Abstract
We consider D1-D5-P states in the untwisted sector of the D1-D5 orbifold CFT where one copy of the seed CFT has been excited by a pair of oscillators, each being either bosonic or fermionic. While such states are BPS at the orbifold point, they will in general ‘lift’ as the theory is deformed towards general values of the couplings. We compute the expectation value of this lift at second order in the deformation parameter for the above mentioned states. We write this lift in terms of a fixed number of nested contour integrals on a given integrand; this integrand depends on the mode numbers of the oscillators in the state. We evaluate these integrals to obtain the explicit value of the lift for various subfamilies of states. At large mode numbers one observes a smooth increase of the lift with the dimension of the state h; this increase appears to follow \( \textrm{a}\sim \sqrt{h} \) behavior similar to that found analytically in earlier computations for other classes of states.
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References
A. Strominger and C. Vafa, Microscopic origin of the Bekenstein-Hawking entropy, Phys. Lett. B 379 (1996) 99 [hep-th/9601029] [INSPIRE].
J.M. Maldacena, G.W. Moore and A. Strominger, Counting BPS black holes in toroidal Type II string theory, hep-th/9903163 [INSPIRE].
I. Bena, E.J. Martinec, S.D. Mathur and N.P. Warner, Snowmass White Paper: Micro- and Macro-Structure of Black Holes, arXiv:2203.04981 [INSPIRE].
I. Bena, E.J. Martinec, S.D. Mathur and N.P. Warner, Fuzzballs and Microstate Geometries: Black-Hole Structure in String Theory, arXiv:2204.13113 [INSPIRE].
O. Lunin and S.D. Mathur, AdS / CFT duality and the black hole information paradox, Nucl. Phys. B 623 (2002) 342 [hep-th/0109154] [INSPIRE].
S.D. Mathur, The fuzzball proposal for black holes: An elementary review, Fortsch. Phys. 53 (2005) 793 [hep-th/0502050] [INSPIRE].
I. Kanitscheider, K. Skenderis and M. Taylor, Fuzzballs with internal excitations, JHEP 06 (2007) 056 [arXiv:0704.0690] [INSPIRE].
I. Bena and N.P. Warner, Black holes, black rings and their microstates, Lect. Notes Phys. 755 (2008) 1 [hep-th/0701216] [INSPIRE].
B.D. Chowdhury and A. Virmani, Modave Lectures on Fuzzballs and Emission from the D1-D5 System, in the proceedings of the 5th Modave Summer School in Mathematical Physics, Modave, Belgium, August 17–21 (2009) [arXiv:1001.1444] [INSPIRE].
M. Shigemori, Superstrata, Gen. Rel. Grav. 52 (2020) 51 [arXiv:2002.01592] [INSPIRE].
C. Vafa, Instantons on D-branes, Nucl. Phys. B 463 (1996) 435 [hep-th/9512078] [INSPIRE].
R. Dijkgraaf, Instanton strings and hyperKahler geometry, Nucl. Phys. B 543 (1999) 545 [hep-th/9810210] [INSPIRE].
F. Larsen and E.J. Martinec, U(1) charges and moduli in the D1-D5 system, JHEP 06 (1999) 019 [hep-th/9905064] [INSPIRE].
N. Seiberg and E. Witten, The D1 / D5 system and singular CFT, JHEP 04 (1999) 017 [hep-th/9903224] [INSPIRE].
G.E. Arutyunov and S.A. Frolov, Four graviton scattering amplitude from SN R8 supersymmetric orbifold sigma model, Nucl. Phys. B 524 (1998) 159 [hep-th/9712061] [INSPIRE].
G.E. Arutyunov and S.A. Frolov, Virasoro amplitude from the SN R24 orbifold sigma model, Theor. Math. Phys. 114 (1998) 43 [hep-th/9708129] [INSPIRE].
A. Jevicki, M. Mihailescu and S. Ramgoolam, Gravity from CFT on SN (X): Symmetries and interactions, Nucl. Phys. B 577 (2000) 47 [hep-th/9907144] [INSPIRE].
J.R. David, G. Mandal and S.R. Wadia, Microscopic formulation of black holes in string theory, Phys. Rept. 369 (2002) 549 [hep-th/0203048] [INSPIRE].
J.M. Maldacena, The large N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys. 2 (1998) 231 [hep-th/9711200] [INSPIRE].
E. Gava and K.S. Narain, Proving the PP wave / CFT2 duality, JHEP 12 (2002) 023 [hep-th/0208081] [INSPIRE].
C.-M. Chang and Y.-H. Lin, Words to describe a black hole, JHEP 02 (2023) 109 [arXiv:2209.06728] [INSPIRE].
A.A. Lima, G.M. Sotkov and M. Stanishkov, Microstate Renormalization in Deformed D1-D5 SCFT, Phys. Lett. B 808 (2020) 135630 [arXiv:2005.06702] [INSPIRE].
A.A. Lima, G.M. Sotkov and M. Stanishkov, Renormalization of twisted Ramond fields in D1-D5 SCFT2, JHEP 03 (2021) 202 [arXiv:2010.00172] [INSPIRE].
A.A. Lima, G.M. Sotkov and M. Stanishkov, Correlation functions of composite Ramond fields in deformed D1-D5 orbifold SCFT2, Phys. Rev. D 102 (2020) 106004 [arXiv:2006.16303] [INSPIRE].
A.A. Lima, G.M. Sotkov and M. Stanishkov, Dynamics of R-neutral Ramond fields in the D1-D5 SCFT, JHEP 07 (2021) 211 [arXiv:2012.08021] [INSPIRE].
A.A. Lima, G.M. Sotkov and M. Stanishkov, On the dynamics of protected ramond ground states in the D1-D5 CFT, JHEP 07 (2021) 120 [arXiv:2103.04459] [INSPIRE].
A.A. Lima, G.M. Sotkov and M. Stanishkov, Ramond States of the D1-D5 CFT Away from the Free Orbifold Point, Springer Proc. Math. Stat. 396 (2022) 185 [arXiv:2112.10832] [INSPIRE].
A. Alves Lima, G.M. Sotkov and M. Stanishkov, Four-point functions with multi-cycle fields in symmetric orbifolds and the D1-D5 CFT, JHEP 05 (2022) 106 [arXiv:2202.12424] [INSPIRE].
N. Benjamin, S. Bintanja, A. Castro and J. Hollander, The stranger things of symmetric product orbifold CFTs, JHEP 11 (2022) 054 [arXiv:2208.11141] [INSPIRE].
B. Guo and S.D. Mathur, Dynamical evolution in the D1D5 CFT, JHEP 12 (2022) 107 [arXiv:2208.05992] [INSPIRE].
B. Guo and S.D. Hampton, Bootstrapping the effect of the twist operator in symmetric orbifold CFTs, JHEP 02 (2023) 184 [arXiv:2206.01623] [INSPIRE].
B. Guo and S.D. Hampton, Bootstrapping multi-wound twist effects in symmetric orbifold CFTs, arXiv:2307.14255 [INSPIRE].
B. Guo, M.R.R. Hughes, S.D. Mathur and M. Mehta, Universal lifting in the D1-D5 CFT, JHEP 10 (2022) 148 [arXiv:2208.07409] [INSPIRE].
B. Guo and S.D. Mathur, Lifting of level-1 states in the D1D5 CFT, JHEP 03 (2020) 028 [arXiv:1912.05567] [INSPIRE].
B. Guo and S.D. Mathur, Lifting at higher levels in the D1D5 CFT, JHEP 11 (2020) 145 [arXiv:2008.01274] [INSPIRE].
S. Hampton, S.D. Mathur and I.G. Zadeh, Lifting of D1-D5-P states, JHEP 01 (2019) 075 [arXiv:1804.10097] [INSPIRE].
M.R. Gaberdiel, C. Peng and I.G. Zadeh, Higgsing the stringy higher spin symmetry, JHEP 10 (2015) 101 [arXiv:1506.02045] [INSPIRE].
N. Benjamin, C.A. Keller and I.G. Zadeh, Lifting 1/4-BPS states in AdS3 × S3 × T4, JHEP 10 (2021) 089 [arXiv:2107.00655] [INSPIRE].
G. Giribet et al., Superstrings on AdS3 at k = 1, JHEP 08 (2018) 204 [arXiv:1803.04420] [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].
L. Eberhardt, AdS3/CFT2 at higher genus, JHEP 05 (2020) 150 [arXiv:2002.11729] [INSPIRE].
L. Eberhardt, A perturbative CFT dual for pure NS-NS AdS3 strings, J. Phys. A 55 (2022) 064001 [arXiv:2110.07535] [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. Dei, L. Eberhardt and M.R. Gaberdiel, Three-point functions in AdS3/CFT2 holography, JHEP 12 (2019) 012 [arXiv:1907.13144] [INSPIRE].
A. Brollo, D. le Plat, A. Sfondrini and R. Suzuki, Tensionless Limit of Pure-Ramond-Ramond Strings and AdS3/CFT2, Phys. Rev. Lett. 131 (2023) 161604 [arXiv:2303.02120] [INSPIRE].
A. Brollo, D. le Plat, A. Sfondrini and R. Suzuki, More on the tensionless limit of pure-Ramond-Ramond AdS3/CFT2, JHEP 12 (2023) 160 [arXiv:2308.11576] [INSPIRE].
A. Schwimmer and N. Seiberg, Comments on the N = 2, N = 3, N = 4 Superconformal Algebras in Two-Dimensions, Phys. Lett. B 184 (1987) 191 [INSPIRE].
A. Sevrin, W. Troost and A. Van Proeyen, Superconformal Algebras in Two-Dimensions with N = 4, Phys. Lett. B 208 (1988) 447 [INSPIRE].
M.R. Gaberdiel and R. Gopakumar, Stringy Symmetries and the Higher Spin Square, J. Phys. A 48 (2015) 185402 [arXiv:1501.07236] [INSPIRE].
B. Guo and S. Hampton, Partial Spectral Flow in the D1D5 CFT, arXiv:2112.10573 [INSPIRE].
O. Lunin and S.D. Mathur, Metric of the multiply wound rotating string, Nucl. Phys. B 610 (2001) 49 [hep-th/0105136] [INSPIRE].
O. Lunin and S.D. Mathur, Correlation functions for MN / SN orbifolds, Commun. Math. Phys. 219 (2001) 399 [hep-th/0006196] [INSPIRE].
Acknowledgments
We would like to thank Bin Guo for discussions. This work is supported in part by DOE grant DE-SC0011726.
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Hughes, M.R.R., Mathur, S.D. & Mehta, M. Lifting of two-mode states in the D1-D5 CFT. J. High Energ. Phys. 2024, 183 (2024). https://doi.org/10.1007/JHEP01(2024)183
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DOI: https://doi.org/10.1007/JHEP01(2024)183