Dirichlet Branes and Ramond-Ramond Charges

Joseph Polchinski

doi:10.1103/PhysRevLett.75.4724

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Dirichlet Branes and Ramond-Ramond Charges

Joseph Polchinski

Institute for Theoretical Physics, University of California, Santa Barbara, California 93106-4030

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Phys. Rev. Lett. 75, 4724 – Published 25 December, 1995

DOI: https://doi.org/10.1103/PhysRevLett.75.4724

Abstract

We show that D-branes, extended objects defined by mixed Dirichlet-Neumann boundary conditions, break half the supersymmetries of the type II superstring and carry a complete set of electric and magnetic Ramond-Ramond charges. The product of the electric and magnetic charges is a single Dirac unit, and the quantum of charge is that required by string duality. This is strong evidence that D-branes are intrinsic to type II string theory and are the Ramond-Ramond sources needed for string duality. Also, we find in the IIa string a 9-form potential, which gives an effective cosmological constant.

References (20)

For a review of string theory, see M. B. Green, J. H. Schwarz, and E. Witten, Superstring Theory (Cambridge, Cambridge, 1987).
D. Friedan, E. Martinec, and S. Shenker, Nucl. Phys. B271, 93 (1986).
C. M. Hull and P. K. Townsend, Nucl. Phys. B438, 109 (1995) E. Witten, B443, 85 (1995) A. Strominger, B451, 96 (1995).
G. T. Horowitz and A. Strominger, Nucl. Phys. B360, 197 (1991).
J. Dai, R. G. Leigh, and J. Polchinski, Mod. Phys. Lett. A4, 2073 (1989) R. G. Leigh, A4, 2767 (1989).
P. Horava, Phys. Lett. B 231, 251 (1989) M. B. Green, 266, 325 (1991).
After Witten's talk at Strings '95, both M. Green and the author noticed this parallel. Some of the work in the present paper is anticipated in J. Polchinski, M. B. GreenPhys. Rev. D 50, 6041 (1994); , Phys. Lett. B 354, 271 (1995); Ref. [[8]].
M. B. Green, Phys. Lett. B 329, 435 (1994).
C. Lovelace, Phys. Lett. 34B, 500 (1971) L. Clavelli and J. Shapiro, Nucl. Phys. B57, 490 (1973) M. Ademollo, R. D' Auria, F. Gliozzi, E. Napolitano, S. Sciuto, and P. di Vecchia, B94, 221 (1975) C. G. Callan, C. Lovelace, C. R. Nappi, and S. A. Yost, B293, 83 (1987).
J. Polchinski and Y. Cai, Nucl. Phys. B296, 91 (1988) C. G. Callan, C. Lovelace, C. R. Nappi, and S. A. Yost, B308, 221 (1988).
A. Sagnotti, M. Bianchi and A. Sagnotti, P. HoravaNon-Perturbative Quantum Field Theory, G. Mack (Pergamon Press, New York, 1988), p. 521; Phys. Lett. B 247, 517 (1990); Nucl. Phys. B361, 519 (1991); , Nucl. Phys. B327, 461 (1989).
More explicitly, $F_{μ_{1} \dots μ_{p + 2}} = (p + 2) \partial_{[μ_{1}} A_{μ_{2} \dots μ_{p + 2}]}$ and $F^{*} {F = d}^{10} x \sqrt{g} F_{μ_{1} \dots μ_{p + 2}} F^{μ_{1} \dots μ_{p + 2}} / (p + 2)!$ .
R. I. Nepomechie, Phys. Rev. D 31, 1921 (1985) C. Teitelboim, Phys. Lett. 167B, 63 (1986) 167B, 69 (1986).
J. A. Harvey and A. Strominger, Nucl. Phys. B 449, 535 (1995).
C. Vafa and E. Witten, Nucl. Phys. B447, 261 (1995).
S. H. Shenker, in Proceedings of the Random Surfaces and Quantum Gravity, Cargese 1990 (Plenum Press, New York, 1990), p. 191.
C. Vafa and E. Witten, Report No. HUTP-95-A023, hep-th/9507050, 1995.
The question of the consistency of orientifold compactifications has arisen. In this paper we have encountered two necessary conditions: that the projections in the closed string channel of the one loop open string graph agree with the actual closed string spectrum, and that the RR forms have consistent field equations. We believe that these, together with the usual modular invariance and operator product expansion closure and associativity conditions, are also sufficient. See D. C. Lewellen, E. GimonNucl. Phys. B372, 654 (1992) and, in particular, [[11]] for more discussion of some of these points. This is under further investigation [ and J. Polchinski (to be published)].
L. J. Romans, Phys. Lett. 169B, 374 (1986).
J. Polchinski and A. Strominger, Report No. UCSBTH-95-30, NSF-ITP-95-136, hep-th/9510227, 1995.

[c1] For a review of string theory, see M. B. Green, J. H. Schwarz, and E. Witten, Superstring Theory (Cambridge, Cambridge, 1987).

[c2] D. Friedan, E. Martinec, and S. Shenker, Nucl. Phys. B271, 93 (1986).

[c3] C. M. Hull and P. K. Townsend, Nucl. Phys. B438, 109 (1995) E. Witten, B443, 85 (1995) A. Strominger, B451, 96 (1995).

[c4] G. T. Horowitz and A. Strominger, Nucl. Phys. B360, 197 (1991).

[c5] J. Dai, R. G. Leigh, and J. Polchinski, Mod. Phys. Lett. A4, 2073 (1989) R. G. Leigh, A4, 2767 (1989).

[c6] P. Horava, Phys. Lett. B 231, 251 (1989) M. B. Green, 266, 325 (1991).

[c7] After Witten's talk at Strings '95, both M. Green and the author noticed this parallel. Some of the work in the present paper is anticipated in J. Polchinski, M. B. GreenPhys. Rev. D 50, 6041 (1994); , Phys. Lett. B 354, 271 (1995); Ref. [[8]].

[c8] M. B. Green, Phys. Lett. B 329, 435 (1994).

[c9] C. Lovelace, Phys. Lett. 34B, 500 (1971) L. Clavelli and J. Shapiro, Nucl. Phys. B57, 490 (1973) M. Ademollo, R. D' Auria, F. Gliozzi, E. Napolitano, S. Sciuto, and P. di Vecchia, B94, 221 (1975) C. G. Callan, C. Lovelace, C. R. Nappi, and S. A. Yost, B293, 83 (1987).

[c10] J. Polchinski and Y. Cai, Nucl. Phys. B296, 91 (1988) C. G. Callan, C. Lovelace, C. R. Nappi, and S. A. Yost, B308, 221 (1988).

[c11] A. Sagnotti, M. Bianchi and A. Sagnotti, P. HoravaNon-Perturbative Quantum Field Theory, G. Mack (Pergamon Press, New York, 1988), p. 521; Phys. Lett. B 247, 517 (1990); Nucl. Phys. B361, 519 (1991); , Nucl. Phys. B327, 461 (1989).

[c12] More explicitly, $F_{μ_{1} \dots μ_{p + 2}} = (p + 2) \partial_{[μ_{1}} A_{μ_{2} \dots μ_{p + 2}]}$ and $F^{*} {F = d}^{10} x \sqrt{g} F_{μ_{1} \dots μ_{p + 2}} F^{μ_{1} \dots μ_{p + 2}} / (p + 2)!$ .

[c13] R. I. Nepomechie, Phys. Rev. D 31, 1921 (1985) C. Teitelboim, Phys. Lett. 167B, 63 (1986) 167B, 69 (1986).

[c14] J. A. Harvey and A. Strominger, Nucl. Phys. B 449, 535 (1995).

[c15] C. Vafa and E. Witten, Nucl. Phys. B447, 261 (1995).

[c16] S. H. Shenker, in Proceedings of the Random Surfaces and Quantum Gravity, Cargese 1990 (Plenum Press, New York, 1990), p. 191.

[c17] C. Vafa and E. Witten, Report No. HUTP-95-A023, hep-th/9507050, 1995.

[c18] The question of the consistency of orientifold compactifications has arisen. In this paper we have encountered two necessary conditions: that the projections in the closed string channel of the one loop open string graph agree with the actual closed string spectrum, and that the RR forms have consistent field equations. We believe that these, together with the usual modular invariance and operator product expansion closure and associativity conditions, are also sufficient. See D. C. Lewellen, E. GimonNucl. Phys. B372, 654 (1992) and, in particular, [[11]] for more discussion of some of these points. This is under further investigation [ and J. Polchinski (to be published)].

[c19] L. J. Romans, Phys. Lett. 169B, 374 (1986).

[c20] J. Polchinski and A. Strominger, Report No. UCSBTH-95-30, NSF-ITP-95-136, hep-th/9510227, 1995.

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