Abstract
Nonrelativistic string theory is a unitary, ultraviolet finite quantum gravity theory with a nonrelativistic string spectrum. The vertex operators of the worldsheet theory determine the spacetime geometry of nonrelativistic string theory, known as the string Newton-Cartan geometry. We compute the Weyl anomaly of the nonrelativistic string worldsheet sigma model describing strings propagating in a string Newton-Cartan geometry, Kalb-Ramond and dilaton background. We derive the equations of motion that dictate the backgrounds on which nonrelativistic string theory can be consistently defined quantum mechanically. The equations of motion we find from our study of the conformal anomaly of the worldsheet theory are to nonrelativistic string theory what the (super)gravity equations of motion are to relativistic string theory.
Highlights
Naturally splits the target space into a longitudinal and transverse sector
The equations of motion we find from our study of the conformal anomaly of the worldsheet theory are to nonrelativistic string theory what thegravity equations of motion are to relativistic string theory
Nonrelativistic string theory deformed by suitable vertex operators gives rise to strings propagating in a string Newton-Cartan geometry, B-field and dilaton background
Summary
We introduce the Zweibein field eαa, a = 1, 2 on Σ such that hαβ = eαaeβbδab. The worldsheet fields of nonrelativistic string theory consist of worldsheet scalars parametrizing the spacetime coordinates xμ, μ = 0, 1, · · · , d − 1 and two additional worldsheet fields, which we denote by λ and λ. We show that λ and λ are worldsheet (1, 0) and (0, 1) forms, respectively, after fixing the conformal gauge. Δλ = ξ ∂zλ + λ ∂zξ , δλ = ξ ∂zλ + λ ∂zξ This concludes the proof that λ and λ are worldsheet one-forms. The worldsheet action (2.7) was shown in [1] to lead to a unitary, ultraviolet finite string theory with a well-defined perturbative expansion
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
