D3-brane action in a supergravity background: The fermionic story

Mariana Graña

doi:10.1103/PhysRevD.66.045014

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D3-brane action in a supergravity background: The fermionic story

Mariana Graña^*

Department of Physics, University of California, Santa Barbara, California 93106

^*Email address: mariana@physics.ucsb.edu

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Phys. Rev. D 66, 045014 – Published 19 August, 2002

DOI: https://doi.org/10.1103/PhysRevD.66.045014

Abstract

Using the $κ$ -symmetric action for a D3-brane, we study the interaction between its world-volume fermions and a bosonic type IIB supergravity background preserving 4-dimensional Lorentz invariance. We find that the renormalizable terms in the action include only coupling between the fermions and the 3-form flux in the combination ${(*}_{6} G_{(3)} - {iG}_{(3)}),$ which is zero for a class of supersymmetric and nonsupersymmetric solutions. We also find the magnetic and electric dipole moments for the fermions, which are proportional to the derivative of the dilaton axion. We show that different gauges to fix the $κ$ symmetry give the same interaction terms, and prove that these terms are also $S L (2, R)$ self-dual. We interpret our results in terms of $N = 1$ supersymmetric gauge theory on the D-brane.

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[c1] J. Polchinski, Phys. Rev. Lett. 75, 4724 (1995).

[c2] C. V. Johnson, “D-brane primer,” hep-th/0007170.

[c3] M. Cederwall, A. von Gussich, B. E. Nilsson, and A. Westerberg, Nucl. Phys. B490, 163 (1997).

[c4] M. Cederwall, A. von Gussich, B. E. Nilsson, P. Sundell, and A. Westerberg, Nucl. Phys. B490, 179 (1997).

[c5] E. Bergshoeff and P. K. Townsend, Nucl. Phys. B490, 145 (1997).

[c6] M. Aganagic, C. Popescu, and J. H. Schwarz, Phys. Lett. B 393, 311 (1997).

[c7] M. Aganagic, C. Popescu, and J. H. Schwarz, Nucl. Phys. B495, 99 (1997).

[c8] R. R. Metsaev and A. A. Tseytlin, Phys. Lett. B 436, 281 (1998).

[c9] K. Millar, W. Taylor, and M. V. Raamsdonk, “D-particle polarizations with multipole moments of higher-dimensional branes,” hep-th/0007157.

[c10] B. de Wit, K. Peeters, and J. Plefka, Nucl. Phys. B532, 99 (1998).

[c11] M. Graña and J. Polchinski, Phys. Rev. D 63, 026001 (2001).

[c12] S. S. Gubser, “Supersymmetry and F-theory realization of the deformed conifold with three-form flux,” hep-th/0010010.

[c13] M. Graña and J. Polchinski, Phys. Rev. D 65, 126005 (2002).

[c14] M. Bertolini, P. Di Vecchia, M. Frau, A. Lerda, and R. Marotta, Nucl. Phys. B621, 157 (2002).

[c15] J. H. Schwarz, Nucl. Phys. B226, 269 (1983).

[c16] P. S. Howe and P. C. West, Nucl. Phys. B238, 181 (1984).

[c17] M. T. Grisaru and M. E. Knutt, Phys. Lett. B 500, 188 (2001).

[c18] E. Bergshoeff, R. Kallosh, T. Ortin, and G. Papadopoulos, Nucl. Phys. B502, 149 (1997); E. A. Bergshoeff, M. de Roo, and A. Sevrin, J. Math. Phys. 42, 2872 (2001).

[c19] I. R. Klebanov and M. J. Strassler, J. High Energy Phys. 08, 052 (2000).

[c20] S. B. Giddings, S. Kachru, and J. Polchinski, Phys. Rev. D (to be published), hep-th/0105097.

[c21] N. Seiberg and E. Witten, Nucl. Phys. B426, 19 (1994).

[c22] M. Aganagic, J. Park, C. Popescu, and J. H. Schwarz, Nucl. Phys. B496, 215 (1997).

[c23] S. F. Hassan, Nucl. Phys. B568, 145 (2000); ibid.E. Bergshoeff, M. de Roo, B. Janssen, and T. Ortin, B550, 289 (1999).

[c24] L. Randall and R. Sundrum, Nucl. Phys. B557, 79 (1999); A. Anisimov, M. Dine, M. Graesser, and S. Thomas, Phys. Rev. D 65, 105011 (2002).

[c25] E. K. Akhmedov, A. Lanza, and S. T. Petcov, Phys. Lett. B 348, 124 (1995).

[c26] M. Leurer and M. Golden, “A Model For A Large Neutrino Magnetic Transition Moment,” FERMILAB-PUB-89-175-T.

[c27] K. S. Babu and R. N. Mohapatra, Phys. Rev. Lett. 64, 1705 (1990); H. Dykstra, Phys. Lett. B 257, 341 (1991).

[c28] J. Polchinski and M. J. Strassler, “The string dual of a confining four-dimensional gauge theory,” hep-th/0003136.

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D3-brane action in a supergravity background: The fermionic story

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