Abstract
I investigate the higher-derivative conformal theory which shows how the Nambu-Goto and Polyakov strings can be told apart. Its energy-momentum tensor is conserved, traceless but does not belong to the conformal family of the unit operator. To implement conformal invariance in such a case I develop the new technique that explicitly accounts for the quantum equation of motion and results in singular products. I show that the conformal transformations generated by the nonprimary energy-momentum tensor form a Lie algebra with a central extension which in the path-integral formalism gives a logarithmically divergent contribution to the central charge. I demonstrate how the logarithmic divergence is canceled in the string susceptibility and reproduce the previously obtained deviation from KPZ-DDK at one loop.
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References
Y. Makeenko, Opus on conformal symmetry of the Nambu-Goto versus Polyakov strings, Int. J. Mod. Phys. A, in press, arXiv:2204.10205 [INSPIRE].
Y. Makeenko, Private life of the Liouville field that causes new anomalies in the Nambu-Goto string, Nucl. Phys. B 967 (2021) 115398 [arXiv:2102.04753] [INSPIRE].
V.G. Knizhnik, A.M. Polyakov and A.B. Zamolodchikov, Fractal Structure of 2D Quantum Gravity, Mod. Phys. Lett. A 3 (1988) 819 [INSPIRE].
F. David, Conformal Field Theories Coupled to 2D Gravity in the Conformal Gauge, Mod. Phys. Lett. A 3 (1988) 1651 [INSPIRE].
J. Distler and H. Kawai, Conformal Field Theory and 2D Quantum Gravity, Nucl. Phys. B 321 (1989) 509 [INSPIRE].
A.M. Polyakov, Gauge fields and strings, Harwood Acad. Pub. (1987).
Y. Makeenko, Mean field quantization of effective string, JHEP 07 (2018) 104 [arXiv:1802.07541] [INSPIRE].
H. Kawai and R. Nakayama, Quantum R2 gravity in two-dimensions, Phys. Lett. B 306 (1993) 224 [hep-th/9303006] [INSPIRE].
S. Ichinose, Renormalization of two-dimensional R2 gravity, Nucl. Phys. B 445 (1995) 311 [INSPIRE].
V.A. Kazakov, M. Staudacher and T. Wynter, Exact solution of discrete two-dimensional R2 gravity, Nucl. Phys. B 471 (1996) 309 [hep-th/9601069] [INSPIRE].
J. Ambjørn and Y. Makeenko, The use of Pauli–Villars regularization in string theory, Int. J. Mod. Phys. A 32 (2017) 1750187 [arXiv:1709.00995] [INSPIRE].
A.A. Belavin, A.M. Polyakov and A.B. Zamolodchikov, Infinite Conformal Symmetry in Two-Dimensional Quantum Field Theory, Nucl. Phys. B 241 (1984) 333 [INSPIRE].
A.B. Zamolodchikov, On the entropy of random surfaces, Phys. Lett. 117B (1982) 87.
S. Chaudhuri, H. Kawai and S.H.H. Tye, Path Integral Formulation of Closed Strings, Phys. Rev. D 36 (1987) 1148 [INSPIRE].
I.K. Kostov and A. Krzywicki, On the Entropy of Random Surfaces With Arbitrary Genus, Phys. Lett. B 187 (1987) 149 [INSPIRE].
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Makeenko, Y. Notes on higher-derivative conformal theory with nonprimary energy-momentum tensor that applies to the Nambu-Goto string. J. High Energ. Phys. 2023, 110 (2023). https://doi.org/10.1007/JHEP01(2023)110
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DOI: https://doi.org/10.1007/JHEP01(2023)110