An infinite family of complex saddles plus a bootstrap on multiplicities yields a precise high-energy asymptotic expansion for one-loop string amplitudes with oscillatory terms.
Witten,The Feynmaniϵin String Theory,JHEP04(2015) 055 [1307.5124]
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abstract
The Feynman $i\varepsilon$ is an important ingredient in defining perturbative scattering amplitudes in field theory. Here we describe its analog in string theory. Roughly one takes the string worldsheet to have Lorentz signature when a string is going on-shell although it has Euclidean signature generically.
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High-energy string amplitudes have asymptotic expansions governed by Bernoulli numbers, upgraded via resurgence to transseries whose Stokes data encode non-perturbative monodromy between kinematic regions.
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An infinite family of complex saddles plus a bootstrap on multiplicities yields a precise high-energy asymptotic expansion for one-loop string amplitudes with oscillatory terms.
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