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2020

Divergent to Complex Amplitudes in Two Dimensional String Theory

Sen, Ashoke

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In a recent paper, Balthazar, Rodriguez and Yin found remarkable agreement between the one instanton contribution to the scattering amplitudes of two dimensional string theory and those in the matrix model to the first subleading order.

The comparison was carried out numerically by analytically continuing the external energies to imaginary values, since for real energies the string theory result diverges.
We use insights from string field theory to give finite expressions for the string theory amplitudes for real energies.
We also show analytically that the imaginary parts of the string theory amplitudes computed this way reproduce the full matrix model results for general scattering amplitudes involving multiple closed strings.

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Similar

D. J. Gross and I. R. Klebanov, “Fermionic string field theory of c = 1 two-dimensional quantum gravity,” Nucl. Phys. B 352
1991
Cited alongside, same era.
I. R. Klebanov, “String theory in two-dimensions,” In *Trieste 1991, Proceedings, String theory and quantum gravity ’91* 30-101 and Princeton Univ. - PUPT-1271 (91/07,rec.Oct.) 72 p [hep-th/9108019]
1991
Cited alongside, same era.
B. Zwiebach, “Closed string field theory: Quantum action and the B-V master equation,” Nucl. Phys. B 390
1993
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E. D’Hoker and D. H. Phong, “Momentum analyticity and finiteness of the one loop superstring amplitude,” Phys. Rev. Lett. 70
1993
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E. D’Hoker and D. H. Phong, “Dispersion relations in string theory,” Theor. Math. Phys. 98
1994
Cited alongside, same era.

Then

B. Zwiebach, “Oriented open - closed string theory revisited,” Annals Phys. 267
1998
Later among the works it cites.
A. Sen, “D-instanton Perturbation Theory,” arXiv:2002.04043 [hep-th]
Original
2002
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E. Witten, “The Feynman i ϵ i\epsilon in String Theory,” JHEP 1504
Original
2015
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A. Sen, “One Loop Mass Renormalization of Unstable Particles in Superstring Theory,” JHEP 1611
Original
2016
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R. Pius and A. Sen, “Cutkosky rules for superstring field theory,” JHEP 1610
Original
2016
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A. Berera, “Unitary string amplitudes,” Nucl. Phys. B 411

1994

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1994

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E. D’Hoker and D. H. Phong, “The Box graph in superstring theory,” Nucl. Phys. B 440

1995

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A. B. Zamolodchikov and A. B. Zamolodchikov, “Structure constants and conformal bootstrap in Liouville field theory,” Nucl. Phys. B 477

1996

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A. Sen, to appear

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C. de Lacroix, H. Erbin, S. P. Kashyap, A. Sen and M. Verma, “Closed Superstring Field Theory and its Applications,” Int. J. Mod. Phys. A 32

2017

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P. V. Larocca and C. Maccaferri, “BCFT and OSFT moduli: an exact perturbative comparison,” Eur. Phys. J. C 77

2017

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B. Balthazar, V. A. Rodriguez and X. Yin, “The c c = 1 string theory S-matrix revisited,” JHEP 1904

2019

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