Journal of High Energy Physics

, 2018:133 | Cite as

Nonrelativistic string theory and T-duality

  • Eric Bergshoeff
  • Jaume Gomis
  • Ziqi YanEmail author
Open Access
Regular Article - Theoretical Physics


Nonrelativistic string theory in flat spacetime is described by a two-dimensional quantum field theory with a nonrelativistic global symmetry acting on the worldsheet fields. Nonrelativistic string theory is unitary, ultraviolet complete and has a string spectrum and spacetime S-matrix enjoying nonrelativistic symmetry. The worldsheet theory of nonrelativistic string theory is coupled to a curved spacetime background and to a Kalb-Ramond two-form and dilaton field. The appropriate spacetime geometry for nonrelativistic string theory is dubbed string Newton-Cartan geometry, which is distinct from Riemannian geometry. This defines the sigma model of nonrelativistic string theory describing strings propagating and interacting in curved background fields. We also implement T-duality transformations in the path integral of this sigma model and uncover the spacetime interpretation of T-duality. We show that T-duality along the longitudinal direction of the string Newton-Cartan geometry describes relativistic string theory on a Lorentzian geometry with a compact lightlike isometry, which is otherwise only defined by a subtle infinite boost limit. This relation provides a first principles definition of string theory in the discrete light cone quantization (DLCQ) in an arbitrary background, a quantization that appears in nonperturbative approaches to quantum field theory and string/M-theory, such as in Matrix theory. T-duality along a transverse direction of the string Newton-Cartan geometry equates nonrelativistic string theory in two distinct, T-dual backgrounds.


String Duality Sigma Models Bosonic Strings Classical Theories of Gravity 


Open Access

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Copyright information

© The Author(s) 2018

Authors and Affiliations

  1. 1.Van Swinderen InstituteUniversity of GroningenGroningenThe Netherlands
  2. 2.Perimeter Institute for Theoretical PhysicsWaterlooCanada

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