On the Solution of a Non-Linear Equation in String Theory

Document Type : Research Article

Author

Canadian Quantum Research Center, 204-3002 32 Ave Vernon, Canada

Abstract

We investigate the structure and possible solutions of a non-linear equation arising in the context of closed string dynamics. Specifically, we focus on a reduced form of the worldsheet equations of motion with a background field configuration that induces non-linear corrections. Using a combination of perturbative expansion and analytic continuation, we provide approximate solutions and discuss their implications for consistency conditions in string theory. This approach highlights the interplay between geometry, non-linearity, and physical interpretation in the framework of two-dimensional conformal field theory.

Keywords

Main Subjects

Full Text

 

Article PDF

References

[1] M. B. Green, J. H. Schwarz, and E. Witten, Superstring Theory, Vols. I and II, Cambridge University Press, 1987.
[2] J. Polchinski, String Theory, Vols. I and II, Cambridge University Press, 1998.
[3] K. Becker, M. Becker, and J. H. Schwarz, String Theory and M-Theory: A Modern Introduction, Cambridge University Press, 2007.
[4] C. G. Callan, D. Friedan, E. J. Martinec, and M. J. Perry, Strings in background fields, Nucl. Phys. B, 262, 593–609, (1985).
[5] E. S. Fradkin and A. A. Tseytlin, Effective action approach to superstring theory, Phys. Lett. B, 160, 69–76, (1985).
[6] A. Strominger, Heterotic solitons, Nucl. Phys. B, 343, 167–184, (1990).
[7] G. T. Horowitz and A. Strominger, Black strings and p-branes, Nucl. Phys. B, 360, 197–209, (1991).
[8] C. V. Johnson, D-Branes, Cambridge University Press, 2003.
[9] H. Erbin, et al., Classical algebraic structures in string theory effective actions, JHEP, 11, 123, (2020).
[10] R. R. Metsaev and A. A. Tseytlin, Order α0 (two-loop) equivalence of the string equations of motion and the sigma model Weyl invariance conditions: Dependence on the dilaton and the antisymmetric tensor, Nucl. Phys. B, 293, 385–419, (1987).
[11] F. Lund and T. Regge, Unified approach to strings and vortices with soliton solutions, Phys. Rev. D, 14, 1524–1535, (1976).
[12] T. J. Hollowood, Solitons in affine Toda field theories, Nucl. Phys. B, 384, 523–540, (1992).
[13] J. M. Maldacena, The large N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys., 2, 231–252, (1998).
[14] N. Beisert et al., Review of AdS/CFT integrability: An overview, Lett. Math. Phys., 99, 3–32, (2012).
[15] G. Arutyunov and S. Frolov, Foundations of the AdS5 x S5 superstring. Part I, J. Phys. A: Math. Theor., 42, 254003, (2009).
[16] A. M. Polyakov, Quantum geometry of bosonic strings, Phys. Lett. B, 103, 207–210, (1981).
[17] B. Zwiebach, A First Course in String Theory, Cambridge University Press, 2009.
[18] H. J. de Vega, A. L. Larsen, and N. G. Sanchez, Quantum string dynamics in curved backgrounds: A semiclassical approach, Phys. Rev. D, 58, 026001, (1998). 
Analytical and Numerical Solutions for Nonlinear Equations
Volume 10, Issue 1
December 2025
Pages 82-90

Files

History

  • Receive Date: 11 October 2025
  • Accept Date: 15 December 2025
  • Publish Date: 17 December 2025

Share

How to cite

Statistics