Abstract
The tensionless limit of string theory has recently been formulated in terms of worldsheet Rindler physics. In this paper, by considering closed strings moving in background Rindler spacetimes, we provide a concrete exemplification of this phenomenon. We first show that strings probing the near-horizon region of a generic non-extremal blackhole become tensionless thereby linking a spacetime Carroll limit to a worldsheet Carroll limit. Then, considering strings in d-dimensional Rindler spacetime we find a Rindler structure induced on the worldsheet. Novelties, including folds, appear on the closed string worldsheet pertaining to the formation of the worldsheet horizon. The closed string becomes segmented at these folding points and different segments go into the formation of closed strings in the different Rindler wedges. The Bondi-Metzner-Sachs (BMS) or the Conformal Carroll algebra emerges from the closed string Virasoro algebra as the horizon is hit. Quantum states on these accelerated worldsheets are discussed and we show the formation of boundary states from gluing conditions of the different segments of the accelerated closed string.
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References
Event Horizon Telescope collaboration, First M87 Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole, Astrophys. J. Lett. 875 (2019) L1 [arXiv:1906.11238] [INSPIRE].
LIGO Scientific and Virgo collaborations, Properties of the Binary Black Hole Merger GW150914, Phys. Rev. Lett. 116 (2016) 241102 [arXiv:1602.03840] [INSPIRE].
A. Bagchi, A. Banerjee and S. Chakrabortty, Rindler Physics on the String Worldsheet, Phys. Rev. Lett. 126 (2021) 031601 [arXiv:2009.01408] [INSPIRE].
A. Bagchi, Correspondence between Asymptotically Flat Spacetimes and Nonrelativistic Conformal Field Theories, Phys. Rev. Lett. 105 (2010) 171601 [arXiv:1006.3354] [INSPIRE].
A. Bagchi and R. Fareghbal, BMS/GCA Redux: Towards Flatspace Holography from Non-Relativistic Symmetries, JHEP 10 (2012) 092 [arXiv:1203.5795] [INSPIRE].
G. Barnich, A. Gomberoff and H. A. Gonzalez, The Flat limit of three dimensional asymptotically anti-de Sitter spacetimes, Phys. Rev. D 86 (2012) 024020 [arXiv:1204.3288] [INSPIRE].
A. Bagchi, S. Detournay and D. Grumiller, Flat-Space Chiral Gravity, Phys. Rev. Lett. 109 (2012) 151301 [arXiv:1208.1658] [INSPIRE].
A. Bagchi, S. Detournay, R. Fareghbal and J. Simón, Holography of 3D Flat Cosmological Horizons, Phys. Rev. Lett. 110 (2013) 141302 [arXiv:1208.4372] [INSPIRE].
G. Barnich, Entropy of three-dimensional asymptotically flat cosmological solutions, JHEP 10 (2012) 095 [arXiv:1208.4371] [INSPIRE].
G. Barnich, A. Gomberoff and H. A. González, Three-dimensional Bondi-Metzner-Sachs invariant two-dimensional field theories as the flat limit of Liouville theory, Phys. Rev. D 87 (2013) 124032 [arXiv:1210.0731] [INSPIRE].
A. Bagchi, S. Detournay, D. Grumiller and J. Simon, Cosmic Evolution from Phase Transition of Three-Dimensional Flat Space, Phys. Rev. Lett. 111 (2013) 181301 [arXiv:1305.2919] [INSPIRE].
A. Bagchi, R. Basu, D. Grumiller and M. Riegler, Entanglement entropy in Galilean conformal field theories and flat holography, Phys. Rev. Lett. 114 (2015) 111602 [arXiv:1410.4089] [INSPIRE].
J. Hartong, Gauging the Carroll Algebra and Ultra-Relativistic Gravity, JHEP 08 (2015) 069 [arXiv:1505.05011] [INSPIRE].
J. Hartong, Holographic Reconstruction of 3D Flat Space-Time, JHEP 10 (2016) 104 [arXiv:1511.01387] [INSPIRE].
A. Bagchi, R. Basu, A. Kakkar and A. Mehra, Flat Holography: Aspects of the dual field theory, JHEP 12 (2016) 147 [arXiv:1609.06203] [INSPIRE].
C. Duval, G. W. Gibbons and P. A. Horvathy, Conformal Carroll groups, J. Phys. A 47 (2014) 335204 [arXiv:1403.4213] [INSPIRE].
C. Duval, G. W. Gibbons and P. A. Horvathy, Conformal Carroll groups and BMS symmetry, Class. Quant. Grav. 31 (2014) 092001 [arXiv:1402.5894] [INSPIRE].
H. Bondi, M. G. J. van der Burg and A. W. K. Metzner, Gravitational waves in general relativity. 7. Waves from axisymmetric isolated systems, Proc. Roy. Soc. Lond. A 269 (1962) 21 [INSPIRE].
R. Sachs, Asymptotic symmetries in gravitational theory, Phys. Rev. 128 (1962) 2851 [INSPIRE].
J. de Boer, J. Hartong, N. A. Obers, W. Sybesma and S. Vandoren, Carroll symmetry, dark energy and inflation, arXiv:2110.02319 [INSPIRE].
L. Donnay and C. Marteau, Carrollian Physics at the Black Hole Horizon, Class. Quant. Grav. 36 (2019) 165002 [arXiv:1903.09654] [INSPIRE].
S. Carlip, Black Hole Entropy from Bondi-Metzner-Sachs Symmetry at the Horizon, Phys. Rev. Lett. 120 (2018) 101301 [arXiv:1702.04439] [INSPIRE].
S. Carlip, Near-horizon Bondi-Metzner-Sachs symmetry, dimensional reduction, and black hole entropy, Phys. Rev. D 101 (2020) 046002 [arXiv:1910.01762] [INSPIRE].
A. Bagchi, Tensionless Strings and Galilean Conformal Algebra, JHEP 05 (2013) 141 [arXiv:1303.0291] [INSPIRE].
B. Cardona, J. Gomis and J. M. Pons, Dynamics of Carroll Strings, JHEP 07 (2016) 050 [arXiv:1605.05483] [INSPIRE].
R. Andringa, E. Bergshoeff, J. Gomis and M. de Roo, ‘Stringy’ Newton-Cartan Gravity, Class. Quant. Grav. 29 (2012) 235020 [arXiv:1206.5176] [INSPIRE].
H. J. de Vega and N. G. Sanchez, String Quantization in Accelerated Frames and Black Holes, Nucl. Phys. B 299 (1988) 818 [INSPIRE].
N. G. Sanchez, Reparametrization Invariance, Analytic Mappings and the Hawking-unruh Effect in String Theory, Phys. Lett. B 195 (1987) 160 [INSPIRE].
D. A. Lowe and A. Strominger, Strings near a Rindler or black hole horizon, Phys. Rev. D 51 (1995) 1793 [hep-th/9410215] [INSPIRE].
A. Bagchi, A. Banerjee and P. Parekh, Tensionless Path from Closed to Open Strings, Phys. Rev. Lett. 123 (2019) 111601 [arXiv:1905.11732] [INSPIRE].
A. Bagchi, S. Chakrabortty and P. Parekh, Tensionless Strings from Worldsheet Symmetries, JHEP 01 (2016) 158 [arXiv:1507.04361] [INSPIRE].
A. Schild, Classical Null Strings, Phys. Rev. D 16 (1977) 1722 [INSPIRE].
D. J. Gross and P. F. Mende, String Theory Beyond the Planck Scale, Nucl. Phys. B 303 (1988) 407 [INSPIRE].
D. J. Gross and P. F. Mende, The High-Energy Behavior of String Scattering Amplitudes, Phys. Lett. B 197 (1987) 129 [INSPIRE].
D. J. Gross, High-Energy Symmetries of String Theory, Phys. Rev. Lett. 60 (1988) 1229 [INSPIRE].
R. D. Pisarski and O. Alvarez, Strings at Finite Temperature and Deconfinement, Phys. Rev. D 26 (1982) 3735 [INSPIRE].
J. Isberg, U. Lindström, B. Sundborg and G. Theodoridis, Classical and quantized tensionless strings, Nucl. Phys. B 411 (1994) 122 [hep-th/9307108] [INSPIRE].
R. K. Sachs, Gravitational waves in general relativity. 8. Waves in asymptotically flat space-times, Proc. Roy. Soc. Lond. A 270 (1962) 103 [INSPIRE].
A. Bagchi, S. Chakrabortty and P. Parekh, Tensionless Superstrings: View from the Worldsheet, JHEP 10 (2016) 113 [arXiv:1606.09628] [INSPIRE].
A. Bagchi, A. Banerjee, S. Chakrabortty and P. Parekh, Inhomogeneous Tensionless Superstrings, JHEP 02 (2018) 065 [arXiv:1710.03482] [INSPIRE].
A. Bagchi, A. Banerjee, S. Chakrabortty, S. Dutta and P. Parekh, A tale of three — tensionless strings and vacuum structure, JHEP 04 (2020) 061 [arXiv:2001.00354] [INSPIRE].
A. Bagchi, M. Mandlik and P. Sharma, Tensionless tales: vacua and critical dimensions, JHEP 08 (2021) 054 [arXiv:2105.09682] [INSPIRE].
A. Karlhede and U. Lindström, The Classical Bosonic String in the Zero Tension Limit, Class. Quant. Grav. 3 (1986) L73 [INSPIRE].
F. Lizzi, B. Rai, G. Sparano and A. Srivastava, Quantization of the Null String and Absence of Critical Dimensions, Phys. Lett. B 182 (1986) 326 [INSPIRE].
J. Gamboa, C. Ramirez and M. Ruiz-Altaba, Quantum null (super)strings, Phys. Lett. B 225 (1989) 335 [INSPIRE].
H. Gustafsson, U. Lindström, P. Saltsidis, B. Sundborg and R. van Unge, Hamiltonian BRST quantization of the conformal string, Nucl. Phys. B 440 (1995) 495 [hep-th/9410143] [INSPIRE].
U. Lindström and M. Zabzine, Tensionless strings, WZW models at critical level and massless higher spin fields, Phys. Lett. B 584 (2004) 178 [hep-th/0305098] [INSPIRE].
C. Duval, G. W. Gibbons, P. A. Horvathy and P. M. Zhang, Carroll versus Newton and Galilei: two dual non-Einsteinian concepts of time, Class. Quant. Grav. 31 (2014) 085016 [arXiv:1402.0657] [INSPIRE].
P. Olesen, Strings, Tachyons and Deconfinement, Phys. Lett. B 160 (1985) 408 [INSPIRE].
J. J. Atick and E. Witten, The Hagedorn Transition and the Number of Degrees of Freedom of String Theory, Nucl. Phys. B 310 (1988) 291 [INSPIRE].
E. Casali and P. Tourkine, On the null origin of the ambitwistor string, JHEP 11 (2016) 036 [arXiv:1606.05636] [INSPIRE].
M. B. Green, J. H. Schwarz and E. Witten, Superstring theory. Vol. 1: Introduction, Cambridge Monographs on Mathematical Physics, Cambridge University Press, Cambridge, U.K. (1988) [INSPIRE].
S. S. Gubser, I. R. Klebanov and A. M. Polyakov, Gauge theory correlators from noncritical string theory, Phys. Lett. B 428 (1998) 105 [hep-th/9802109] [INSPIRE].
A. Bagchi and R. Gopakumar, Galilean Conformal Algebras and AdS/CFT, JHEP 07 (2009) 037 [arXiv:0902.1385] [INSPIRE].
N. D. Birrell and P. C. W. Davies, Quantum Fields in Curved Space, Cambridge Monographs on Mathematical Physics, Cambridge University Press, Cambridge, U.K. (1984) [DOI] [INSPIRE].
W. G. Unruh, Notes on black hole evaporation, Phys. Rev. D 14 (1976) 870 [INSPIRE].
L. Susskind, L. Thorlacius and J. Uglum, The Stretched horizon and black hole complementarity, Phys. Rev. D 48 (1993) 3743 [hep-th/9306069] [INSPIRE].
L. Susskind and J. Uglum, Black hole entropy in canonical quantum gravity and superstring theory, Phys. Rev. D 50 (1994) 2700 [hep-th/9401070] [INSPIRE].
L. Susskind and J. Uglum, Black holes, interactions, and strings, in Particles, Strings, and Cosmology (PASCOS 94), pp. 0254–270 (1994) [hep-th/9410074] [INSPIRE].
A. Giveon and N. Itzhaki, Stringy Information and Black Holes, JHEP 06 (2020) 117 [arXiv:1912.06538] [INSPIRE].
D. L. Jafferis and E. Schneider, Stringy ER = EPR, arXiv:2104.07233 [INSPIRE].
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Bagchi, A., Banerjee, A., Chakrabortty, S. et al. A Rindler road to Carrollian worldsheets. J. High Energ. Phys. 2022, 82 (2022). https://doi.org/10.1007/JHEP04(2022)082
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DOI: https://doi.org/10.1007/JHEP04(2022)082