Journal of High Energy Physics

, 2019:53 | Cite as

String memory effect

  • Hamid Afshar
  • Erfan EsmaeiliEmail author
  • M. M. Sheikh-Jabbari
Open Access
Regular Article - Theoretical Physics


In systems with local gauge symmetries, the memory effect corresponds to traces inscribed on a suitable probe when a pure gauge configuration at infinite past dynamically evolves to another pure gauge configuration at infinite future. In this work, we study the memory effect of 2-form gauge fields which is probed by strings. We discuss the “string memory effect” for closed and open strings at classical and quantum levels. The closed string memory is encoded in the internal excited modes of the string, and in the open string case, it is encoded in the relative position of the two endpoints and the non-commutativity parameter associated with the D-brane where the open string endpoints are attached. We also discuss 2-form memory with D-brane probes using boundary state formulation and, the relation between string memory and 2-form soft charges analyzed in [1].


Bosonic Strings Gauge Symmetry D-branes 


Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.


  1. [1]
    H. Afshar, E. Esmaeili and M.M. Sheikh-Jabbari, Asymptotic symmetries in p-form theories, JHEP 05 (2018) 042 [arXiv:1801.07752] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  2. [2]
    A. Strominger, Asymptotic symmetries of Yang-Mills theory, JHEP 07 (2014) 151 [arXiv:1308.0589] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  3. [3]
    A. Strominger, On BMS invariance of gravitational scattering, JHEP 07 (2014) 152 [arXiv:1312.2229] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  4. [4]
    T. He, P. Mitra, A.P. Porfyriadis and A. Strominger, New symmetries of massless QED, JHEP 10 (2014) 112 [arXiv:1407.3789] [INSPIRE].ADSCrossRefGoogle Scholar
  5. [5]
    A. Strominger and A. Zhiboedov, Gravitational memory, BMS supertranslations and soft theorems, JHEP 01 (2016) 086 [arXiv:1411.5745] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  6. [6]
    A. Strominger, Lectures on the infrared structure of gravity and gauge theory, arXiv:1703.05448 [INSPIRE].
  7. [7]
    D. Christodoulou, Nonlinear nature of gravitation and gravitational wave experiments, Phys. Rev. Lett. 67 (1991) 1486 [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  8. [8]
    Y. Zel’dovich and A. Polnarev, Radiation of gravitational waves by a cluster of superdense stars, Sov. Astron. 18 (1974) 017.ADSGoogle Scholar
  9. [9]
    S. Pasterski, A. Strominger and A. Zhiboedov, New gravitational memories, JHEP 12 (2016) 053 [arXiv:1502.06120] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  10. [10]
    G. Compère, A. Fiorucci and R. Ruzziconi, Superboost transitions, refraction memory and super-Lorentz charge algebra, JHEP 11 (2018) 200 [arXiv:1810.00377] [INSPIRE].ADSCrossRefGoogle Scholar
  11. [11]
    A. Laddha and A. Sen, Observational signature of the logarithmic terms in the soft graviton theorem, arXiv:1806.01872 [INSPIRE].
  12. [12]
    M. O’Loughlin and H. Demirchian, Geodesic congruences, impulsive gravitational waves and gravitational memory, Phys. Rev. D 99 (2019) 024031 [arXiv:1808.04886] [INSPIRE].ADSGoogle Scholar
  13. [13]
    P.M. Zhang, C. Duval, G.W. Gibbons and P.A. Horvathy, Velocity memory effect for polarized gravitational waves, JCAP 05 (2018) 030 [arXiv:1802.09061] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  14. [14]
    L. Bieri and D. Garfinkle, An electromagnetic analogue of gravitational wave memory, Class. Quant. Grav. 30 (2013) 195009 [arXiv:1307.5098] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  15. [15]
    J. Winicour, Global aspects of radiation memory, Class. Quant. Grav. 31 (2014) 205003 [arXiv:1407.0259] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  16. [16]
    L. Susskind, Electromagnetic memory, arXiv:1507.02584 [INSPIRE].
  17. [17]
    S. Pasterski, Asymptotic symmetries and electromagnetic memory, JHEP 09 (2017) 154 [arXiv:1505.00716] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  18. [18]
    P. Mao, H. Ouyang, J.-B. Wu and X. Wu, New electromagnetic memories and soft photon theorems, Phys. Rev. D 95 (2017) 125011 [arXiv:1703.06588] [INSPIRE].ADSMathSciNetGoogle Scholar
  19. [19]
    M. Campiglia, L. Freidel, F. Hopfmueller and R.M. Soni, Scalar asymptotic charges and dual large gauge transformations, arXiv:1810.04213 [INSPIRE].
  20. [20]
    D. Francia and C. Heissenberg, Two-form asymptotic symmetries and scalar soft theorems, Phys. Rev. D 98 (2018) 105003 [arXiv:1810.05634] [INSPIRE].ADSGoogle Scholar
  21. [21]
    F. Ardalan, H. Arfaei and M.M. Sheikh-Jabbari, Dirac quantization of open strings and noncommutativity in branes, Nucl. Phys. B 576 (2000) 578 [hep-th/9906161] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  22. [22]
    M.M. Sheikh-Jabbari, Open strings in a B field background as electric dipoles, Phys. Lett. B 455 (1999) 129 [hep-th/9901080] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  23. [23]
    C.-S. Chu and P.-M. Ho, Noncommutative open string and D-brane, Nucl. Phys. B 550 (1999) 151 [hep-th/9812219] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  24. [24]
    C.-S. Chu and P.-M. Ho, Constrained quantization of open string in background B field and noncommutative D-brane, Nucl. Phys. B 568 (2000) 447 [hep-th/9906192] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  25. [25]
    N. Seiberg and E. Witten, String theory and noncommutative geometry, JHEP 09 (1999) 032 [hep-th/9908142] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  26. [26]
    P. Di Vecchia et al., Classical p-branes from boundary state, Nucl. Phys. B 507 (1997) 259 [hep-th/9707068] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  27. [27]
    H. Arfaei and D. Kamani, Branes with back-ground fields in boundary state formalism, Phys. Lett. B 452 (1999) 54 [hep-th/9909167] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  28. [28]
    C. Bachas, Relativistic string in a pulse, Annals Phys. 305 (2003) 286 [hep-th/0212217] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  29. [29]
    H. Afshar and E. Esmaieli, More on p-form soft charges, work in progress.Google Scholar
  30. [30]
    R. Blumenhagen, D. Lüst and S. Theisen, Basic concepts of string theory, Theoretical and Mathematical Physics, Springer, Germany (2013).Google Scholar
  31. [31]
    C.V. Johnson, D-branes, Cambridge Monographs on Mathematical Physics, Cambridge University Press, Cambridge U.K. (2005).Google Scholar
  32. [32]
    E. Witten, Bound states of strings and p-branes, Nucl. Phys. B 460 (1996) 335 [hep-th/9510135] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  33. [33]
    M.M. Sheikh-Jabbari, A note on the deformation of Λ symmetry in B field background, Phys. Lett. B 477 (2000) 325 [hep-th/9910258] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  34. [34]
    M.M. Sheikh-Jabbari, More on mixed boundary conditions and D-branes bound states, Phys. Lett. B 425 (1998) 48 [hep-th/9712199] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  35. [35]
    M.M. Sheikh-Jabbari and A. Shirzad, Boundary conditions as Dirac constraints, Eur. Phys. J. C 19 (2001) 383 [hep-th/9907055] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  36. [36]
    M.M. Sheikh-Jabbari, Super-Yang-Mills theory on noncommutative torus from open strings interactions, Phys. Lett. B 450 (1999) 119 [hep-th/9810179] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  37. [37]
    M.R. Douglas and C.M. Hull, D-branes and the noncommutative torus, JHEP 02 (1998) 008 [hep-th/9711165] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  38. [38]
    A. Micu and M.M. Sheikh Jabbari, Noncommutative ϕ 4 theory at two loops, JHEP 01 (2001) 025 [hep-th/0008057] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  39. [39]
    J. Polchinski, S. Chaudhuri and C.V. Johnson, Notes on D-branes, hep-th/9602052 [INSPIRE].
  40. [40]
    J. Polchinski, TASI lectures on D-branes, in the proceedings of Fields, strings and duality. Summer School (TASI’96), June 2–28, Boulder, U.S.A. (1996), hep-th/9611050 [INSPIRE].
  41. [41]
    J. Polchinski, Dirichlet branes and Ramond-Ramond charges, Phys. Rev. Lett. 75 (1995) 4724 [hep-th/9510017] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  42. [42]
    P. Di Vecchia and A. Liccardo, D branes in string theory, I, NATO Sci. Ser. C 556 (2000) 1 [hep-th/9912161] [INSPIRE].MathSciNetzbMATHGoogle Scholar
  43. [43]
    P. Di Vecchia and A. Liccardo, D-branes in string theory. 2., talk given at the YITP Workshop on Developments in Superstring and M-theory, October 27–29, Kyoto, Japan (1999), hep-th/9912275 [INSPIRE].
  44. [44]
    P. Di Vecchia, M. Frau, A. Lerda and A. Liccardo, (F, D(p)) bound states from the boundary state, Nucl. Phys. B 565 (2000) 397 [hep-th/9906214] [INSPIRE].
  45. [45]
    J. Polchinski, String theory. Volume 2: superstring theory and beyond, Cambridge Monographs on Mathematical Physics, Cambridge University Press, Cambridge U.K. (2007).Google Scholar
  46. [46]
    D. Grumiller and M.M. Sheikh-Jabbari, Membrane paradigm from near horizon soft hair, Int. J. Mod. Phys. D 27 (2018) 1847006 [arXiv:1805.11099] [INSPIRE].ADSCrossRefGoogle Scholar
  47. [47]
    P. Di Vecchia, R. Marotta and M. Mojaza, Soft theorem for the graviton, dilaton and the Kalb-Ramond field in the bosonic string, JHEP 05 (2015) 137 [arXiv:1502.05258] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  48. [48]
    P. Di Vecchia, R. Marotta and M. Mojaza, Soft theorems from string theory, Fortsch. Phys. 64 (2016) 389 [arXiv:1511.04921] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  49. [49]
    P. Di Vecchia, R. Marotta and M. Mojaza, The B-field soft theorem and its unification with the graviton and dilaton, JHEP 10 (2017) 017 [arXiv:1706.02961] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  50. [50]
    A. Sen, Soft theorems in superstring theory, JHEP 06 (2017) 113 [arXiv:1702.03934] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  51. [51]
    A. Laddha and A. Sen, Sub-subleading soft graviton theorem in generic theories of quantum gravity, JHEP 10 (2017) 065 [arXiv:1706.00759] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© The Author(s) 2019

Authors and Affiliations

  1. 1.School of PhysicsInstitute for Research in Fundamental Sciences (IPM)TehranIran

Personalised recommendations