 2013 372 (2014)

  51. S Hellerman and S Maeda, On vertex operators in effective string theories. arXiv: 1701.06406(hep-th); Simeone Hellerman and Ian Swanson, Boundary Operators in effective string theories, JHEP 04 085 (2017)

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Hari Dass, N.D. In search of QCD-strings. Indian J Phys 95, 1591–1598 (2021). https://doi.org/10.1007/s12648-021-02128-8

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