Abstract
String theory with one unit of NS-NS flux on AdS3 × S3 × 𝕋4 has been recently realised to be the exact dual of the symmetric orbifold of 𝕋4. In the hybrid formalism of Berkovits, Vafa and Witten and using the free-field realisation of \( \mathfrak{psu} \)(1, 1|2)1, the DDF operators of the free bosons and the free fermions of 𝕋4 are constructed. It is shown that these DDF operators reproduce the whole spectrum of the space-time theory on the world-sheet and therefore provide a derivation of the dual spectrum from first-principles.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
J.M. Maldacena, The Large N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys. 2 (1998) 231 [hep-th/9711200] [INSPIRE].
M.R. Gaberdiel, R. Gopakumar and C. Hull, Stringy AdS3 from the worldsheet, JHEP 07 (2017) 090 [arXiv:1704.08665] [INSPIRE].
K. Ferreira, M.R. Gaberdiel and J.I. Jottar, Higher spins on AdS3 from the worldsheet, JHEP 07 (2017) 131 [arXiv:1704.08667] [INSPIRE].
M.R. Gaberdiel and R. Gopakumar, Tensionless string spectra on AdS3, JHEP 05 (2018) 085 [arXiv:1803.04423] [INSPIRE].
L. Eberhardt, M.R. Gaberdiel and R. Gopakumar, The Worldsheet Dual of the Symmetric Product CFT, JHEP 04 (2019) 103 [arXiv:1812.01007] [INSPIRE].
L. Eberhardt, M.R. Gaberdiel and R. Gopakumar, Deriving the AdS3/CFT2 correspondence, JHEP 02 (2020) 136 [arXiv:1911.00378] [INSPIRE].
A. Dei, M.R. Gaberdiel, R. Gopakumar and B. Knighton, Free field world-sheet correlators for AdS3, JHEP 02 (2021) 081 [arXiv:2009.11306] [INSPIRE].
L. Eberhardt, A perturbative CFT dual for pure NS–NS AdS3 strings, J. Phys. A 55 (2022) 064001 [arXiv:2110.07535] [INSPIRE].
N. Seiberg and E. Witten, The D1/D5 system and singular CFT, JHEP 04 (1999) 017 [hep-th/9903224] [INSPIRE].
R. Argurio, A. Giveon and A. Shomer, Superstrings on AdS3 and symmetric products, JHEP 12 (2000) 003 [hep-th/0009242] [INSPIRE].
A. Giveon, D. Kutasov, E. Rabinovici and A. Sever, Phases of quantum gravity in AdS3 and linear dilaton backgrounds, Nucl. Phys. B 719 (2005) 3 [hep-th/0503121] [INSPIRE].
G. Giribet, C. Hull, M. Kleban, M. Porrati and E. Rabinovici, Superstrings on AdS3 at k = 1, JHEP 08 (2018) 204 [arXiv:1803.04420] [INSPIRE].
L. Eberhardt, AdS3/CFT2 at higher genus, JHEP 05 (2020) 150 [arXiv:2002.11729] [INSPIRE].
B. Knighton, Higher genus correlators for tensionless AdS3 strings, JHEP 04 (2021) 211 [arXiv:2012.01445] [INSPIRE].
M.R. Gaberdiel, B. Knighton and J. Vošmera, D-branes in AdS3 × S3 × 𝕋4 at k = 1 and their holographic duals, JHEP 12 (2021) 149 [arXiv:2110.05509] [INSPIRE].
M.R. Gaberdiel and R. Gopakumar, String Dual to Free N = 4 Supersymmetric Yang-Mills Theory, Phys. Rev. Lett. 127 (2021) 131601 [arXiv:2104.08263] [INSPIRE].
M.R. Gaberdiel and R. Gopakumar, The worldsheet dual of free super Yang-Mills in 4D, JHEP 11 (2021) 129 [arXiv:2105.10496] [INSPIRE].
N. Berkovits, Sketching a Proof of the Maldacena Conjecture at Small Radius, JHEP 06 (2019) 111 [arXiv:1903.08264] [INSPIRE].
M.R. Gaberdiel and F. Galvagno, Worldsheet dual of free \( \mathcal{N} \) = 2 quiver gauge theories, JHEP 10 (2022) 077 [arXiv:2206.08795] [INSPIRE].
J.M. Maldacena and H. Ooguri, Strings in AdS3 and SL(2, R) WZW model 1.: The Spectrum, J. Math. Phys. 42 (2001) 2929 [hep-th/0001053] [INSPIRE].
N. Berkovits, C. Vafa and E. Witten, Conformal field theory of AdS background with Ramond-Ramond flux, JHEP 03 (1999) 018 [hep-th/9902098] [INSPIRE].
M.R. Gaberdiel, K. Naderi and V. Sriprachyakul, The free field realisation of the BVW string, JHEP 08 (2022) 274 [arXiv:2202.11392] [INSPIRE].
L. Eberhardt and M.R. Gaberdiel, String theory on AdS3 and the symmetric orbifold of Liouville theory, Nucl. Phys. B 948 (2019) 114774 [arXiv:1903.00421] [INSPIRE].
A. Giveon, D. Kutasov and N. Seiberg, Comments on string theory on AdS3, Adv. Theor. Math. Phys. 2 (1998) 733 [hep-th/9806194] [INSPIRE].
E. Del Giudice, P. Di Vecchia and S. Fubini, General properties of the dual resonance model, Annals Phys. 70 (1972) 378 [INSPIRE].
S. Gerigk, Superstring Theory on AdS3 × S3 and the PSL(2|2) WZW Model, DISS. ETH No. 20713 (2012).
D. Lüst and S. Theisen, Lectures on string theory, vol. 346 (1989), https://doi.org/10.1007/BFb0113507 [INSPIRE].
M.R. Gaberdiel and K. Naderi, The physical states of the Hybrid Formalism, JHEP 10 (2021) 168 [arXiv:2106.06476] [INSPIRE].
P. Goddard, W. Nahm, D.I. Olive and A. Schwimmer, Vertex Operators for Nonsimply Laced Algebras, Commun. Math. Phys. 107 (1986) 179 [INSPIRE].
B.A. Burrington, A.W. Peet and I.G. Zadeh, Bosonization, cocycles, and the D1-D5 CFT on the covering surface, Phys. Rev. D 93 (2016) 026004 [arXiv:1509.00022] [INSPIRE].
A. Dei and L. Eberhardt, Correlators of the symmetric product orbifold, JHEP 01 (2020) 108 [arXiv:1911.08485] [INSPIRE].
R. Dijkgraaf, G.W. Moore, E.P. Verlinde and H.L. Verlinde, Elliptic genera of symmetric products and second quantized strings, Commun. Math. Phys. 185 (1997) 197 [hep-th/9608096] [INSPIRE].
L.J. Dixon, D. Friedan, E.J. Martinec and S.H. Shenker, The Conformal Field Theory of Orbifolds, Nucl. Phys. B 282 (1987) 13 [INSPIRE].
P. Di Francesco, P. Mathieu and D. Senechal, Conformal Field Theory, Graduate Texts in Contemporary Physics, Springer-Verlag (1997).
H. Bertle, A. Dei and M.R. Gaberdiel, Stress-energy tensor correlators from the world-sheet, JHEP 03 (2021) 036 [arXiv:2012.08486] [INSPIRE].
M.R. Gaberdiel and B. Nairz, BPS correlators for AdS3/CFT2, JHEP 09 (2022) 244 [arXiv:2207.03956] [INSPIRE].
A. Dei, L. Eberhardt and M.R. Gaberdiel, Three-point functions in AdS3/CFT2 holography, JHEP 12 (2019) 012 [arXiv:1907.13144] [INSPIRE].
N. Berkovits and C. Vafa, On the Uniqueness of string theory, Mod. Phys. Lett. A 9 (1994) 653 [hep-th/9310170] [INSPIRE].
J. Bienkowska, The Generalized no ghost theorem for N = 2 SUSY critical strings, Phys. Lett. B 281 (1992) 59 [hep-th/9111047] [INSPIRE].
P. Goddard and C.B. Thorn, Compatibility of the Dual Pomeron with Unitarity and the Absence of Ghosts in the Dual Resonance Model, Phys. Lett. B 40 (1972) 235 [INSPIRE].
S. Hwang, No ghost theorem for SU(1, 1) string theories, Nucl. Phys. B 354 (1991) 100 [INSPIRE].
S. Hwang, Cosets as gauge slices in SU(1, 1) strings, Phys. Lett. B 276 (1992) 451 [hep-th/9110039] [INSPIRE].
J.M. Evans, M.R. Gaberdiel and M.J. Perry, The no ghost theorem for AdS3 and the stringy exclusion principle, Nucl. Phys. B 535 (1998) 152 [hep-th/9806024] [INSPIRE].
M.R. Gaberdiel and T. Hartman, Symmetries of Holographic Minimal Models, JHEP 05 (2011) 031 [arXiv:1101.2910] [INSPIRE].
M.R. Gaberdiel and R. Gopakumar, Minimal Model Holography, J. Phys. A 46 (2013) 214002 [arXiv:1207.6697] [INSPIRE].
M.R. Gaberdiel and R. Gopakumar, Stringy Symmetries and the Higher Spin Square, J. Phys. A 48 (2015) 185402 [arXiv:1501.07236] [INSPIRE].
M.A. Fiset, M.R. Gaberdiel, K. Naderi and V. Sriprachyakul, work in progress.
M.R. Gaberdiel, C. Peng and I.G. Zadeh, Higgsing the stringy higher spin symmetry, JHEP 10 (2015) 101 [arXiv:1506.02045] [INSPIRE].
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2208.01617
Rights and permissions
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.
About this article
Cite this article
Naderi, K. DDF operators in the hybrid formalism. J. High Energ. Phys. 2022, 43 (2022). https://doi.org/10.1007/JHEP12(2022)043
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP12(2022)043