- Letter
- Open Access
Nambu-Goto string as a higher-derivative Liouville theory
Phys. Rev. D 110, L081903 – Published 25 October, 2024
DOI: https://doi.org/10.1103/PhysRevD.110.L081903
Abstract
I propose a generalization of the Liouville action which corresponds to the Nambu-Goto string like the usual Liouville action corresponds to the Polyakov string. The two differ by higher-derivative terms which are negligible classically but revive quantumly. An equivalence with the four-derivative action suggests that the Nambu-Goto string in four dimensions can be described by the (4,3) minimal model analogously to the critical Ising model on a dynamical lattice. While critical indices are the same as in the usual Liouville theory, the domain of applicability becomes broader.
Physics Subject Headings (PhySH)
Article Text
References (25)
- A. M. Polyakov, Quantum geometry of bosonic strings, Phys. Lett. 103B, 207 (1981).
- E. S. Fradkin and A. Tseytlin, Quantized string models, Ann. Phys. (N.Y.) 143, 413 (1982).
- V. G. Knizhnik, A. M. Polyakov, and A. B. Zamolodchikov, Fractal structure of 2D quantum gravity, Mod. Phys. Lett. A 03, 819 (1988).
- F. David, Conformal field theories coupled to 2D gravity in the conformal gauge, Mod. Phys. Lett. A 03, 1651 (1988).
- J. Distler and H. Kawai, Conformal field theory and 2D quantum gravity, Nucl. Phys. B321, 509 (1989).
- V. A. Kazakov, Ising model on a dynamical planar random lattice: Exact solution, Phys. Lett. A 119, 140 (1986).
- S. Dubovsky, R. Flauger, and V. Gorbenko, Effective string theory revisited, J. High Energy Phys. 09 (2012) 044.
- O. Aharony and Z. Komargodski, The effective theory of long strings, J. High Energy Phys. 05 (2013) 118.
- S. Hellerman, S. Maeda, J. Maltz, and I. Swanson, Effective string theory simplified, J. High Energy Phys. 09 (2014) 183.
- Y. Makeenko, Exact solution of higher-derivative conformal theory and minimal models, Phys. Lett. 845, 138170 (2023).
- O. Alvarez, Static potential in string theory, Phys. Rev. D 24, 440 (1981).
- Y. Makeenko, Singular products and universality in higher-derivative conformal theory, J. High Energy Phys. 09 (2023) 086.
- H. Kawai and R. Nakayama, Quantum gravity in two-dimensions, Phys. Lett. B 306, 224 (1993).
- J. Ambjorn and Y. Makeenko, Scaling behavior of regularized bosonic strings, Phys. Rev. D 93, 066007 (2016). String theory as a Lilliputian world, Phys. Lett. B756, 142 (2016).
- C. G. Callan, S. R. Coleman, and R. Jackiw, A new improved energy-momentum tensor, Ann. Phys. (N.Y.) 59, 42 (1970).
- S. Deser and R. Jackiw, Energy-momentum tensor improvements in two dimensions, Int. J. Mod. Phys. B 10, 1499 (1996).
- Y. Makeenko, Opus on conformal symmetry of the Nambu-Goto versus Polyakov strings, Int. J. Mod. Phys. A 38, 2350010 (2023).
- A. Belavin, A. Polyakov, and A. Zamolodchikov, Infinite conformal symmetry in two-dimensional quantum field theory, Nucl. Phys. B241, 333 (1984).
- Y. Makeenko, Notes on higher-derivative conformal theory with nonprimary energy-momentum tensor that applies to the Nambu-Goto string, J. High Energy Phys. 01 (2023) 110.
- A. M. Polyakov, Gauge Fields and Strings (Harwood Academic Publishers, Chur, Switzerland, 1987).
- A. Zamolodchikov and A. Zamolodchikov, Lectures on Liouville theory and matrix models, http://qft.itp.ac.ru/ZZ.pdf.
- D. Friedan, Z. Qiu, and S. H. Shenker, Conformal invariance, unitarity and two-dimensional critical exponents, Phys. Rev. Lett. 52, 1575 (1984).
- I. Kogan, C. Mudry, and A. Tsvelik, The Liouville theory as a model for prelocalized states in disordered conductors, Phys. Rev. Lett. 77, 707 (1996).
- R. J. Riegert, A nonlocal action for the trace anomaly, Phys. Lett. 134B, 56 (1984).
- E. S. Fradkin and A. Tseytlin, Conformal anomaly in Weyl theory and anomaly free superconformal theories, Phys. Lett. 134B, 187 (1984).