Abstract
Nonrelativistic open string theory is defined by a worldsheet theory that produces a Galilean invariant string spectrum and is described at low energies by a nonrelativistic Yang-Mills theory [1]. We study T-duality transformations in the path integral for the sigma model that describes nonrelativistic open string theory coupled to an arbitrary closed string background, described by a string Newton-Cartan geometry, Kalb-Ramond, and dilaton field. We prove that T-duality transformations map nonrelativistic open string theory to relativistic and noncommutative open string theory in the discrete light cone quantization (DLCQ), a quantization scheme relevant for Matrix string theory. We also show how the worldvolume dynamics of nonrelativistic open string theory described by the Dirac-Born-Infeld type action found in [1] maps to the Dirac-Born-Infeld actions describing the worldvolume theories of the DLCQ of open string theory and noncommutative open string theory.
Highlights
JHEP02(2021)087 which has a nonrelativistic open string spectrum with a Galilean invariant dispersion relation [1, 15]
We study T-duality transformations in the path integral for the sigma model that describes nonrelativistic open string theory coupled to an arbitrary closed string background, described by a string Newton-Cartan geometry, Kalb-Ramond, and dilaton field
We prove that T-duality transformations map nonrelativistic open string theory to relativistic and noncommutative open string theory in the discrete light cone quantization (DLCQ), a quantization scheme relevant for Matrix string theory
Summary
We first review nonrelativistic string theory in conformal gauge and with zero background fields, following closely [1]. ∂σX0 σ=0 = ∂σXA σ=0 = 0 , ∂σX1 + i ∂τ X0 σ=0 = 0 These boundary conditions define nonrelativistic open string theory on a D(d−2)-brane transverse to the longitudinal spatial X1-direction. The symmetry preserved by the Dbrane is the Bargmann symmetry.7 This theory has an open string spectrum with a Galilean invariant dispersion relation. To have a nonempty spectrum, it is required that the longitudinal sector has a nontrivial topology; to be specific, we will consider the case where X1 is compactified on a circle of radius R.8.
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