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On free 4D Abelian 2-form and anomalous 2D Abelian 1-form gauge theories

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Abstract

We demonstrate a few striking similarities and some glaring differences between (i) the free four- (3+1)-dimensional (4D) Abelian 2-form gauge theory, and (ii) the anomalous two- (1+1)-dimensional (2D) Abelian 1-form gauge theory, within the framework of Becchi–Rouet–Stora–Tyutin (BRST) formalism. We demonstrate that the Lagrangian densities of the above two theories transform in a similar fashion under a set of symmetry transformations even though they are endowed with a drastically different variety of constraint structures. With the help of our understanding of the 4D Abelian 2-form gauge theory, we prove that the gauge-invariant version of the anomalous 2D Abelian 1-form gauge theory is a new field-theoretic model for the Hodge theory where all the de Rham cohomological operators of differential geometry find their physical realizations in the language of proper symmetry transformations. The corresponding conserved charges obey an algebra that is reminiscent of the algebra of the cohomological operators. We briefly comment on the consistency of the 2D anomalous 1-form gauge theory in the language of restrictions on the harmonic state of the (anti-) BRST and (anti-) co-BRST invariant version of the above 2D theory.

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References

  1. P.A.M. Dirac, Lectures on Quantum Mechanics, Belfer Graduate School of Science (Yeshiva University Press, New York, 1964)

    Google Scholar 

  2. K. Sundermeyer, Constrained Dynamics. Lecture Notes in Physics, vol. 169 (Springer, Berlin, 1982)

    MATH  Google Scholar 

  3. K. Nishijima, Czechoslov. J. Phys. 46, 1 (1996)

    Article  MathSciNet  ADS  Google Scholar 

  4. N. Nakanishi, I. Ojima, Covariant Operator Formalism of Gauge Theories and Quantum Gravity (World Scientific, Singapore, 1990)

    Google Scholar 

  5. I.J.R. Aitchison, A.J.G. Hey, Gauge Theories in Particle Physics: A Practical Introduction (Hilger, Bristol, 1982)

    Google Scholar 

  6. V.I. Ogievetsky, I.V. Palubarinov, Yad. Fiz. 4, 216 (1966)

    Google Scholar 

  7. V.I. Ogievetsky, I.V. Palubarinov, Sov. J. Nucl. Phys. 4, 156 (1967)

    Google Scholar 

  8. A. Salam, E. Sezgin, Supergravities in Diverse Dimensions (World Scientific, Singapore, 1989)

    Google Scholar 

  9. M.B. Green, J.H. Schwarz, E. Witten, Superstring Theory (Cambridge University Press, Cambridge, 1987)

    MATH  Google Scholar 

  10. J. Polchinski, String Theory (Cambridge University Press, Cambridge, 1998)

    Google Scholar 

  11. N. Seiberg, E. Witten, J. High Energy Phys. 9909, 032 (1999)

    Article  MathSciNet  ADS  Google Scholar 

  12. R.P. Malik, J. Phys. A, Math. Gen. 36, 5095 (2003). hep-th/0209136

    Article  MATH  MathSciNet  ADS  Google Scholar 

  13. E. Harikumar, R.P. Malik, M. Sivakumar, J. Phys. A, Math. Gen. 33, 7149 (2000). hep-th/0004145

    MATH  MathSciNet  Google Scholar 

  14. S. Gupta, R.P. Malik, Eur. Phys. J. C 58, 517 (2008). arXiv:0807.2306 [hep-th]

    Article  MathSciNet  ADS  Google Scholar 

  15. R.P. Malik, Notoph gauge theory as the Hodge theory, in Proc. of the International Workshop on Supersymmetries and Quantum Symmetries (SQS’03), BLTP, JINR, Dubna, 24–29 July 2003, pp. 321–326. hep-th/0309245

  16. R.K. Kaul, Phys. Rev. D 18, 1127 (1978)

    Article  MathSciNet  ADS  Google Scholar 

  17. P.K. Townsend, Phys. Lett. B 88, 97 (1979)

    Article  MathSciNet  ADS  Google Scholar 

  18. H. Hata, T. Kugo, N. Ohta, Nucl. Phys. B 178, 527 (1981)

    Article  ADS  Google Scholar 

  19. T. Kimura, Prog. Theor. Phys. 64, 357 (1980)

    Article  ADS  Google Scholar 

  20. R.P. Malik, Eur. Phys. J. C 60, 457 (2009). hep-th/0702039

    Article  MathSciNet  ADS  Google Scholar 

  21. G. Curci, R. Ferrari, Phys. Lett. B 63, 91 (1976)

    Article  MathSciNet  ADS  Google Scholar 

  22. L. Bonora, R.P. Malik, Phys. Lett. B 655, 75 (2007). 0707.3922 [hep-th]

    Article  MathSciNet  ADS  Google Scholar 

  23. R. Jackiw, R. Rajaraman, Phys. Rev. Lett. 54, 1219 (1985)

    Article  ADS  Google Scholar 

  24. R. Rajaraman, Phys. Lett. B 184, 369 (1987)

    Article  ADS  Google Scholar 

  25. R.P. Malik, Phys. Lett. B 212, 445 (1988)

    Article  MathSciNet  ADS  Google Scholar 

  26. S. Gupta, R.P. Malik, arXiv:0805.1102 [hep-th]

  27. S. Deser, A. Gomberoff, M. Henneaux, C. Teitelboim, Phys. Lett. B 400, 80 (1997)

    Article  MathSciNet  ADS  Google Scholar 

  28. R.P. Malik, Int. J. Mod. Phys. A 19, 5663 (2004). hep-th/0212240

    Article  MATH  MathSciNet  ADS  Google Scholar 

  29. R.P. Malik, Int. J. Mod. Phys. A 21, 6513 (2006). hep-th/0212240 (Errata)

    Article  MathSciNet  ADS  Google Scholar 

  30. N.K. Falk, G. Kramer, Ann. Phys. 176, 330 (1987)

    Article  ADS  Google Scholar 

  31. T. Eguchi, P.B. Gilkey, A. Hanson, Phys. Rep. 66, 213 (1980)

    Article  MathSciNet  ADS  Google Scholar 

  32. S. Mukhi, N. Mukunda, Introduction to Topology, Differential Geometry and Group Theory to Physicists (Wiley, New Delhi, 1990)

    MATH  Google Scholar 

  33. J.W. van Holten, Phys. Rev. Lett. 64, 2863 (1990)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  34. R.P. Malik, J. Phys. A, Math. Gen. 33, 2437 (2000). hep-th/9902146

    Article  MATH  MathSciNet  ADS  Google Scholar 

  35. R.P. Malik, Int. J. Mod. Phys. A 15, 1685 (2000). hep-th/9808040

    MATH  MathSciNet  ADS  Google Scholar 

  36. R.P. Malik, J. Phys. A, Math. Gen. 34, 4167 (2001). hep-th/0012085

    Article  MATH  MathSciNet  ADS  Google Scholar 

  37. R.P. Malik, Mod. Phys. Lett. A 16, 477 (2001). hep-th/9711056

    Article  MathSciNet  ADS  Google Scholar 

  38. R.P. Malik, Mod. Phys. Lett. A 15, 2079 (2000). hep-th/0003128

    Article  MATH  MathSciNet  ADS  Google Scholar 

  39. S. Das, S. Ghosh, arXiv:0812.3512 [math-ph]

  40. R. Rajaraman, Phys. Lett. B 162, 148 (1985)

    Article  MathSciNet  ADS  Google Scholar 

  41. S. Gupta, R. Kumar, R.P. Malik, in preparation

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Authors and Affiliations

  1. Physics Department, Centre of Advanced Studies, Banaras Hindu University, Varanasi, 221 005, India

    S. Gupta, R. Kumar & R. P. Malik

  2. DST Centre for Interdisciplinary Mathematical Sciences, Faculty of Science, Banaras Hindu University, Varanasi, 221 005, India

    R. P. Malik

Authors
  1. S. Gupta
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  2. R. Kumar
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  3. R. P. Malik
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Correspondence to R. P. Malik.

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Gupta, S., Kumar, R. & Malik, R.P. On free 4D Abelian 2-form and anomalous 2D Abelian 1-form gauge theories. Eur. Phys. J. C 65, 311–329 (2010). https://doi.org/10.1140/epjc/s10052-009-1205-x

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  • DOI: https://doi.org/10.1140/epjc/s10052-009-1205-x

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