Abstract
We present an analytic solution for tachyon condensation on a non-BPS D-brane in Berkovits’ open superstring field theory. The solution is presented as a product of 2 × 2 matrices in two distinct GL 2 subgroups of the open string star algebra. All string fields needed for computation of the nonpolynomial action can be derived in closed form, and the action produces the expected non-BPS D-brane tension in accordance with Sen’s conjecture. We also comment on how D-brane charges may be encoded in the topology of the tachyon vacuum gauge orbit.
Similar content being viewed by others
References
A. Sen, Tachyon dynamics in open string theory, Int. J. Mod. Phys. A 20 (2005) 5513 [hep-th/0410103] [INSPIRE].
A. Sen and B. Zwiebach, Tachyon condensation in string field theory, JHEP 03 (2000) 002 [hep-th/9912249] [INSPIRE].
N. Moeller and W. Taylor, Level truncation and the tachyon in open bosonic string field theory, Nucl. Phys. B 583 (2000) 105 [hep-th/0002237] [INSPIRE].
D. Gaiotto and L. Rastelli, Experimental string field theory, JHEP 08 (2003) 048 [hep-th/0211012] [INSPIRE].
N. Berkovits, A. Sen and B. Zwiebach, Tachyon condensation in superstring field theory, Nucl. Phys. B 587 (2000) 147 [hep-th/0002211] [INSPIRE].
P.-J. De Smet and J. Raeymaekers, Level four approximation to the tachyon potential in superstring field theory, JHEP 05 (2000) 051 [hep-th/0003220] [INSPIRE].
A. Iqbal and A. Naqvi, Tachyon condensation on a nonBPS D-brane, hep-th/0004015 [INSPIRE].
P.-J. De Smet, Tachyon condensation: Calculations in string field theory, hep-th/0109182 [INSPIRE].
J. Raeymaekers, Tachyon Condensation in String Field Theory, PhD Thesis, KULeuven (2001).
M. Schnabl, Analytic solution for tachyon condensation in open string field theory, Adv. Theor. Math. Phys. 10 (2006) 433 [hep-th/0511286] [INSPIRE].
E. Witten, Noncommutative Geometry and String Field Theory, Nucl. Phys. B 268 (1986) 253 [INSPIRE].
I. Ellwood and M. Schnabl, Proof of vanishing cohomology at the tachyon vacuum, JHEP 02 (2007) 096 [hep-th/0606142] [INSPIRE].
A. Sen, Stable nonBPS bound states of BPS D-branes, JHEP 08 (1998) 010 [hep-th/9805019] [INSPIRE].
A. Sen, Tachyon condensation on the brane anti-brane system, JHEP 08 (1998) 012 [hep-th/9805170] [INSPIRE].
A. Sen, Universality of the tachyon potential, JHEP 12 (1999) 027 [hep-th/9911116] [INSPIRE].
N. Berkovits, SuperPoincaré invariant superstring field theory, Nucl. Phys. B 450 (1995) 90 [Erratum ibid. B 459 (1996) 439-451] [hep-th/9503099] [INSPIRE].
N. Berkovits, A New approach to superstring field theory, Fortsch. Phys. 48 (2000) 31 [hep-th/9912121] [INSPIRE].
T. Erler, Tachyon Vacuum in Cubic Superstring Field Theory, JHEP 01 (2008) 013 [arXiv:0707.4591] [INSPIRE].
C.R. Preitschopf, C.B. Thorn and S.A. Yost, Superstring field theory, Nucl. Phys. B 337 (1990) 363 [INSPIRE].
I.Y. Arefeva, P. Medvedev and A. Zubarev, New Representation for String Field Solves the Consistency Problem for Open Superstring Field Theory, Nucl. Phys. B 341 (1990) 464 [INSPIRE].
M. Schnabl, private communication.
E. Fuchs and M. Kroyter, Marginal deformation for the photon in superstring field theory, JHEP 11 (2007) 005 [arXiv:0706.0717] [INSPIRE].
T. Erler, Comments on the tachyon vacuum in nonpolynomial superstring field theory, Talk delivered at the APCTP Focus Program on Current Trends in String Field Theory, Pohang, Korea, Dec. 2009, http://newton.skku.ac.kr/workshop/SFT2009/program.html.
L. Rastelli and B. Zwiebach, Tachyon potentials, star products and universality, JHEP 09 (2001) 038 [hep-th/0006240] [INSPIRE].
T. Erler and M. Schnabl, A Simple Analytic Solution for Tachyon Condensation, JHEP 10 (2009) 066 [arXiv:0906.0979] [INSPIRE].
N. Berkovits, The Ramond sector of open superstring field theory, JHEP 11 (2001) 047 [hep-th/0109100] [INSPIRE].
Y. Michishita, A Covariant action with a constraint and Feynman rules for fermions in open superstring field theory, JHEP 01 (2005) 012 [hep-th/0412215] [INSPIRE].
L. Barosi and C. Tello, GSO(−) vertex operators and open superstring field theory in hybrid variables, JHEP 05 (2003) 004 [hep-th/0303246] [INSPIRE].
A. Bagchi and A. Sen, Tachyon Condensation on Separated Brane-Antibrane System, JHEP 05 (2008) 010 [arXiv:0801.3498] [INSPIRE].
D. Friedan, E.J. Martinec and S.H. Shenker, Conformal Invariance, Supersymmetry and String Theory, Nucl. Phys. B 271 (1986) 93 [INSPIRE].
E. Witten, Nonabelian Bosonization in Two-Dimensions, Commun. Math. Phys. 92 (1984) 455 [INSPIRE].
N. Berkovits, Y. Okawa and B. Zwiebach, WZW-like action for heterotic string field theory, JHEP 11 (2004) 038 [hep-th/0409018] [INSPIRE].
T. Erler, Exotic Universal Solutions in Cubic Superstring Field Theory, JHEP 04 (2011) 107 [arXiv:1009.1865] [INSPIRE].
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] [INSPIRE].
T. Erler, Split String Formalism and the Closed String Vacuum, JHEP 05 (2007) 083 [hep-th/0611200] [INSPIRE].
Y. Okawa, Analytic methods in open string field theory, Prog. Theor. Phys. 128 (2012) 1001 [INSPIRE].
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] [INSPIRE].
L. Rastelli and B. Zwiebach, Solving Open String Field Theory with Special Projectors, JHEP 01 (2008) 020 [hep-th/0606131] [INSPIRE].
Y. Okawa, L. Rastelli and B. Zwiebach, Analytic Solutions for Tachyon Condensation with General Projectors, hep-th/0611110 [INSPIRE].
M. Schnabl, Wedge states in string field theory, JHEP 01 (2003) 004 [hep-th/0201095] [INSPIRE].
T. Erler, Split String Formalism and the Closed String Vacuum, II, JHEP 05 (2007) 084 [hep-th/0612050] [INSPIRE].
T. Erler, The Identity String Field and the Sliver Frame Level Expansion, JHEP 11 (2012) 150 [arXiv:1208.6287] [INSPIRE].
M.R. Gaberdiel and B. Zwiebach, Tensor constructions of open string theories. 1: Foundations, Nucl. Phys. B 505 (1997) 569 [hep-th/9705038] [INSPIRE].
T. Erler, A simple analytic solution for tachyon condensation, Theor. Math. Phys. 163 (2010) 705 [INSPIRE].
T. Masuda, T. Noumi and D. Takahashi, Constraints on a class of classical solutions in open string field theory, JHEP 10 (2012) 113 [arXiv:1207.6220] [INSPIRE].
H. Hata and T. Kojita, Singularities in K-space and Multi-brane Solutions in Cubic String Field Theory, JHEP 02 (2013) 065 [arXiv:1209.4406] [INSPIRE].
T. Masuda, Comments on new multiple-brane solutions based on Hata-Kojita duality in open string field theory, arXiv:1211.2649 [INSPIRE].
E.A. Arroyo, Comments on multibrane solutions in cubic superstring field theory, arXiv:1306.1865 [INSPIRE].
H. Hata and T. Kojita, Inversion Symmetry of Gravitational Coupling in Cubic String Field Theory, arXiv:1307.6636 [INSPIRE].
M. Murata and M. Schnabl, On Multibrane Solutions in Open String Field Theory, Prog. Theor. Phys. Suppl. 188 (2011) 50 [arXiv:1103.1382] [INSPIRE].
M. Murata and M. Schnabl, Multibrane Solutions in Open String Field Theory, JHEP 07 (2012) 063 [arXiv:1112.0591] [INSPIRE].
R. Gorbachev, New solution of the superstring equation of motion, Theor. Math. Phys. 162 (2010) 90 [INSPIRE].
M. Kiermaier, Y. Okawa and P. Soler, Solutions from boundary condition changing operators in open string field theory, JHEP 03 (2011) 122 [arXiv:1009.6185] [INSPIRE].
T. Erler and C. Maccaferri, The Phantom Term in Open String Field Theory, JHEP 06 (2012) 084 [arXiv:1201.5122] [INSPIRE].
I. Ellwood, The Closed string tadpole in open string field theory, JHEP 08 (2008) 063 [arXiv:0804.1131] [INSPIRE].
Y. Michishita, On-shell gauge invariants and field strengths in open superstring field theory, Nucl. Phys. B 698 (2004) 111 [hep-th/0406242] [INSPIRE].
T. Erler and C. Maccaferri, Connecting Solutions in Open String Field Theory with Singular Gauge Transformations, JHEP 04 (2012) 107 [arXiv:1201.5119] [INSPIRE].
K. Ohmori, Level expansion analysis in NS superstring field theory revisited, hep-th/0305103 [INSPIRE].
T. Erler, Marginal Solutions for the Superstring, JHEP 07 (2007) 050 [arXiv:0704.0930] [INSPIRE].
Y. Okawa, Real analytic solutions for marginal deformations in open superstring field theory, JHEP 09 (2007) 082 [arXiv:0704.3612] [INSPIRE].
Y. Okawa, Analytic solutions for marginal deformations in open superstring field theory, JHEP 09 (2007) 084 [arXiv:0704.0936] [INSPIRE].
M. Kiermaier and Y. Okawa, General marginal deformations in open superstring field theory, JHEP 11 (2009) 042 [arXiv:0708.3394] [INSPIRE].
T. Noumi and Y. Okawa, Solutions from boundary condition changing operators in open superstring field theory, JHEP 12 (2011) 034 [arXiv:1108.5317] [INSPIRE].
M. Kroyter, Democratic Superstring Field Theory: Gauge Fixing, JHEP 03 (2011) 081 [arXiv:1010.1662] [INSPIRE].
M. Kroyter, Superstring field theory in the democratic picture, Adv. Theor. Math. Phys. 15 (2011) 741 [arXiv:0911.2962] [INSPIRE].
M. Kudrna, C. Maccaferri and M. Schnabl, Boundary State from Ellwood Invariants, JHEP 07 (2013) 033 [arXiv:1207.4785] [INSPIRE].
T. Baba and N. Ishibashi, Energy from the gauge invariant observables, JHEP 04 (2013) 050 [arXiv:1208.6206] [INSPIRE].
N. Berkovits, The Tachyon potential in open Neveu-Schwarz string field theory, JHEP 04 (2000) 022 [hep-th/0001084] [INSPIRE].
I. Ellwood, Singular gauge transformations in string field theory, JHEP 05 (2009) 037 [arXiv:0903.0390] [INSPIRE].
L. Bonora, C. Maccaferri and D. Tolla, Relevant Deformations in Open String Field Theory: a Simple Solution for Lumps, JHEP 11 (2011) 107 [arXiv:1009.4158] [INSPIRE].
T. Erler and C. Maccaferri, Comments on Lumps from RG flows, JHEP 11 (2011) 092 [arXiv:1105.6057] [INSPIRE].
G. Calcagni and G. Nardelli, Kinks of open superstring field theory, Nucl. Phys. B 823 (2009) 234 [arXiv:0904.3744] [INSPIRE].
L. Rastelli, Comments on the open string C ∗ algebra, Talk presented at the Simons Center workshop on String Field Theory, Stony Brook University, New York U.S.A. (2009).
M. Kiermaier, Y. Okawa and B. Zwiebach, The boundary state from open string fields, arXiv:0810.1737 [INSPIRE].
R. Minasian and G.W. Moore, K theory and Ramond-Ramond charge, JHEP 11 (1997) 002 [hep-th/9710230] [INSPIRE].
E. Witten, D-branes and k-theory, JHEP 12 (1998) 019 [hep-th/9810188] [INSPIRE].
E. Witten, Overview of k-theory applied to strings, Int. J. Mod. Phys. A 16 (2001) 693 [hep-th/0007175] [INSPIRE].
E. Fuchs and M. Kroyter, On the classical equivalence of superstring field theories, JHEP 10 (2008) 054 [arXiv:0805.4386] [INSPIRE].
M. Kroyter, Y. Okawa, M. Schnabl, S. Torii and B. Zwiebach, Open superstring field theory I: gauge fixing, ghost structure and propagator, JHEP 03 (2012) 030 [arXiv:1201.1761] [INSPIRE].
N. Berkovits, Constrained BV Description of String Field Theory, JHEP 03 (2012) 012 [arXiv:1201.1769] [INSPIRE].
S. Torii, Gauge fixing of open superstring field theory in the Berkovits non-polynomial formulation, Prog. Theor. Phys. Suppl. 188 (2011) 272 [arXiv:1201.1763] [INSPIRE].
S. Torii, Validity of Gauge-Fixing Conditions and the Structure of Propagators in Open Superstring Field Theory, JHEP 04 (2012) 050 [arXiv:1201.1762] [INSPIRE].
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1308.4400
Rights and permissions
About this article
Cite this article
Erler, T. Analytic solution for tachyon condensation in Berkovits’ open superstring field theory. J. High Energ. Phys. 2013, 7 (2013). https://doi.org/10.1007/JHEP11(2013)007
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP11(2013)007