Abstract
We construct analytic solutions of open string field theory using boundary condition changing (bcc) operators. We focus on bcc operators with vanishing conformal weight such as those for regular marginal deformations of the background. For any Fock space state ϕ, the component string field \( \left\langle {\phi, \Psi } \right\rangle \) of the solution Ψ exhibits a remarkable factorization property: it is given by the matter three-point function of ϕ with a pair of bcc operators, multiplied by a universal function that only depends on the conformal weight of ϕ. This universal function is given by a simple integral expression that can be computed once and for all. The three-point functions with bcc operators are thus the only needed physical input of the particular open string background described by the solution. We illustrate our solution with the example of the rolling tachyon profile, for which we prove convergence analytically. The form of our solution, which involves bcc operators instead of explicit insertions of the marginal operator, can be a natural starting point for the construction of analytic solutions for arbitrary backgrounds.
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References
E. Witten, Noncommutative geometry and string field theory, Nucl. Phys. B 268 (1986) 253 [SPIRES].
M. Schnabl, Analytic solution for tachyon condensation in open string field theory, Adv. Theor. Math. Phys. 10 (2006) 433 [hep-th/0511286] [SPIRES].
Y. Okawa, Comments on Schnabl’s analytic solution for tachyon condensation in Witten’s open string field theory, JHEP 04 (2006) 055 [hep-th/0603159] [SPIRES].
E. Fuchs and M. Kroyter, On the validity of the solution of string field theory, JHEP 05 (2006) 006 [hep-th/0603195] [SPIRES].
E. Fuchs and M. Kroyter, Schnabl’s \( {\mathcal{L}_0} \) operator in the continuous basis, JHEP 10 (2006) 067 [hep-th/0605254] [SPIRES].
L. Rastelli and B. Zwiebach, Solving open string field theory with special projectors, JHEP 01 (2008) 020 [hep-th/0606131] [SPIRES].
I. Ellwood and M. Schnabl, Proof of vanishing cohomology at the tachyon vacuum, JHEP 02 (2007) 096 [hep-th/0606142] [SPIRES].
H. Fuji, S. Nakayama and H. Suzuki, Open string amplitudes in various gauges, JHEP 01 (2007) 011 [hep-th/0609047] [SPIRES].
E. Fuchs and M. Kroyter, Universal regularization for string field theory, JHEP 02 (2007) 038 [hep-th/0610298] [SPIRES].
Y. Okawa, L. Rastelli and B. Zwiebach, Analytic solutions for tachyon condensation with general projectors, hep-th/0611110 [SPIRES].
T. Erler, Split string formalism and the closed string vacuum, JHEP 05 (2007) 083 [hep-th/0611200] [SPIRES].
T. Erler, Split string formalism and the closed string vacuum. II, JHEP 05 (2007) 084 [hep-th/0612050] [SPIRES].
M. Schnabl, Comments on marginal deformations in open string field theory, Phys. Lett. B 654 (2007) 194 [hep-th/0701248] [SPIRES].
M. Kiermaier, Y. Okawa, L. Rastelli and B. Zwiebach, Analytic solutions for marginal deformations in open string field theory, JHEP 01 (2008) 028 [hep-th/0701249] [SPIRES].
T. Erler, Marginal solutions for the superstring, JHEP 07 (2007) 050 [arXiv:0704.0930] [SPIRES].
Y. Okawa, Analytic solutions for marginal deformations in open superstring field theory, JHEP 09 (2007) 084 [arXiv:0704.0936] [SPIRES].
E. Fuchs, M. Kroyter and R. Potting, Marginal deformations in string field theory, JHEP 09 (2007) 101 [arXiv:0704.2222] [SPIRES].
Y. Okawa, Real analytic solutions for marginal deformations in open superstring field theory, JHEP 09 (2007) 082 [arXiv:0704.3612] [SPIRES].
I. Ellwood, Rolling to the tachyon vacuum in string field theory, JHEP 12 (2007) 028 [arXiv:0705.0013] [SPIRES].
I. Kishimoto and Y. Michishita, Comments on solutions for nonsingular currents in open string field theories, Prog. Theor. Phys. 118 (2007) 347 [arXiv:0706.0409] [SPIRES].
E. Fuchs and M. Kroyter, Marginal deformation for the photon in superstring field theory, JHEP 11 (2007) 005 [arXiv:0706.0717] [SPIRES].
M. Kiermaier and Y. Okawa, Exact marginality in open string field theory: a general framework, JHEP 11 (2009) 041 [arXiv:0707.4472] [SPIRES].
T. Erler, Tachyon vacuum in cubic superstring field theory, JHEP 01 (2008) 013 [arXiv:0707.4591] [SPIRES].
L. Rastelli and B. Zwiebach, The off-shell Veneziano amplitude in Schnabl gauge, JHEP 01 (2008) 018 [arXiv:0708.2591] [SPIRES].
M. Kiermaier and Y. Okawa, General marginal deformations in open superstring field theory, JHEP 11 (2009) 042 [arXiv:0708.3394] [SPIRES].
O.-K. Kwon, B.-H. Lee, C. Park and S.-J. Sin, Fluctuations around the tachyon vacuum in open string field theory, JHEP 12 (2007) 038 [arXiv:0709.2888] [SPIRES].
T. Takahashi, Level truncation analysis of exact solutions in open string field theory, JHEP 01 (2008) 001 [arXiv:0710.5358] [SPIRES].
M. Kiermaier, A. Sen and B. Zwiebach, Linear b-gauges for open string fields, JHEP 03 (2008) 050 [arXiv:0712.0627] [SPIRES].
O.-K. Kwon, Marginally deformed rolling tachyon around the tachyon vacuum in open string field theory, Nucl. Phys. B 804 (2008) 1 [arXiv:0801.0573] [SPIRES].
S. Hellerman and M. Schnabl, Light-like tachyon condensation in open string field theory, arXiv:0803.1184 [SPIRES].
I. Ellwood, The closed string tadpole in open string field theory, JHEP 08 (2008) 063 [arXiv:0804.1131] [SPIRES].
T. Kawano, I. Kishimoto and T. Takahashi, Gauge invariant overlaps for classical solutions in open string field theory, Nucl. Phys. B 803 (2008) 135 [arXiv:0804.1541] [SPIRES].
I.Y. Aref’eva, R.V. Gorbachev and P.B. Medvedev, Tachyon solution in cubic Neveu-Schwarz string field theory, Theor. Math. Phys. 158 (2009) 320 [arXiv:0804.2017] [SPIRES].
A. Ishida, C. Kim, Y. Kim, O.-K. Kwon and D.D. Tolla, Tachyon vacuum solution in open string field theory with constant B field, J. Phys. A 42 (2009) 395402 [arXiv:0804.4380] [SPIRES].
T. Kawano, I. Kishimoto and T. Takahashi, Schnabl’s solution and boundary states in open string field theory, Phys. Lett. B 669 (2008) 357 [arXiv:0804.4414] [SPIRES].
M. Kiermaier and B. Zwiebach, One-loop riemann surfaces in Schnabl gauge, JHEP 07 (2008) 063 [arXiv:0805.3701] [SPIRES].
E. Fuchs and M. Kroyter, Analytical solutions of open string field theory, arXiv:0807.4722 [SPIRES].
M. Asano and M. Kato, General linear gauges and amplitudes in open string field theory, Nucl. Phys. B 807 (2009) 348 [arXiv:0807.5010] [SPIRES].
I. Kishimoto, Comments on gauge invariant overlaps for marginal solutions in open string field theory, Prog. Theor. Phys. 120 (2008) 875 [arXiv:0808.0355] [SPIRES].
M. Kiermaier, Y. Okawa and B. Zwiebach, The boundary state from open string fields, arXiv:0810.1737 [SPIRES].
N. Barnaby, D.J. Mulryne, N.J. Nunes and P. Robinson, Dynamics and stability of light-like tachyon condensation, JHEP 03 (2009) 018 [arXiv:0811.0608] [SPIRES].
I.Y. Aref’eva et al., Pure gauge configurations and tachyon solutions to string field theories equations of motion, JHEP 05 (2009) 050 [arXiv:0901.4533] [SPIRES].
I. Kishimoto and T. Takahashi, Numerical evaluation of gauge invariants for a-gauge solutions in open string field theory, Prog. Theor. Phys. 121 (2009) 695 [arXiv:0902.0445] [SPIRES].
I. Ellwood, Singular gauge transformations in string field theory, JHEP 05 (2009) 037 [arXiv:0903.0390] [SPIRES].
I.Y. Aref’eva, R.V. Gorbachev and P.B. Medvedev, Pure gauge configurations and solutions to fermionic superstring field theories equations of motion, J. Phys. A 42 (2009) 304001 [arXiv:0903.1273] [SPIRES].
E.A. Arroyo, Cubic interaction term for Schnabl’s solution using Pade approximants, J. Phys. A 42 (2009) 375402 [arXiv:0905.2014] [SPIRES].
M. Kroyter, Comments on superstring field theory and its vacuum solution, JHEP 08 (2009) 048 [arXiv:0905.3501] [SPIRES].
T. Erler and M. Schnabl, A simple analytic solution for tachyon condensation, JHEP 10 (2009) 066 [arXiv:0906.0979] [SPIRES].
E. Aldo Arroyo, The tachyon potential in the sliver frame, JHEP 10 (2009) 056 [arXiv:0907.4939] [SPIRES].
F. Beaujean and N. Moeller, Delays in open string field theory, arXiv:0912.1232 [SPIRES].
E.A. Arroyo, Generating Erler-Schnabl-type solution for tachyon vacuum in cubic superstring field theory, J. Phys. A 43 (2010) 445403 [arXiv:1004.3030] [SPIRES].
S. Zeze, Tachyon potential in KBc subalgebra, Prog. Theor. Phys. 124 (2011) 567 [arXiv:1004.4351] [SPIRES].
M. Schnabl, Algebraic solutions in open string field theory — A lightning review, arXiv:1004.4858 [SPIRES].
I.Y. Arefeva and R.V. Gorbachev, On gauge equivalence of tachyon solutions in cubic Neveu-Schwarz string field theory, Theor. Math. Phys. 165 (2010) 1512 [arXiv:1004.5064] [SPIRES].
S. Zeze, Regularization of identity based solution in string field theory, JHEP 10 (2010) 070 [arXiv:1008.1104] [SPIRES].
E.A. Arroyo, Comments on regularization of identity based solutions in string field theory, JHEP 11 (2010) 135 [arXiv:1009.0198] [SPIRES].
T. Erler, Exotic universal solutions in cubic superstring field theory, arXiv:1009.1865 [SPIRES].
L. Bonora, C. Maccaferri and D.D. Tolla, Relevant deformations in open string field theory: a simple solution for lumps, arXiv:1009.4158 [SPIRES].
A. Hashimoto and N. Itzhaki, Observables of string field theory, JHEP 01 (2002) 028 [hep-th/0111092] [SPIRES].
D. Gaiotto, L. Rastelli, A. Sen and B. Zwiebach, Ghost structure and closed strings in vacuum string field theory, Adv. Theor. Math. Phys. 6 (2003) 403 [hep-th/0111129] [SPIRES].
L. Rastelli and B. Zwiebach, Tachyon potentials, star products and universality, JHEP 09 (2001) 038 [hep-th/0006240] [SPIRES].
A. Bagchi and A. Sen, Tachyon condensation on separated brane-antibrane system, JHEP 05 (2008) 010 [arXiv:0801.3498] [SPIRES].
M.R. Gaberdiel and B. Zwiebach, Tensor constructions of open string theories I: foundations, Nucl. Phys. B 505 (1997) 569 [hep-th/9705038] [SPIRES].
A. Sen, Rolling tachyon, JHEP 04 (2002) 048 [hep-th/0203211] [SPIRES].
A. Sen, Tachyon matter, JHEP 07 (2002) 065 [hep-th/0203265] [SPIRES].
A. Sen, Time evolution in open string theory, JHEP 10 (2002) 003 [hep-th/0207105] [SPIRES].
N. Moeller and B. Zwiebach, Dynamics with infinitely many time derivatives and rolling tachyons, JHEP 10 (2002) 034 [hep-th/0207107] [SPIRES].
F. Larsen, A. Naqvi and S. Terashima, Rolling tachyons and decaying branes, JHEP 02 (2003) 039 [hep-th/0212248] [SPIRES].
N.D. Lambert, H. Liu and J.M. Maldacena, Closed strings from decaying D-branes, JHEP 03 (2007) 014 [hep-th/0303139] [SPIRES].
M. Fujita and H. Hata, Time dependent solution in cubic string field theory, JHEP 05 (2003) 043 [hep-th/0304163] [SPIRES].
D. Gaiotto, N. Itzhaki and L. Rastelli, Closed strings as imaginary D-branes, Nucl. Phys. B 688 (2004) 70 [hep-th/0304192] [SPIRES].
T. Erler, Level truncation and rolling the tachyon in the lightcone basis for open string field theory, hep-th/0409179 [SPIRES].
A. Sen, Tachyon dynamics in open string theory, Int. J. Mod. Phys. A 20 (2005) 5513 [hep-th/0410103] [SPIRES].
E. Coletti, I. Sigalov and W. Taylor, Taming the tachyon in cubic string field theory, JHEP 08 (2005) 104 [hep-th/0505031] [SPIRES].
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ArXiv ePrint: 1009.6185
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Kiermaier, M., Okawa, Y. & Soler, P. Solutions from boundary condition changing operators in open string field theory. J. High Energ. Phys. 2011, 122 (2011). https://doi.org/10.1007/JHEP03(2011)122
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DOI: https://doi.org/10.1007/JHEP03(2011)122