Dimensional reduction of the generalized DBI. (English) Zbl 1329.83189
Summary: We study the generalized Dirac-Born-Infeld (DBI) action, which describes a \(q\)-brane ending on a \(p\)-brane with a \((q + 1)\)-form background. This action has the equivalent descriptions in commutative and non-commutative settings, which can be shown from the generalized metric and Nambu-Sigma model. We mainly discuss the dimensional reduction of the generalized DBI at the massless level on the flat spacetime and constant antisymmetric background in the case of flat spacetime, constant antisymmetric background and the gauge potential vanishes for all time-like components. In the case of \(q = 2\), we can do the dimensional reduction to get the DBI theory. We also try to extend this theory by including a one-form gauge potential.
MSC:
| 83E30 | String and superstring theories in gravitational theory |
| 83D05 | Relativistic gravitational theories other than Einstein’s, including asymmetric field theories |
| 83C65 | Methods of noncommutative geometry in general relativity |
| 83C47 | Methods of quantum field theory in general relativity and gravitational theory |
| 83E15 | Kaluza-Klein and other higher-dimensional theories |
References:
| [1] | Zwiebach, B., Closed string field theory: quantum action and the B-V master equation, Nucl. Phys. B, 390, 33-152 (1993) |
| [2] | Saadi, M.; Zwiebach, B., Closed string field theory from polyhedra, Ann. Phys., 192, 213 (1989) |
| [3] | Zwiebach, B., Curvature squared terms and string theories, Phys. Lett. B, 156, 315 (1985) |
| [4] | Hull, C.; Zwiebach, B., Double field theory, J. High Energy Phys., 0909, 099 (2009) |
| [5] | Hull, C.; Zwiebach, B., The Gauge algebra of double field theory and Courant brackets, J. High Energy Phys., 0909, 090 (2009) |
| [6] | Hohm, O.; Hull, C.; Zwiebach, B., Background independent action for double field theory, J. High Energy Phys., 1007, 016 (2010) · Zbl 1290.81069 |
| [7] | Hohm, O.; Hull, C.; Zwiebach, B., Generalized metric formulation of double field theory, J. High Energy Phys., 1008, 008 (2010) · Zbl 1291.81255 |
| [8] | Lee, K.; Park, J.-H., Covariant action for a string in “doubled yet gauged” spacetime, Nucl. Phys. B, 880, 134-154 (2014) · Zbl 1284.81238 |
| [9] | Tseytlin, A. A., Duality symmetric closed string theory and interacting chiral scalars, Nucl. Phys. B, 350, 395-440 (1991) |
| [10] | Tseytlin, A. A., Duality symmetric formulation of string world sheet dynamics, Phys. Lett. B, 242, 163-174 (1990) |
| [11] | Copland, N. B., A double sigma model for double field theory, J. High Energy Phys., 1204, 044 (2012) · Zbl 1348.81363 |
| [12] | Berman, D. S.; Thompson, D. C., Duality symmetric strings, dilatons and \(O(d, d)\) effective actions, Phys. Lett. B, 662, 279-284 (2008) · Zbl 1282.81140 |
| [13] | Berman, D. S.; Copland, N. B.; Thompson, D. C., Background field equations for the duality symmetric string, Nucl. Phys. B, 791, 175-191 (2008) · Zbl 1225.81111 |
| [14] | Avramis, S. D.; Derendinger, J.-P.; Prezas, N., Conformal chiral boson models on twisted doubled tori and non-geometric string vacua, Nucl. Phys. B, 827, 281-310 (2010) · Zbl 1203.81131 |
| [15] | Berkeley, J.; Berman, D. S.; Rudolph, F. J., Strings and branes are waves, J. High Energy Phys., 1406, 006 (2014) · Zbl 1333.81311 |
| [16] | Duff, M., Duality rotations in string theory, Nucl. Phys. B, 335, 610 (1990) · Zbl 0967.81519 |
| [17] | Siegel, W., Two vierbein formalism for string inspired axionic gravity, Phys. Rev. D, 47, 5453-5459 (1993) |
| [18] | Siegel, W., Superspace duality in low-energy superstrings, Phys. Rev. D, 48, 2826-2837 (1993) |
| [19] | Siegel, W., Manifest duality in low-energy superstrings · Zbl 0844.58101 |
| [20] | Gualtieri, M., Generalized complex geometry · Zbl 1235.32020 |
| [21] | Hitchin, N., Generalized Calabi-Yau manifolds, Quart. J. Math. Oxford Ser., 54, 281-308 (2003) · Zbl 1076.32019 |
| [22] | Cavalcanti, G. R.; Gualtieri, M., Generalized complex geometry and T-duality · Zbl 1200.53062 |
| [23] | Hohm, O.; Kwak, S. K.; Zwiebach, B., Double field theory of type II strings, J. High Energy Phys., 1109, 013 (2011) · Zbl 1301.81219 |
| [24] | Hohm, O.; Kwak, S. K., Frame-like geometry of double field theory, J. Phys. A, 44, 085404 (2011) · Zbl 1209.81168 |
| [25] | Aldazabal, G.; Baron, W.; Marques, D.; Nunez, C., The effective action of double field theory, J. High Energy Phys., 1111, 052 (2011) · Zbl 1306.81178 |
| [26] | Andriot, D.; Hohm, O.; Larfors, M.; Lust, D.; Patalong, P., Non-geometric fluxes in supergravity and double field theory, Fortschr. Phys., 60, 1150-1186 (2012) · Zbl 1255.83123 |
| [27] | Geissbuhler, D.; Marques, D.; Nunez, C.; Penas, V., Exploring double field theory, J. High Energy Phys., 1306, 101 (2013) · Zbl 1342.83368 |
| [28] | Grana, M.; Marques, D., Gauged double field theory, J. High Energy Phys., 1204, 020 (2012) · Zbl 1348.81368 |
| [29] | Ma, C.-T.; Shen, C.-M., Cosmological implications from \(O(D, D)\), Fortschr. Phys., 62, 921-941 (2014) · Zbl 1338.83171 |
| [30] | Hohm, O.; Siegel, W.; Zwiebach, B., Doubled \(\alpha^\prime \)-geometry, J. High Energy Phys., 1402, 065 (2014) · Zbl 1333.83190 |
| [31] | Bedoya, O. A.; Marques, D.; Nunez, C., Heterotic \(\alpha^\prime \)-corrections in double field theory, J. High Energy Phys., 1412, 074 (2014) |
| [32] | Berman, D. S.; Perry, M. J., Generalized geometry and M theory, J. High Energy Phys., 1106, 074 (2011) · Zbl 1298.81244 |
| [33] | Hohm, O.; Samtleben, H., Exceptional field theory I: \(E_{6(6)}\) covariant form of M-theory and type IIB, Phys. Rev. D, 89, 066016 (2014) |
| [34] | Hohm, O.; Samtleben, H., Exceptional field theory II: \(E_{7(7)}\), Phys. Rev. D, 89, 066017 (2014) |
| [35] | Hohm, O.; Samtleben, H., Exceptional field theory. III. \(E_{8(8)}\), Phys. Rev. D, 90, 6, 066002 (2014) |
| [36] | Berman, D. S.; Cederwall, M.; Kleinschmidt, A.; Thompson, D. C., The gauge structure of generalised diffeomorphisms, J. High Energy Phys., 1301, 064 (2013) |
| [37] | Hohm, O.; Samtleben, H., Exceptional form of \(D = 11\) supergravity, Phys. Rev. Lett., 111, 231601 (2013) |
| [38] | Hohm, O.; Lüst, D.; Zwiebach, B., The spacetime of double field theory: review, remarks, and outlook, Fortschr. Phys., 61, 926-966 (2013) · Zbl 1338.81328 |
| [39] | Aldazabal, G.; Marques, D.; Nunez, C., Double field theory: a pedagogical review, Class. Quantum Gravity, 30, 163001 (2013) · Zbl 1273.83001 |
| [40] | Berman, D. S.; Thompson, D. C., Duality symmetric string and M-theory, Phys. Rep., 566, 1-60 (2014) |
| [41] | Ho, P.-M.; Matsuo, Y., M5 from M2, J. High Energy Phys., 0806, 105 (2008) |
| [42] | Ho, P.-M.; Ma, C.-T.; Yeh, C.-H., BPS states on M5-brane in large C-field background, J. High Energy Phys., 1208, 076 (2012) · Zbl 1397.81256 |
| [43] | Jurco, B.; Schupp, P., Nambu-sigma model and effective membrane actions, Phys. Lett. B, 713, 313-316 (2012) |
| [44] | Schupp, P.; Jurco, B., Nambu sigma model and branes, PoS, CORFU2011, 045 (2011) |
| [45] | Jurco, B.; Schupp, P.; Vysoky, J., On the generalized geometry origin of noncommutative gauge theory, J. High Energy Phys., 1307, 126 (2013) · Zbl 1342.81637 |
| [46] | Jurčo, B.; Schupp, P.; Vysoký, J., Extended generalized geometry and a DBI-type effective action for branes ending on branes, J. High Energy Phys., 1408, 170 (2014) |
| [47] | Cederwall, M.; Nilsson, B. E.; Sundell, P., An action for the superfive-brane in \(D = 11\) supergravity, J. High Energy Phys., 9804, 007 (1998) · Zbl 0955.83026 |
| [48] | Lee, K.; Park, J.-H., Partonic description of a supersymmetric p-brane, J. High Energy Phys., 1004, 043 (2010) · Zbl 1272.81121 |
| [49] | Park, J.-H.; Sochichiu, C., Taking off the square root of Nambu-Goto action and obtaining Filippov-Lie algebra gauge theory action, Eur. Phys. J. C, 64, 161-166 (2009) · Zbl 1189.81188 |
| [50] | Ho, P.-M.; Ma, C.-T., S-duality for D3-brane in NS-NS and R-R backgrounds, J. High Energy Phys., 1411, 142 (2014) · Zbl 1333.81338 |
| [51] | Ho, P.-M.; Ma, C.-T., Effective action for Dp-brane in large RR \((p - 1)\)-form background, J. High Energy Phys., 1305, 056 (2013) |
| [52] | Ma, C.-T.; Yeh, C.-H., Supersymmetry and BPS states on D4-brane in large C-field background, J. High Energy Phys., 1303, 131 (2013) · Zbl 1342.81600 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
