String Gauge Symmetries in the Conformally Gauge-Fixed Polyakov D1 Brane Action in the Presence of Background Gauge Fields

ABSTRACT

Recently we have studied the instant-form quantization (IFQ) and the light-front quantization (LFQ) of the conformally gauge-fixed Polyakov D1 brane action using the Hamiltonian and path integral formulations. The IFQ is studied in the equal world-sheet time framework on the hyperplanes defined by the world- sheet time σ0 = τ = constant and the LFQ in the equal light-cone world-sheet time framework, on the hyperplanes of the light-front defined by the light-cone world-sheet time . The light-front theory is seen to be a constrained system in the sense of Dirac in contrast to the instant-form theory. However, owing to the gauge anomalous nature of these theories, both of these theories are seen to lack the usual string gauge symmetries defined by the world-sheet reparametrization invariance (WSRI) and the Weyl invariance (WI). In the present work we show that these theories when considered in the presence of background gauge fields such as the NSNS 2-form gauge field or in the presence of gauge field and the constant scalar axion field , then they are seen to possess the usual string gauge symmetries (WSRI and WI). In fact, these background gauge fields are seen to behave as the Wess-Zumino/Stueckelberg fields and the terms containing these fields are seen to behave as Wess-Zumino or Stueckelberg terms for these theories.

Recently we have studied the instant-form quantization (IFQ) and the light-front quantization (LFQ) of the conformally gauge-fixed Polyakov D1 brane action using the Hamiltonian and path integral formulations. The IFQ is studied in the equal world-sheet time framework on the hyperplanes defined by the world- sheet time σ0 = τ = constant and the LFQ in the equal light-cone world-sheet time framework, on the hyperplanes of the light-front defined by the light-cone world-sheet time . The light-front theory is seen to be a constrained system in the sense of Dirac in contrast to the instant-form theory. However, owing to the gauge anomalous nature of these theories, both of these theories are seen to lack the usual string gauge symmetries defined by the world-sheet reparametrization invariance (WSRI) and the Weyl invariance (WI). In the present work we show that these theories when considered in the presence of background gauge fields such as the NSNS 2-form gauge field or in the presence of gauge field and the constant scalar axion field , then they are seen to possess the usual string gauge symmetries (WSRI and WI). In fact, these background gauge fields are seen to behave as the Wess-Zumino/Stueckelberg fields and the terms containing these fields are seen to behave as Wess-Zumino or Stueckelberg terms for these theories.

Cite this paper

U. Kulshreshtha and D. Kulshreshtha, "String Gauge Symmetries in the Conformally Gauge-Fixed Polyakov D1 Brane Action in the Presence of Background Gauge Fields,"*Journal of Modern Physics*, Vol. 3 No. 1, 2012, pp. 110-115. doi: 10.4236/jmp.2012.31015.

U. Kulshreshtha and D. Kulshreshtha, "String Gauge Symmetries in the Conformally Gauge-Fixed Polyakov D1 Brane Action in the Presence of Background Gauge Fields,"

References

[1] D. Luest and S. Theisen, “Lectures in String Theory,” Lecture Notes in Physics, Vol. 346, 1989.

[2] L. Brink and M. Henneaux, “Principles of String Theory,” Plenum Press, New York, 1988.

[3] C. V. Johnson, “D-Brane Primer,” Prepared for Theoretical Advanced Study Institute in Elementary Particle Physics (TASI 99): Strings, Branes, and Gravity, Boulder, Colorado, 31 May - 25 Jun 1999 (This is an expanded writeup of lectures given at ICTP, TASI, and BUSSTEPP), Published in ``Boulder 1999: Strings, branes and gravity'', 129-350 (1999) (arXiv: hep-th/0007170); see also, C. V. Johnson, ``D-branes'', Cambridge, USA: Univ. Press (2003) 548 pp.

[4] M. Aganagic, J. Park, C. Popescu and J. Schwarz, “Dual D-Brane Actions,” Nuclear Physics, Vol. B496, No. 1-2, 1997, pp. 215-230. doi:10.1016/S0550-3213(97)00257-5

[5] M. Abou Zeid and C. M. Hull, “Intrinsic Geometry of D-Branes,” Physics Letters, Vol. B404, No. 3-4, 1997, pp. 264-270.

[6] C. Schmidhuber, “D-Brane Actions,” Nuclear Physics, Vol. B467, No. 1-2, 1996, pp. 146-158. doi:10.1016/0550-3213(96)00092-2

[7] S. P. de Alwis and K. Sato, “D-Strings and F-Strings from String Loops,” Physical Review, Vol. D53, No. 12, 1996, pp. 7187-7196.

[8] A. A. Tseytlin, “Self Duality of Born-Infeld Action and Dirichlet Three-Brane of Type IIB Super String Theory,” Nuclear Physics, Vol. B469, No. 1-2, 1996, pp. 51-67. doi:10.1016/0550-3213(96)00173-3

[9] U. kulshreshtha and D. S. Kulshreshtha, “Hamiltonian and Path Integral Formulations of the Nambu-Goto D1 Brane Action with and without a Dilaton Field under Gauge-Fixing,” International Journal of Theoretical Physics, Vol. 43, No. 12, 2004, pp. 2355-2369. doi:10.1007/s10773-004-7704-5

[10] U. kulshreshtha and D. S. Kulshreshtha, “Hamiltonian and Path Integral Formulations of the Born-Infeld- Nambu-Goto D1 Brane Action with and without a Dilaton Field under Gauge-Fixing,” International Journal of Theoretical Physics, Vol. 44, No. 5, 2005, pp. 587-603. doi:10.1007/s10773-005-3985-6

[11] U. kulshreshtha and D. S. Kulshreshtha, “Hamiltonian and Path Integral Formulations of the Dirac-Born-Infeld- Nambu-Goto D1 Brane Action with and without a Dilaton Field under Gauge-Fixing,” European Physical Journal, Vol. C29, No. 3, 2003, pp. 453-461.

[12] U. Kulshreshtha and D. S. Kulshreshtha, “Hamiltonian and Path Integral Quantization of the Conformally Gauge- Fixed Polyakov D1 Brane Action in the Presence of a Scalar Dilation Field,” International Journal of Theoretical Physics, Vol. 48, No. 4, 2009, pp. 937-944. doi:10.1007/s10773-008-9866-z

[13] U. kulshreshtha and D. S. Kulshreshtha, “Conformally Gauge-Fixed Polyakov D1 Brane Action in the Presence of a 2-Form Gauge Field: The Instant-Form and Front- Form Hamiltonian and Path Integral Formulations,” Physics Letters, Vol. B555, No. 3-4, 2003, pp. 255-263.

[14] D. S. Kulshreshtha, “Polyakov D1 Brane Action on the Light-Front,” Light-Cone 2008: Relativistic Nuclear and Particle Physics, Mulhouse, 7-11 July 2008.

[15] U. Kulshreshtha and D. S. Kulshreshtha, “Light-Front Hamiltonian and Path Integral Quantization of the Conformally Guage-Fixed Polyakov D1 Brane Action,” Journal of Modern Physics, Vol. 2, No. 5, 2011, pp. 335- 340. doi:10.4236/jmp.2011.25041

[16] U. Kulshreshtha and D. S. Kulshreshtha, “Light-Front Hamiltonian and Path Integral Formulations of the Conformally Gauge-Fixed Polyakov D1 Brane Action in the Presence of a Scalar Dilaton Field,” Journal of Modern Physics, Vol. 2, No. 8, 2011, pp. 826-833. doi:10.4236/jmp.2011.28097

[17] D. S. Kulshreshtha, “Light-Front Quantization of the Polyakov D1 Brane Action with a Scalar Dilaton Field,” Light-Cone 2007: Relativistic Hadronic and Nuclear Physics, Columbus, 14-18 May 2007.

[18] D. S. Kulshreshtha, “String Gauge Symmetries of the Light-Front Polyakov D1 Brane Action,” Light-Cone International Workshop on Relativistic Hadronic and Particle Physics, Valencia, 14-18 June 2010.

[19] D. S. Kulshreshtha, “Light-Front Quantization of Conformally Gauge-Fixed Polyakov D1-Brane Action in the presence of a Scalar Axion Field and an Gauge Field,” Few Body Systems, Vol. 42, No. 1-4, 2011.

[20] P. A. M. Dirac, “Generalized Hamiltonian Dynamics,” Canadian Journal of Mathematics, Vol. 2, 1950, pp. 129- 148. doi:10.4153/CJM-1950-012-1

[21] M. Henneaux and C. Teitleboim, “Quantization of Gauge Systems,” Princeton University Press, Princeton, 1992.

[22] P. Senjanovic, “Path Integral Quantization of Field Theories with Second-Class Constraints,” Annals Physics, Vol. 100, No. 1-2, 1976, pp. 227-261. doi:10.1016/0003-4916(76)90062-2

[23] U. Kulshreshtha, “Hamiltonian, Path Integral and BRST Formulations of the Chern-Simons-Higgs Theory in the Broken Symmetry Phase,” Physica Scripta, Vol. 75, No. 6, 2007, pp. 795-802. doi:10.1088/0031-8949/75/6/009

[24] U. Kulshreshtha and D. S. Kulshreshtha, “Gauge-Invariant Reformulation of the Vector Schwinger Model with a Photon Mass Term and Its Hamiltonian, Path Integral and BRST Formulations,” International Journal of Modern Physics, Vol. A22, No. 32, 2007, pp. 6183-6201.

[25] U. Kulshreshtha, “Hamiltonian and BRST Formulations of the Nelsen-Olesen Model,” International Journal of Theoretical Physics, Vol. 41, No. 2, 2002, pp. 273-291. doi:10.1023/A:1014058806710

[26] P. A. M. Dirac, “Forms of Relativistic Dynamics,” Reviews of Modern Physics, Vol. 21, No. 3, 1949, pp. 392- 399. doi:10.1103/RevModPhys.21.392

[27] S. J. Brodsky, H. C. Pauli and S. S. Pinsky, “Quantum Chromodynamics and Other Field Theories on the Light- Cone,” Vol. 301, No. 4-6, 1998, pp. 299-486.

[28] U. Kulshreshtha, “Light-Front Hamiltonian, Path Integral and BRST Formulations of the Nelsen-Olsen (Bogomol’nyi) Model in the Light-Cone Gauges,” International Journal of Theoretical Physics, Vol. 46, No. 10, 2007, pp. 2516-2530. doi:10.1007/s10773-007-9367-5

[29] U. Kulshreshtha, D. S. Kulshreshtha and J. P. Vary, “Light-Front Hamiltonian, Path Integral and BRST Formulations of the Chern-Simons-Higgs Theory under Appropriate Gauge-Fixing,” Physics Scripta, Vol. 82, No. 5, 2010, p. 055101. doi:10.1088/0031-8949/82/05/055101

[30] U. Kulshreshtha, D. S. Kulshreshtha and J. P. Vary, “Light-Front Hamiltonian, Path Integral and BRST Formulations of the Chern-Simons Theory under Appropriate Gauge-Fixing,” Journal of Modern Physics, Vol. 1, No. 6, 2010, pp. 385-392.

[31] U. Kulshreshtha, D. S. Kulshreshtha and J. P. Vary, “Light-Front Hamiltonian, Path Integral and BRST Formulations of the Chern-Simons Theory under Appropriate Gauge-Fixing,” Journal of Modern Physics, Vol. 1, No. 6, 2010, pp. 85-392.

[32] U. Kulshreshtha, D. S. Kulshreshtha and J. P. Vary, “Light-Front Hamiltonian, Path Integral and BRST Formulations of the Chern-Simons-Higgs Theory under Appropriate Gauge-Fixing,” Physics Scripta, Vol. 82, No. 5, 2010, p. 055101. doi:10.1088/0031-8949/82/05/055101

[1] D. Luest and S. Theisen, “Lectures in String Theory,” Lecture Notes in Physics, Vol. 346, 1989.

[2] L. Brink and M. Henneaux, “Principles of String Theory,” Plenum Press, New York, 1988.

[3] C. V. Johnson, “D-Brane Primer,” Prepared for Theoretical Advanced Study Institute in Elementary Particle Physics (TASI 99): Strings, Branes, and Gravity, Boulder, Colorado, 31 May - 25 Jun 1999 (This is an expanded writeup of lectures given at ICTP, TASI, and BUSSTEPP), Published in ``Boulder 1999: Strings, branes and gravity'', 129-350 (1999) (arXiv: hep-th/0007170); see also, C. V. Johnson, ``D-branes'', Cambridge, USA: Univ. Press (2003) 548 pp.

[4] M. Aganagic, J. Park, C. Popescu and J. Schwarz, “Dual D-Brane Actions,” Nuclear Physics, Vol. B496, No. 1-2, 1997, pp. 215-230. doi:10.1016/S0550-3213(97)00257-5

[5] M. Abou Zeid and C. M. Hull, “Intrinsic Geometry of D-Branes,” Physics Letters, Vol. B404, No. 3-4, 1997, pp. 264-270.

[6] C. Schmidhuber, “D-Brane Actions,” Nuclear Physics, Vol. B467, No. 1-2, 1996, pp. 146-158. doi:10.1016/0550-3213(96)00092-2

[7] S. P. de Alwis and K. Sato, “D-Strings and F-Strings from String Loops,” Physical Review, Vol. D53, No. 12, 1996, pp. 7187-7196.

[8] A. A. Tseytlin, “Self Duality of Born-Infeld Action and Dirichlet Three-Brane of Type IIB Super String Theory,” Nuclear Physics, Vol. B469, No. 1-2, 1996, pp. 51-67. doi:10.1016/0550-3213(96)00173-3

[9] U. kulshreshtha and D. S. Kulshreshtha, “Hamiltonian and Path Integral Formulations of the Nambu-Goto D1 Brane Action with and without a Dilaton Field under Gauge-Fixing,” International Journal of Theoretical Physics, Vol. 43, No. 12, 2004, pp. 2355-2369. doi:10.1007/s10773-004-7704-5

[10] U. kulshreshtha and D. S. Kulshreshtha, “Hamiltonian and Path Integral Formulations of the Born-Infeld- Nambu-Goto D1 Brane Action with and without a Dilaton Field under Gauge-Fixing,” International Journal of Theoretical Physics, Vol. 44, No. 5, 2005, pp. 587-603. doi:10.1007/s10773-005-3985-6

[11] U. kulshreshtha and D. S. Kulshreshtha, “Hamiltonian and Path Integral Formulations of the Dirac-Born-Infeld- Nambu-Goto D1 Brane Action with and without a Dilaton Field under Gauge-Fixing,” European Physical Journal, Vol. C29, No. 3, 2003, pp. 453-461.

[12] U. Kulshreshtha and D. S. Kulshreshtha, “Hamiltonian and Path Integral Quantization of the Conformally Gauge- Fixed Polyakov D1 Brane Action in the Presence of a Scalar Dilation Field,” International Journal of Theoretical Physics, Vol. 48, No. 4, 2009, pp. 937-944. doi:10.1007/s10773-008-9866-z

[13] U. kulshreshtha and D. S. Kulshreshtha, “Conformally Gauge-Fixed Polyakov D1 Brane Action in the Presence of a 2-Form Gauge Field: The Instant-Form and Front- Form Hamiltonian and Path Integral Formulations,” Physics Letters, Vol. B555, No. 3-4, 2003, pp. 255-263.

[14] D. S. Kulshreshtha, “Polyakov D1 Brane Action on the Light-Front,” Light-Cone 2008: Relativistic Nuclear and Particle Physics, Mulhouse, 7-11 July 2008.

[15] U. Kulshreshtha and D. S. Kulshreshtha, “Light-Front Hamiltonian and Path Integral Quantization of the Conformally Guage-Fixed Polyakov D1 Brane Action,” Journal of Modern Physics, Vol. 2, No. 5, 2011, pp. 335- 340. doi:10.4236/jmp.2011.25041

[16] U. Kulshreshtha and D. S. Kulshreshtha, “Light-Front Hamiltonian and Path Integral Formulations of the Conformally Gauge-Fixed Polyakov D1 Brane Action in the Presence of a Scalar Dilaton Field,” Journal of Modern Physics, Vol. 2, No. 8, 2011, pp. 826-833. doi:10.4236/jmp.2011.28097

[17] D. S. Kulshreshtha, “Light-Front Quantization of the Polyakov D1 Brane Action with a Scalar Dilaton Field,” Light-Cone 2007: Relativistic Hadronic and Nuclear Physics, Columbus, 14-18 May 2007.

[18] D. S. Kulshreshtha, “String Gauge Symmetries of the Light-Front Polyakov D1 Brane Action,” Light-Cone International Workshop on Relativistic Hadronic and Particle Physics, Valencia, 14-18 June 2010.

[19] D. S. Kulshreshtha, “Light-Front Quantization of Conformally Gauge-Fixed Polyakov D1-Brane Action in the presence of a Scalar Axion Field and an Gauge Field,” Few Body Systems, Vol. 42, No. 1-4, 2011.

[20] P. A. M. Dirac, “Generalized Hamiltonian Dynamics,” Canadian Journal of Mathematics, Vol. 2, 1950, pp. 129- 148. doi:10.4153/CJM-1950-012-1

[21] M. Henneaux and C. Teitleboim, “Quantization of Gauge Systems,” Princeton University Press, Princeton, 1992.

[22] P. Senjanovic, “Path Integral Quantization of Field Theories with Second-Class Constraints,” Annals Physics, Vol. 100, No. 1-2, 1976, pp. 227-261. doi:10.1016/0003-4916(76)90062-2

[23] U. Kulshreshtha, “Hamiltonian, Path Integral and BRST Formulations of the Chern-Simons-Higgs Theory in the Broken Symmetry Phase,” Physica Scripta, Vol. 75, No. 6, 2007, pp. 795-802. doi:10.1088/0031-8949/75/6/009

[24] U. Kulshreshtha and D. S. Kulshreshtha, “Gauge-Invariant Reformulation of the Vector Schwinger Model with a Photon Mass Term and Its Hamiltonian, Path Integral and BRST Formulations,” International Journal of Modern Physics, Vol. A22, No. 32, 2007, pp. 6183-6201.

[25] U. Kulshreshtha, “Hamiltonian and BRST Formulations of the Nelsen-Olesen Model,” International Journal of Theoretical Physics, Vol. 41, No. 2, 2002, pp. 273-291. doi:10.1023/A:1014058806710

[26] P. A. M. Dirac, “Forms of Relativistic Dynamics,” Reviews of Modern Physics, Vol. 21, No. 3, 1949, pp. 392- 399. doi:10.1103/RevModPhys.21.392

[27] S. J. Brodsky, H. C. Pauli and S. S. Pinsky, “Quantum Chromodynamics and Other Field Theories on the Light- Cone,” Vol. 301, No. 4-6, 1998, pp. 299-486.

[28] U. Kulshreshtha, “Light-Front Hamiltonian, Path Integral and BRST Formulations of the Nelsen-Olsen (Bogomol’nyi) Model in the Light-Cone Gauges,” International Journal of Theoretical Physics, Vol. 46, No. 10, 2007, pp. 2516-2530. doi:10.1007/s10773-007-9367-5

[29] U. Kulshreshtha, D. S. Kulshreshtha and J. P. Vary, “Light-Front Hamiltonian, Path Integral and BRST Formulations of the Chern-Simons-Higgs Theory under Appropriate Gauge-Fixing,” Physics Scripta, Vol. 82, No. 5, 2010, p. 055101. doi:10.1088/0031-8949/82/05/055101

[30] U. Kulshreshtha, D. S. Kulshreshtha and J. P. Vary, “Light-Front Hamiltonian, Path Integral and BRST Formulations of the Chern-Simons Theory under Appropriate Gauge-Fixing,” Journal of Modern Physics, Vol. 1, No. 6, 2010, pp. 385-392.

[31] U. Kulshreshtha, D. S. Kulshreshtha and J. P. Vary, “Light-Front Hamiltonian, Path Integral and BRST Formulations of the Chern-Simons Theory under Appropriate Gauge-Fixing,” Journal of Modern Physics, Vol. 1, No. 6, 2010, pp. 85-392.

[32] U. Kulshreshtha, D. S. Kulshreshtha and J. P. Vary, “Light-Front Hamiltonian, Path Integral and BRST Formulations of the Chern-Simons-Higgs Theory under Appropriate Gauge-Fixing,” Physics Scripta, Vol. 82, No. 5, 2010, p. 055101. doi:10.1088/0031-8949/82/05/055101