Abstract
Two types of Carrollian field theories are shown to emerge from finite current-current deformations of toroidal CFT2’s when the deformation coupling is precisely fixed, up to a sign. In both cases the energy and momentum densities fulfill the BMS3 algebra. Applying these results to the bosonic string, one finds that the electric-like deformation (positive coupling) reduces to the standard tensionless string. The magnetic-like deformation (negative coupling) yields to a new theory, still being relativistic, devoid of tension and endowed with an “inner Carrollian structure”. Classical solutions describe a sort of “self-interacting null particle” moving along generic null curves of the original background metric, not necessarily geodesics. This magnetic-like theory is also shown to be recovered from inequivalent limits in the tension of the bosonic string. Electric- and magnetic-like deformations of toroidal CFT2’s can be seen to correspond to limiting cases of continuous exactly marginal (trivial) deformations spanned by an SO(1,1) automorphism of the current algebra. Thus, the absolute value of the current-current deformation coupling is shown to be bounded. When the bound saturates, the deformation ceases to be exactly marginal, but still retains the full conformal symmetry in two alternative ultrarelativistic regimes.
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References
R. Dijkgraaf, E.P. Verlinde and H.L. Verlinde, C = 1 conformal field theories on Riemann surfaces, Commun. Math. Phys. 115 (1988) 649 [INSPIRE].
S. Chaudhuri and J.A. Schwartz, A criterion for integrably marginal operators, Phys. Lett. B 219 (1989) 291 [INSPIRE].
S.F. Hassan and A. Sen, Marginal deformations of WZNW and coset models from O(d, d) transformation, Nucl. Phys. B 405 (1993) 143 [hep-th/9210121] [INSPIRE].
E. Kiritsis, Exact duality symmetries in CFT and string theory, Nucl. Phys. B 405 (1993) 109 [hep-th/9302033] [INSPIRE].
M. Henningson and C.R. Nappi, Duality, marginal perturbations and gauging, Phys. Rev. D 48 (1993) 861 [hep-th/9301005] [INSPIRE].
S. Forste and D. Roggenkamp, Current current deformations of conformal field theories, and WZW models, JHEP 05 (2003) 071 [hep-th/0304234] [INSPIRE].
P. Rodríguez, D. Tempo and R. Troncoso, Mapping relativistic to ultra/non-relativistic conformal symmetries in 2D and finite \( \sqrt{T\overline{T}} \) deformations, JHEP 11 (2021) 133 [arXiv:2106.09750] [INSPIRE].
D. Tempo and R. Troncoso, Nonlinear automorphism of the conformal algebra in 2D and continuous \( \sqrt{T\overline{T}} \) deformations, JHEP 12 (2022) 129 [arXiv:2210.00059] [INSPIRE].
R. Conti, J. Romano and R. Tateo, Metric approach to a \( T\overline{T} \)-like deformation in arbitrary dimensions, JHEP 09 (2022) 085 [arXiv:2206.03415] [INSPIRE].
C. Ferko, A. Sfondrini, L. Smith and G. Tartaglino-Mazzucchelli, Root-\( T\overline{T} \) deformations in two-dimensional quantum field theories, Phys. Rev. Lett. 129 (2022) 201604 [arXiv:2206.10515] [INSPIRE].
H. Babaei-Aghbolagh, K. Babaei Velni, D. Mahdavian Yekta and H. Mohammadzadeh, Marginal \( T\overline{T} \)-like deformation and modified Maxwell theories in two dimensions, Phys. Rev. D 106 (2022) 086022 [arXiv:2206.12677] [INSPIRE].
J. Hou, \( T\overline{T} \) flow as characteristic flows, JHEP 03 (2023) 243 [arXiv:2208.05391] [INSPIRE].
C. Ferko et al., \( T\overline{T} \)-like flows and 3d nonlinear supersymmetry, arXiv:2302.10410 [INSPIRE].
S. Ebert, C. Ferko and Z. Sun, Root-\( T\overline{T} \) deformed boundary conditions in holography, Phys. Rev. D 107 (2023) 126022 [arXiv:2304.08723] [INSPIRE].
C. Ferko and A. Gupta, ModMax oscillators and root-\( T\overline{T} \)-like flows in supersymmetric quantum mechanics, Phys. Rev. D 108 (2023) 046013 [arXiv:2306.14575] [INSPIRE].
J.A. García and R.A. Sánchez-Isidro, \( \sqrt{T\overline{T}} \)-deformed oscillator inspired by ModMax, Eur. Phys. J. Plus 138 (2023) 114 [arXiv:2209.06296] [INSPIRE].
A.B. Zamolodchikov, Expectation value of composite field \( T\overline{T} \) in two-dimensional quantum field theory, hep-th/0401146 [INSPIRE].
F.A. Smirnov and A.B. Zamolodchikov, On space of integrable quantum field theories, Nucl. Phys. B 915 (2017) 363 [arXiv:1608.05499] [INSPIRE].
A. Cavaglià, S. Negro, I.M. Szécsényi and R. Tateo, \( T\overline{T} \)-deformed 2D quantum field theories, JHEP 10 (2016) 112 [arXiv:1608.05534] [INSPIRE].
L. McGough, M. Mezei and H. Verlinde, Moving the CFT into the bulk with \( T\overline{T} \), JHEP 04 (2018) 010 [arXiv:1611.03470] [INSPIRE].
O. Aharony et al., Modular invariance and uniqueness of \( T\overline{T} \) deformed CFT, JHEP 01 (2019) 086 [arXiv:1808.02492] [INSPIRE].
V. Gorbenko, E. Silverstein and G. Torroba, dS/dS and \( T\overline{T} \), JHEP 03 (2019) 085 [arXiv:1811.07965] [INSPIRE].
R. Conti, S. Negro and R. Tateo, Conserved currents and \( T\overline{T} \)s irrelevant deformations of 2D integrable field theories, JHEP 11 (2019) 120 [arXiv:1904.09141] [INSPIRE].
M. Guica and R. Monten, \( T\overline{T} \) and the mirage of a bulk cutoff, SciPost Phys. 10 (2021) 024 [arXiv:1906.11251] [INSPIRE].
G. Jorjadze and S. Theisen, Canonical maps and integrability in \( T\overline{T} \) deformed 2d CFTs, arXiv:2001.03563 [INSPIRE].
S. He, P. Mao and X.-C. Mao, \( T\overline{T} \) deformed soft theorem, Phys. Rev. D 107 (2023) L101901 [arXiv:2209.01953] [INSPIRE].
Y. Jiang, A pedagogical review on solvable irrelevant deformations of 2D quantum field theory, Commun. Theor. Phys. 73 (2021) 057201 [arXiv:1904.13376] [INSPIRE].
M. Henneaux and P. Salgado-Rebolledo, Carroll contractions of Lorentz-invariant theories, JHEP 11 (2021) 180 [arXiv:2109.06708] [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].
J. Gamboa, The tension as perturbative parameter in string theory, Class. Quant. Grav. 7 (1990) 1647 [INSPIRE].
U. Lindstrom, B. Sundborg and G. Theodoridis, The zero tension limit of the superstring, Phys. Lett. B 253 (1991) 319 [INSPIRE].
J. Isberg, U. Lindstrom and B. Sundborg, Space-time symmetries of quantized tensionless strings, Phys. Lett. B 293 (1992) 321 [hep-th/9207005] [INSPIRE].
J. Isberg, U. Lindstrom, B. Sundborg and G. Theodoridis, Classical and quantized tensionless strings, Nucl. Phys. B 411 (1994) 122 [hep-th/9307108] [INSPIRE].
A. Bagchi, Tensionless strings and Galilean conformal algebra, JHEP 05 (2013) 141 [arXiv:1303.0291] [INSPIRE].
A. Bagchi, S. Chakrabortty and P. Parekh, Tensionless strings from worldsheet symmetries, JHEP 01 (2016) 158 [arXiv:1507.04361] [INSPIRE].
A. Bagchi, S. Chakrabortty and P. Parekh, Tensionless superstrings: view from the worldsheet, JHEP 10 (2016) 113 [arXiv:1606.09628] [INSPIRE].
A. Bagchi et al., A tale of three — tensionless strings and vacuum structure, JHEP 04 (2020) 061 [arXiv:2001.00354] [INSPIRE].
P.-X. Hao, W. Song, X. Xie and Y. Zhong, BMS-invariant free scalar model, Phys. Rev. D 105 (2022) 125005 [arXiv:2111.04701] [INSPIRE].
A. Saha, Intrinsic approach to 1 + 1D Carrollian conformal field theory, JHEP 12 (2022) 133 [arXiv:2207.11684] [INSPIRE].
K. Banerjee et al., One-loop quantum effects in Carroll scalars, arXiv:2307.03901 [INSPIRE].
B. Chen and R. Liu, The shadow formalism of Galilean CFT2, JHEP 05 (2023) 224 [arXiv:2203.10490] [INSPIRE].
A. Bagchi et al., Carroll covariant scalar fields in two dimensions, JHEP 01 (2023) 072 [arXiv:2203.13197] [INSPIRE].
A. Banerjee, A. Bhattacharyya, P. Drashni and S. Pawar, From CFTs to theories with Bondi-Metzner-Sachs symmetries: complexity and out-of-time-ordered correlators, Phys. Rev. D 106 (2022) 126022 [arXiv:2205.15338] [INSPIRE].
E. Bergshoeff et al., Carroll versus Galilei gravity, JHEP 03 (2017) 165 [arXiv:1701.06156] [INSPIRE].
J. Figueroa-O’Farrill, A. Pérez and S. Prohazka, Carroll/fracton particles and their correspondence, JHEP 06 (2023) 207 [arXiv:2305.06730] [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, A. Banerjee and H. Muraki, Boosting to BMS, JHEP 09 (2022) 251 [arXiv:2205.05094] [INSPIRE].
A. Bagchi, A. Banerjee, P. Parekh, D. Tempo and R. Troncoso, Magnetic type limits and deformations of bosonic strings, work in progress.
S. He, P. Mao and X.-C. Mao, Loop corrections as marginal deformations in celestial holography, arXiv:2307.02743 [INSPIRE].
T. He, P. Mitra and A. Strominger, 2D Kac-Moody symmetry of 4D Yang-Mills theory, JHEP 10 (2016) 137 [arXiv:1503.02663] [INSPIRE].
S. Pasterski, S.-H. Shao and A. Strominger, Flat space amplitudes and conformal symmetry of the celestial sphere, Phys. Rev. D 96 (2017) 065026 [arXiv:1701.00049] [INSPIRE].
A. Strominger, Lectures on the infrared structure of gravity and gauge theory, arXiv:1703.05448 [INSPIRE].
A.-M. Raclariu, Lectures on celestial holography, arXiv:2107.02075 [INSPIRE].
S. Pasterski, Lectures on celestial amplitudes, Eur. Phys. J. C 81 (2021) 1062 [arXiv:2108.04801] [INSPIRE].
S. Pasterski, M. Pate and A.-M. Raclariu, Celestial holography, in the proceedings of the Snowmass 2021, (2021) [arXiv:2111.11392] [INSPIRE].
Acknowledgments
We thank Arjun Bagchi, Aritra Banerjee, Glenn Barnich, Geoffrey Compère, Stéphane Detournay, José Edelstein, Oscar Fuentealba, Gaston Giribet, Andrés Gomberoff, Hernán González, Marc Henneaux, Diego Hidalgo, Javier Matulich, Alfredo Pérez, Miguel Pino, Pablo Rodríguez and Patricio Salgado-Rebolledo for useful comments and discussions. RT thanks the organizers of the Solvay Workshop on “Progress on gravitational physics: 45 years of Belgian-Chilean collaboration”, during April 2023 in Brussels, for the opportunity of presenting this work in a wonderful atmosphere. DT and RT also thank the Physique Théorique et Mathématique group of the Université Libre de Bruxelles and the International Solvay Institutes for the kind hospitality. RT thanks the support of Vicerrectoría de Investigación y Doctorados de la Universidad San Sebastián, Chile — fund ‘USS-FIN-23-PASI-10’. This research has been partially supported by ANID FONDECYT grants N° 1211226, 1220910, 1221624 and 3210558.
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Parekh, P., Tempo, D. & Troncoso, R. BMS3 (Carrollian) field theories from a bound in the coupling of current-current deformations of CFT2. J. High Energ. Phys. 2023, 83 (2023). https://doi.org/10.1007/JHEP09(2023)083
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DOI: https://doi.org/10.1007/JHEP09(2023)083