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Off-Shell Strings I: S-matrix and Action

by Amr Ahmadain, Aron C. Wall

Submission summary

Authors (as registered SciPost users): Amr Ahmadain
Submission information
Preprint Link: scipost_202308_00047v1  (pdf)
Date submitted: 2023-08-31 12:27
Submitted by: Ahmadain, Amr
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • High-Energy Physics - Theory
Approach: Theoretical


We explain why Tseytlin's off-shell formulation of string theory is well-defined. Although quantizing strings on an off-shell background requires an arbitrary choice of Weyl frame, this choice is not physically significant since it can be absorbed into a field redefinition of the target space fields. The off-shell formalism is particularly subtle at tree-level, due to the treatment of the noncompact conformal Killing group SL(2, $\mathbb{C})$ of the sphere. We prove that Tseytlin's sphere prescriptions recover the standard tree-level Lorentzian S-matrix, and show how to extract the stringy $i \varepsilon$ prescription from the UV cutoff on the worldsheet. We also demonstrate that the correct tree-level equations of motion are obtained to all orders in perturbation theory in $g_s$ and $\alpha^{\prime}$, and illuminate the close connection between the string action and the c-theorem.

Current status:
In refereeing

Submission & Refereeing History

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Submission scipost_202308_00047v1 on 31 August 2023

Reports on this Submission

Anonymous Report 1 on 2023-9-22 (Invited Report)


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  • validity: top
  • significance: top
  • originality: top
  • clarity: good
  • formatting: excellent
  • grammar: excellent

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