Constraints on a class of classical solutions in open string field theory. (English) Zbl 1397.83166
Summary: We calculate boundary states for general string fields in the KBc subalgebra under some regularity conditions based on the construction by Kiermaier, Okawa, and Zwiebach. The resulting boundary states are always proportional to that for the perturbative vacuum \(|B\). In this framework, the equation of motion implies that boundary states are independent of the auxiliary parameter \(s\) associated with the length of the boundary. By requiring the \(s\)-independence, we show that the boundary states for classical solutions in our class are restricted to \(\pm|B\) and 0. In particular, there exist no string fields which reproduce boundary states for multiple D-brane backgrounds. While we know that the boundary states |\(B\) and 0 are reproduced by solutions for the perturbative vacuum and the tachyon vacuum, respectively, no solutions reproducing \(-|B\) have been constructed. In this paper we also propose a candidate for such a solution, which may describe the ghost D-brane.
MSC:
| 83E30 | String and superstring theories in gravitational theory |
References:
| [1] | Witten, E., Noncommutative geometry and string field theory, Nucl. Phys., B 268, 253, (1986) · doi:10.1016/0550-3213(86)90155-0 |
| [2] | Schnabl, M., Analytic solution for tachyon condensation in open string field theory, Adv. Theor. Math. Phys., 10, 433, (2006) · Zbl 1101.81344 |
| [3] | Schnabl, M., Comments on marginal deformations in open string field theory, Phys. Lett., B 654, 194, (2007) · Zbl 1246.81302 |
| [4] | Kiermaier, M.; Okawa, Y.; Rastelli, L.; Zwiebach, B., Analytic solutions for marginal deformations in open string field theory, JHEP, 01, 028, (2008) · doi:10.1088/1126-6708/2008/01/028 |
| [5] | Erler, T., Marginal solutions for the superstring, JHEP, 07, 050, (2007) · doi:10.1088/1126-6708/2007/07/050 |
| [6] | Okawa, Y., Analytic solutions for marginal deformations in open superstring field theory, JHEP, 09, 084, (2007) · doi:10.1088/1126-6708/2007/09/084 |
| [7] | Okawa, Y., Real analytic solutions for marginal deformations in open superstring field theory, JHEP, 09, 082, (2007) · doi:10.1088/1126-6708/2007/09/082 |
| [8] | Ellwood, I., Rolling to the tachyon vacuum in string field theory, JHEP, 12, 028, (2007) · Zbl 1246.81235 · doi:10.1088/1126-6708/2007/12/028 |
| [9] | Kwon, O-K, Marginally deformed rolling tachyon around the tachyon vacuum in open string field theory, Nucl. Phys., B 804, 1, (2008) · Zbl 1190.81109 · doi:10.1016/j.nuclphysb.2008.07.003 |
| [10] | S. Hellerman and M. Schnabl, Light-like tachyon condensation in Open String Field Theory, arXiv:0803.1184 [INSPIRE]. · Zbl 1342.83377 |
| [11] | Kishimoto, I., Comments on gauge invariant overlaps for marginal solutions in open string field theory, Prog. Theor. Phys., 120, 875, (2008) · Zbl 1165.81364 · doi:10.1143/PTP.120.875 |
| [12] | Barnaby, N.; Mulryne, DJ; Nunes, NJ; Robinson, P., Dynamics and stability of light-like tachyon condensation, JHEP, 03, 018, (2009) · doi:10.1088/1126-6708/2009/03/018 |
| [13] | F. Beaujean and N. Moeller, Delays in Open String Field Theory, arXiv:0912.1232 [INSPIRE]. |
| [14] | Kiermaier, M.; Okawa, Y.; Soler, P., Solutions from boundary condition changing operators in open string field theory, JHEP, 03, 122, (2011) · Zbl 1301.81224 · doi:10.1007/JHEP03(2011)122 |
| [15] | Noumi, T.; Okawa, Y., Solutions from boundary condition changing operators in open superstring field theory, JHEP, 12, 034, (2011) · Zbl 1306.81264 · doi:10.1007/JHEP12(2011)034 |
| [16] | Ellwood, I.; Schnabl, M., Proof of vanishing cohomology at the tachyon vacuum, JHEP, 02, 096, (2007) · doi:10.1088/1126-6708/2007/02/096 |
| [17] | Erler, T.; Schnabl, M., A simple analytic solution for tachyon condensation, JHEP, 10, 066, (2009) · doi:10.1088/1126-6708/2009/10/066 |
| [18] | Okawa, Y., Comments on schnabl’s analytic solution for tachyon condensation in witten’s open string field theory, JHEP, 04, 055, (2006) · doi:10.1088/1126-6708/2006/04/055 |
| [19] | Rastelli, L.; Zwiebach, B., Tachyon potentials, star products and universality, JHEP, 09, 038, (2001) · doi:10.1088/1126-6708/2001/09/038 |
| [20] | Schnabl, M., Wedge states in string field theory, JHEP, 01, 004, (2003) · Zbl 1226.81228 · doi:10.1088/1126-6708/2003/01/004 |
| [21] | Rastelli, L.; Zwiebach, B., Solving open string field theory with special projectors, JHEP, 01, 020, (2008) · doi:10.1088/1126-6708/2008/01/020 |
| [22] | Y. Okawa, L. Rastelli and B. Zwiebach, Analytic Solutions for Tachyon Condensation with General Projectors, hep-th/0611110 [INSPIRE]. |
| [23] | Erler, T., Split string formalism and the closed string vacuum, JHEP, 05, 083, (2007) · doi:10.1088/1126-6708/2007/05/083 |
| [24] | Erler, T., Split string formalism and the closed string vacuum, II, JHEP, 05, 084, (2007) · doi:10.1088/1126-6708/2007/05/084 |
| [25] | Fuchs, E.; Kroyter, M.; Potting, R., Marginal deformations in string field theory, JHEP, 09, 101, (2007) · doi:10.1088/1126-6708/2007/09/101 |
| [26] | Fuchs, E.; Kroyter, M., Marginal deformation for the photon in superstring field theory, JHEP, 11, 005, (2007) · Zbl 1245.81164 · doi:10.1088/1126-6708/2007/11/005 |
| [27] | Kiermaier, M.; Okawa, Y., Exact marginality in open string field theory: A general framework, JHEP, 11, 041, (2009) · doi:10.1088/1126-6708/2009/11/041 |
| [28] | Erler, T., Tachyon vacuum in cubic superstring field theory, JHEP, 01, 013, (2008) · doi:10.1088/1126-6708/2008/01/013 |
| [29] | Kiermaier, M.; Okawa, Y., General marginal deformations in open superstring field theory, JHEP, 11, 042, (2009) · doi:10.1088/1126-6708/2009/11/042 |
| [30] | Aref’eva, IY; Gorbachev, RV; Medvedev, PB, Tachyon solution in cubic Neveu-Schwarz string field theory, Theor. Math. Phys., 158, 320, (2009) · Zbl 1174.81007 · doi:10.1007/s11232-009-0026-2 |
| [31] | Aref’eva, IY; Gorbachev, RV; Grigoryev, DA; Khromov, PN; Maltsev, MV; Medvedev, PB, Pure gauge configurations and tachyon solutions to string field theories equations of motion, JHEP, 05, 050, (2009) · doi:10.1088/1126-6708/2009/05/050 |
| [32] | Ellwood, I., Singular gauge transformations in string field theory, JHEP, 05, 037, (2009) · doi:10.1088/1126-6708/2009/05/037 |
| [33] | Arroyo, EA, Generating erler-schnabl-type solution for tachyon vacuum in cubic superstring field theory, J. Phys., A 43, 445403, (2010) · Zbl 1202.81166 |
| [34] | Erler, T., Exotic universal solutions in cubic superstring field theory, JHEP, 04, 107, (2011) · Zbl 1250.81082 · doi:10.1007/JHEP04(2011)107 |
| [35] | Bonora, L.; Maccaferri, C.; Tolla, D., Relevant deformations in open string field theory: a simple solution for lumps, JHEP, 11, 107, (2011) · Zbl 1306.81200 · doi:10.1007/JHEP11(2011)107 |
| [36] | Murata, M.; Schnabl, M., On multibrane solutions in open string field theory, Prog. Theor. Phys. Suppl., 188, 50, (2011) · Zbl 1231.81070 · doi:10.1143/PTPS.188.50 |
| [37] | Bonora, L.; Giaccari, S.; Tolla, D., The energy of the analytic lump solution in SFT, JHEP, 08, 158, (2011) · Zbl 1298.81248 · doi:10.1007/JHEP08(2011)158 |
| [38] | Erler, T.; Maccaferri, C., Comments on lumps from RG flows, JHEP, 11, 092, (2011) · Zbl 1306.81223 · doi:10.1007/JHEP11(2011)092 |
| [39] | Murata, M.; Schnabl, M., Multibrane solutions in open string field theory, JHEP, 07, 063, (2012) · Zbl 1397.81273 · doi:10.1007/JHEP07(2012)063 |
| [40] | Sen, A., Universality of the tachyon potential, JHEP, 12, 027, (1999) · Zbl 0958.81101 · doi:10.1088/1126-6708/1999/12/027 |
| [41] | Hashimoto, A.; Itzhaki, N., Observables of string field theory, JHEP, 01, 028, (2002) · doi:10.1088/1126-6708/2002/01/028 |
| [42] | Gaiotto, D.; Rastelli, L.; Sen, A.; Zwiebach, B., Ghost structure and closed strings in vacuum string field theory, Adv. Theor. Math. Phys., 6, 403, (2003) · Zbl 1042.81067 |
| [43] | Ellwood, I., The closed string tadpole in open string field theory, JHEP, 08, 063, (2008) · doi:10.1088/1126-6708/2008/08/063 |
| [44] | Hata, H.; Kojita, T., Winding number in string field theory, JHEP, 01, 088, (2012) · Zbl 1306.81244 · doi:10.1007/JHEP01(2012)088 |
| [45] | T. Masuda, On the classical solution for the double-brane background in open string field theory, to appear. |
| [46] | Takahashi, D., The boundary state for a class of analytic solutions in open string field theory, JHEP, 11, 054, (2011) · Zbl 1306.81281 · doi:10.1007/JHEP11(2011)054 |
| [47] | M. Kiermaier, Y. Okawa and B. Zwiebach, The boundary state from open string fields, arXiv:0810.1737 [INSPIRE]. |
| [48] | M. Kudrna, C. Maccaferri and M. Schnabl, Boundary State from Ellwood Invariants, arXiv:1207.4785 [INSPIRE]. |
| [49] | Okuda, T.; Takayanagi, T., Ghost \(D\)-branes, JHEP, 03, 062, (2006) · Zbl 1226.81219 · doi:10.1088/1126-6708/2006/03/062 |
| [50] | Kiermaier, M.; Sen, A.; Zwiebach, B., Linear \(b\)-gauges for open string fields, JHEP, 03, 050, (2008) · doi:10.1088/1126-6708/2008/03/050 |
| [51] | Kiermaier, M.; Zwiebach, B., One-loop Riemann surfaces in schnabl gauge, JHEP, 07, 063, (2008) · doi:10.1088/1126-6708/2008/07/063 |
| [52] | Erler, T.; Maccaferri, C., Connecting solutions in open string field theory with singular gauge transformations, JHEP, 04, 107, (2012) · Zbl 1348.81366 · doi:10.1007/JHEP04(2012)107 |
| [53] | Erler, T.; Maccaferri, C., The phantom term in open string field theory, JHEP, 06, 084, (2012) · Zbl 1397.81237 · doi:10.1007/JHEP06(2012)084 |
| [54] | Zeze, S., Regularization of identity based solution in string field theory, JHEP, 10, 070, (2010) · Zbl 1291.81344 · doi:10.1007/JHEP10(2010)070 |
| [55] | Arroyo, EA, Comments on regularization of identity based solutions in string field theory, JHEP, 11, 135, (2010) · Zbl 1294.81157 · doi:10.1007/JHEP11(2010)135 |
| [56] | T. Erler, The Identity String Field and the Sliver Frame Level Expansion, arXiv:1208.6287 [INSPIRE]. |
| [57] | Erler, T., A simple analytic solution for tachyon condensation, Theor. Math. Phys., 163, 705, (2010) · Zbl 1256.81090 · doi:10.1007/s11232-010-0053-z |
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.
