The large \(N\) limit of OPEs in symmetric orbifold CFTs with \(\mathcal{N} = (4, 4)\) supersymmetry. (English) Zbl 1421.81112
Summary: We explore the OPE of certain twist operators in symmetric product \((S_N)\) orbifold CFTs, extending our previous work [B. A. Burrington et al., J. High Energy Phys. 2018, No. 8, Paper No. 202, 31 p. (2018; Zbl 1396.81167)] to the case of \(\mathcal{N} = (4, 4)\) supersymmetry. We consider a class of twist operators related to the chiral primaries by spectral flow parallel to the twist. We conjecture that at large \(N\), the OPE of two such operators contains only fields in this class, along with excitations by fractional modes of the superconformal currents. We provide evidence for this by studying the coincidence limits of two 4-point functions to several non-trivial orders. We show how the fractional excitations of the twist operators in our restricted class fully reproduce the crossing channels appearing in the coincidence limits of the 4-point functions.
MSC:
| 81T40 | Two-dimensional field theories, conformal field theories, etc. in quantum mechanics |
| 81T60 | Supersymmetric field theories in quantum mechanics |
| 83C60 | Spinor and twistor methods in general relativity and gravitational theory; Newman-Penrose formalism |
Citations:
Zbl 1396.81167References:
| [1] | Burrington, BA; Jardine, IT; Peet, AW, The OPE of bare twist operators in bosonic S_Norbifold CFTs at large N, JHEP, 08, 202 (2018) · Zbl 1396.81167 · doi:10.1007/JHEP08(2018)202 |
| [2] | Maldacena, JM, The large N limit of superconformal field theories and supergravity, Int. J. Theor. Phys., 38, 1113 (1999) · Zbl 0969.81047 · doi:10.1023/A:1026654312961 |
| [3] | Witten, E., Anti-de Sitter space and holography, Adv. Theor. Math. Phys., 2, 253 (1998) · Zbl 0914.53048 · doi:10.4310/ATMP.1998.v2.n2.a2 |
| [4] | Heemskerk, I.; Penedones, J.; Polchinski, J.; Sully, J., Holography from conformal field theory, JHEP, 10, 079 (2009) · doi:10.1088/1126-6708/2009/10/079 |
| [5] | Belin, A.; Keller, CA; Maloney, A., String universality for permutation orbifolds, Phys. Rev., D 91, 106005 (2015) |
| [6] | Haehl, FM; Rangamani, M., Permutation orbifolds and holography, JHEP, 03, 163 (2015) · Zbl 1388.83661 · doi:10.1007/JHEP03(2015)163 |
| [7] | Benjamin, N.; Cheng, MCN; Kachru, S.; Moore, GW; Paquette, NM, Elliptic genera and 3d gravity, Annales Henri Poincaré, 17, 2623 (2016) · Zbl 1351.83019 · doi:10.1007/s00023-016-0469-6 |
| [8] | A. Belin, C.A. Keller and A. Maloney, Permutation orbifolds in the large N limit, Annales Henri Poincaré (2016) 1 [arXiv:1509.01256] [INSPIRE]. · Zbl 1357.81150 |
| [9] | Benjamin, N.; Kachru, S.; Keller, CA; Paquette, NM, Emergent space-time and the supersymmetric index, JHEP, 05, 158 (2016) · Zbl 1388.81771 · doi:10.1007/JHEP05(2016)158 |
| [10] | A. Belin, J. de Boer, J. Kruthoff, B. Michel, E. Shaghoulian and M. Shyani, Universality of sparse d > 2 conformal field theory at large N, JHEP03 (2017) 067 [arXiv:1610.06186] [INSPIRE]. · Zbl 1377.81154 |
| [11] | Belin, A., Permutation orbifolds and chaos, JHEP, 11, 131 (2017) · Zbl 1383.81181 · doi:10.1007/JHEP11(2017)131 |
| [12] | Lunin, O.; Mathur, SD, Correlation functions for M^N/S_Norbifolds, Commun. Math. Phys., 219, 399 (2001) · Zbl 0980.81045 · doi:10.1007/s002200100431 |
| [13] | Lunin, O.; Mathur, SD, Three point functions for M_N/S^Norbifolds with N = 4 supersymmetry, Commun. Math. Phys., 227, 385 (2002) · Zbl 1004.81029 · doi:10.1007/s002200200638 |
| [14] | Burrington, BA; Peet, AW; Zadeh, IG, Twist-nontwist correlators in M^N/S_Norbifold CFTs, Phys. Rev., D 87, 106008 (2013) |
| [15] | S.G. Avery, Using the D1-D5 CFT to understand black holes, Ph.D. thesis, Ohio State U., Columbus, OH, U.S.A. (2010) [arXiv:1012.0072] [INSPIRE]. |
| [16] | Keller, CA, Phase transitions in symmetric orbifold CFTs and universality, JHEP, 03, 114 (2011) · Zbl 1301.81223 · doi:10.1007/JHEP03(2011)114 |
| [17] | Strominger, A.; Vafa, C., Microscopic origin of the Bekenstein-Hawking entropy, Phys. Lett., B 379, 99 (1996) · Zbl 1376.83026 · doi:10.1016/0370-2693(96)00345-0 |
| [18] | N. Seiberg and E. Witten, The D1/D5 system and singular CFT, JHEP04 (1999) 017 [hep-th/9903224] [INSPIRE]. · Zbl 0953.81076 |
| [19] | David, JR; Mandal, G.; Wadia, SR, D1/D5 moduli in SCFT and gauge theory and Hawking radiation, Nucl. Phys., B 564, 103 (2000) · Zbl 1028.81523 · doi:10.1016/S0550-3213(99)00620-3 |
| [20] | Giveon, A.; Kutasov, D.; Seiberg, N., Comments on string theory on AdS_3, Adv. Theor. Math. Phys., 2, 733 (1998) · Zbl 1041.81575 · doi:10.4310/ATMP.1998.v2.n4.a3 |
| [21] | Vafa, C., Instantons on D-branes, Nucl. Phys., B 463, 435 (1996) · Zbl 1004.81537 · doi:10.1016/0550-3213(96)00075-2 |
| [22] | Dijkgraaf, R.; Moore, GW; Verlinde, EP; Verlinde, HL, Elliptic genera of symmetric products and second quantized strings, Commun. Math. Phys., 185, 197 (1997) · Zbl 0872.32006 · doi:10.1007/s002200050087 |
| [23] | Larsen, F.; Martinec, EJ, U(1) charges and moduli in the D1-D5 system, JHEP, 06, 019 (1999) · Zbl 0961.81073 · doi:10.1088/1126-6708/1999/06/019 |
| [24] | Boer, J., Six-dimensional supergravity on S^3× AdS_3and 2D conformal field theory, Nucl. Phys., B 548, 139 (1999) · Zbl 0944.83032 · doi:10.1016/S0550-3213(99)00160-1 |
| [25] | Dijkgraaf, R., Instanton strings and hyper-Kähler geometry, Nucl. Phys., B 543, 545 (1999) · Zbl 1097.58503 · doi:10.1016/S0550-3213(98)00869-4 |
| [26] | Maldacena, JM; Ooguri, H., Strings in AdS_3and SL(2, R) WZW model 1: the spectrum, J. Math. Phys., 42, 2929 (2001) · Zbl 1036.81033 · doi:10.1063/1.1377273 |
| [27] | Maldacena, JM; Ooguri, H.; Son, J., Strings in AdS_3and the SL(2, R) WZW model 2: Euclidean black hole, J. Math. Phys., 42, 2961 (2001) · Zbl 1036.81034 · doi:10.1063/1.1377039 |
| [28] | Maldacena, JM; Ooguri, H., Strings in AdS_3and the SL(2, R) WZW model 3: correlation functions, Phys. Rev., D 65, 106006 (2002) |
| [29] | Eberhardt, L.; Gaberdiel, MR, Strings on AdS_3 × S^3 × S^3 × S^1, JHEP, 06, 035 (2019) · Zbl 1416.83117 · doi:10.1007/JHEP06(2019)035 |
| [30] | Hampton, S.; Mathur, SD; Zadeh, IG, Lifting of D1-D5-P states, JHEP, 01, 075 (2019) · Zbl 1409.81122 · doi:10.1007/JHEP01(2019)075 |
| [31] | Gaberdiel, MR; Peng, C.; Zadeh, IG, Higgsing the stringy higher spin symmetry, JHEP, 10, 101 (2015) · Zbl 1388.81814 · doi:10.1007/JHEP10(2015)101 |
| [32] | Burrington, BA; Mathur, SD; Peet, AW; Zadeh, IG, Analyzing the squeezed state generated by a twist deformation, Phys. Rev., D 91, 124072 (2015) |
| [33] | Carson, Z.; Hampton, S.; Mathur, SD; Turton, D., Effect of the deformation operator in the D1-D5 CFT, JHEP, 01, 071 (2015) · doi:10.1007/JHEP01(2015)071 |
| [34] | Carson, Z.; Hampton, S.; Mathur, SD; Turton, D., Effect of the twist operator in the D1-D5 CFT, JHEP, 08, 064 (2014) · doi:10.1007/JHEP08(2014)064 |
| [35] | Carson, Z.; Mathur, SD; Turton, D., Bogoliubov coefficients for the twist operator in the D1-D5 CFT, Nucl. Phys., B 889, 443 (2014) · Zbl 1326.81173 · doi:10.1016/j.nuclphysb.2014.10.018 |
| [36] | Burrington, BA; Peet, AW; Zadeh, IG, Operator mixing for string states in the D1-D5 CFT near the orbifold point, Phys. Rev., D 87, 106001 (2013) |
| [37] | S.G. Avery and B.D. Chowdhury, Intertwining relations for the deformed D1-D5 CFT, JHEP05 (2011) 025 [arXiv:1007.2202] [INSPIRE]. · Zbl 1296.81079 |
| [38] | S.G. Avery, B.D. Chowdhury and S.D. Mathur, Deforming the D1-D5 CFT away from the orbifold point, JHEP06 (2010) 031 [arXiv:1002.3132] [INSPIRE]. · Zbl 1290.81097 |
| [39] | S.G. Avery, B.D. Chowdhury and S.D. Mathur, Excitations in the deformed D1-D5 CFT, JHEP06 (2010) 032 [arXiv:1003.2746] [INSPIRE]. · Zbl 1290.81096 |
| [40] | Avery, SG; Chowdhury, BD, Emission from the D1-D5 CFT: higher twists, JHEP, 01, 087 (2010) · Zbl 1269.81098 · doi:10.1007/JHEP01(2010)087 |
| [41] | Avery, SG; Chowdhury, BD; Mathur, SD, Emission from the D1-D5 CFT, JHEP, 10, 065 (2009) · doi:10.1088/1126-6708/2009/10/065 |
| [42] | A. Pakman, L. Rastelli and S.S. Razamat, A spin chain for the symmetric product CFT_2, JHEP05 (2010) 099 [arXiv:0912.0959] [INSPIRE]. · Zbl 1287.81074 |
| [43] | Pakman, A.; Rastelli, L.; Razamat, SS, Diagrams for symmetric product orbifolds, JHEP, 10, 034 (2009) · doi:10.1088/1126-6708/2009/10/034 |
| [44] | Pakman, A.; Rastelli, L.; Razamat, SS, Extremal correlators and Hurwitz numbers in symmetric product orbifolds, Phys. Rev., D 80, 086009 (2009) |
| [45] | Gava, E.; Narain, KS, Proving the PP wave/CFT_2duality, JHEP, 12, 023 (2002) · doi:10.1088/1126-6708/2002/12/023 |
| [46] | Gomis, J.; Motl, L.; Strominger, A., PP wave/CFT_2duality, JHEP, 11, 016 (2002) · doi:10.1088/1126-6708/2002/11/016 |
| [47] | Burrington, BA; Jardine, IT; Peet, AW, Operator mixing in deformed D1-D5 CFT and the OPE on the cover, JHEP, 06, 149 (2017) · Zbl 1380.83277 · doi:10.1007/JHEP06(2017)149 |
| [48] | David, JR; Mandal, G.; Wadia, SR, Microscopic formulation of black holes in string theory, Phys. Rept., 369, 549 (2002) · Zbl 0998.83032 · doi:10.1016/S0370-1573(02)00271-5 |
| [49] | Schwimmer, A.; Seiberg, N., Comments on the N = 2, N = 3, N = 4 superconformal algebras in two-dimensions, Phys. Lett., B 184, 191 (1987) · doi:10.1016/0370-2693(87)90566-1 |
| [50] | Yu, M., The unitary representations of the N = 4 SU(2) extended superconformal algebras, Nucl. Phys., B 294, 890 (1987) · doi:10.1016/0550-3213(87)90613-4 |
| [51] | Roumpedakis, K., Comments on the S_Norbifold CFT in the large N -limit, JHEP, 07, 038 (2018) · Zbl 1395.81245 · doi:10.1007/JHEP07(2018)038 |
| [52] | E.J. Martinec and W. McElgin, String theory on AdS orbifolds, JHEP04 (2002) 029 [hep-th/0106171] [INSPIRE]. |
| [53] | Giusto, S.; Lunin, O.; Mathur, SD; Turton, D., D1-D5-P microstates at the cap, JHEP, 02, 050 (2013) · doi:10.1007/JHEP02(2013)050 |
| [54] | Chakrabarty, B.; Turton, D.; Virmani, A., Holographic description of non-supersymmetric orbifolded D1-D5-P solutions, JHEP, 11, 063 (2015) · Zbl 1388.83405 · doi:10.1007/JHEP11(2015)063 |
| [55] | Bena, I.; Martinec, E.; Turton, D.; Warner, NP, Momentum fractionation on superstrata, JHEP, 05, 064 (2016) · Zbl 1388.83741 · doi:10.1007/JHEP05(2016)064 |
| [56] | Lerche, W.; Vafa, C.; Warner, NP, Chiral rings in N = 2 superconformal theories, Nucl. Phys., B 324, 427 (1989) · doi:10.1016/0550-3213(89)90474-4 |
| [57] | J. Polchinski, String theory. Volume 1: an introduction to the bosonic string, Cambridge University Press, Cambridge, U.K. (1998) [INSPIRE]. · Zbl 1006.81521 · doi:10.1017/CBO9780511816079 |
| [58] | Burrington, BA; Peet, AW; Zadeh, IG, Bosonization, cocycles and the D1-D5 CFT on the covering surface, Phys. Rev., D 93, 026004 (2016) |
| [59] | Eberhardt, L.; Zadeh, IG, N = (3, 3) holography on AdS_3 × (S^3 × S^3 × S^1)/Z_2, JHEP, 07, 143 (2018) · Zbl 1395.81214 · doi:10.1007/JHEP07(2018)143 |
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