Off-shell strings I: S-matrix and action

Ahmadain, Amr; Wall, Aron C.

doi:10.21468/SciPostPhys.17.1.005

SciPost Physics

Off-shell strings I: S-matrix and action

Amr Ahmadain, Aron C. Wall

SciPost Phys. 17, 005 (2024) · published 5 July 2024

doi: 10.21468/SciPostPhys.17.1.005
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Abstract

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.

TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.17.1.005
TI  - Off-shell strings I: S-matrix and action
PY  - 2024/07/05
UR  - https://scipost.org/SciPostPhys.17.1.005
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 17
IS  - 1
SP  - 005
A1  - Ahmadain, Amr
AU  - Wall, Aron C.
AB  - 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.
ER  -

@Article{10.21468/SciPostPhys.17.1.005,
	title={{Off-shell strings I: S-matrix and action}},
	author={Amr Ahmadain and Aron C. Wall},
	journal={SciPost Phys.},
	volume={17},
	pages={005},
	year={2024},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.17.1.005},
	url={https://scipost.org/10.21468/SciPostPhys.17.1.005},
}

Cited by 3

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¹ Amr Ahmadain,
¹ Aron C. Wall

¹ University of Cambridge

Funders for the research work leading to this publication