https://doi.org/10.1140/epjc/s10052-021-09399-9
Regular Article - Theoretical Physics
On the existence of the global conformal gauge in string theory
Steklov Mathematical Institute, ul. Gubkina, 8, 119991, Moscow, Russia
Received:
30
April
2021
Accepted:
30
June
2021
Published online:
5
July
2021
The global conformal gauge is playing the crucial role in string theory providing the basis for quantization. Its existence for two-dimensional Lorentzian metric is known locally for a long time. We prove that if a Lorentzian metric is given on a plain then the conformal gauge exists globally on the whole 
. Moreover, we prove the existence of the conformal gauge globally on the whole worldsheets represented by infinite strips with straight boundaries for open and closed bosonic strings. The global existence of the conformal gauge on the whole plane is also proved for the positive definite Riemannian metric.
© The Author(s) 2021
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