Abstract
We formulate a strategy for computing the complete set of non-perturbative corrections to closed string scattering in c = 1 string theory from the worldsheet perspective. This requires taking into account the effect of multiple ZZ-instantons, including higher instantons constructed from ZZ boundary conditions of type (m, 1), with a careful treatment of the measure and contour in the integration over the instanton moduli space. The only a priori ambiguity in our prescription is a normalization constant \( \mathcal{N} \)m that appears in the integration measure for the (m, 1)-type ZZ instanton, at each positive integer m. We investigate leading corrections to the closed string reflection amplitude at the n-instanton level, i.e. of order \( {e}^{-n/{g}_s} \), and find striking agreement with our recent proposal on the non-perturbative completion of the dual matrix quantum mechanics, which in turn fixes \( \mathcal{N} \)m for all m.
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B. Balthazar, V.A. Rodriguez and X. Yin, ZZ Instantons and the Non-Perturbative Dual of c = 1 String Theory, arXiv:1907.07688 [INSPIRE].
A. Sen, Fixing an Ambiguity in Two Dimensional String Theory Using String Field Theory, JHEP 03 (2020) 005 [arXiv:1908.02782] [INSPIRE].
I.R. Klebanov, String theory in two-dimensions, in Spring School on String Theory and Quantum Gravity (to be followed by Workshop), Trieste, Italy (1991), pg. 30 [hep-th/9108019] [INSPIRE].
P.H. Ginsparg and G.W. Moore, Lectures on 2-D gravity and 2-D string theory, in Theoretical Advanced Study Institute (TASI 92): From Black Holes and Strings to Particles, Boulder, U.S.A. (1993), pg. 277 [hep-th/9304011] [INSPIRE].
A. Jevicki, Development in 2-d string theory, in Workshop on String Theory, Gauge Theory and Quantum Gravity, Trieste, Italy, (1993), pg. 96, [hep-th/9309115] [INSPIRE].
E.J. Martinec, Matrix models and 2D string theory, in in 9th Frontiers of Mathematical Physics Summer School on Strings, Gravity and Cosmology, Vancouver, Canada (2004), pg. 403 [hep-th/0410136] [INSPIRE].
J. McGreevy and H.L. Verlinde, Strings from tachyons: the c = 1 matrix reloaded, JHEP 12 (2003) 054 [hep-th/0304224] [INSPIRE].
G.W. Moore, M.R. Plesser and S. Ramgoolam, Exact S matrix for 2-D string theory, Nucl. Phys. B 377 (1992) 143 [hep-th/9111035] [INSPIRE].
T. Takayanagi and N. Toumbas, A Matrix model dual of type 0B string theory in two-dimensions, JHEP 07 (2003) 064 [hep-th/0307083] [INSPIRE].
M.R. Douglas, I.R. Klebanov, D. Kutasov, J.M. Maldacena, E.J. Martinec and N. Seiberg, A New hat for the c = 1 matrix model, hep-th/0307195 [INSPIRE].
G.W. Moore and R. Plesser, Classical scattering in (1 + 1)-dimensional string theory, Phys. Rev. D 46 (1992) 1730 [hep-th/9203060] [INSPIRE].
B. Balthazar, V.A. Rodriguez and X. Yin, The c = 1 string theory S-matrix revisited, JHEP 04 (2019) 145 [arXiv:1705.07151] [INSPIRE].
A.B. Zamolodchikov and A.B. Zamolodchikov, Liouville field theory on a pseudosphere, hep-th/0101152 [INSPIRE].
H. Dorn and H.J. Otto, Two and three point functions in Liouville theory, Nucl. Phys. B 429 (1994) 375 [hep-th/9403141] [INSPIRE].
A.B. Zamolodchikov and A.B. Zamolodchikov, Structure constants and conformal bootstrap in Liouville field theory, Nucl. Phys. B 477 (1996) 577 [hep-th/9506136] [INSPIRE].
J. Polchinski, Combinatorics of boundaries in string theory, Phys. Rev. D 50 (1994) R6041 [hep-th/9407031] [INSPIRE].
M.B. Green and M. Gutperle, Effects of D instantons, Nucl. Phys. B 498 (1997) 195 [hep-th/9701093] [INSPIRE].
V. Fateev, A.B. Zamolodchikov and A.B. Zamolodchikov, Boundary Liouville field theory. 1. Boundary state and boundary two point function, hep-th/0001012 [INSPIRE].
J. Teschner, Remarks on Liouville theory with boundary, PoS tmr2000 (2000) 041 [hep-th/0009138] [INSPIRE].
I.R. Klebanov, J.M. Maldacena and N. Seiberg, D-brane decay in two-dimensional string theory, JHEP 07 (2003) 045 [hep-th/0305159] [INSPIRE].
S. Giombi and X. Yin, ZZ boundary states and fragmented AdS(2) spaces, JHEP 07 (2009) 002 [arXiv:0808.0923] [INSPIRE].
W. Fischler and L. Susskind, Dilaton Tadpoles, String Condensates and Scale Invariance, Phys. Lett. B 171 (1986) 383 [INSPIRE].
W. Fischler and L. Susskind, Dilaton Tadpoles, String Condensates and Scale Invariance. 2, Phys. Lett. B 173 (1986) 262 [INSPIRE].
Acknowledgments
We would like to thank Igor Klebanov, Juan Maldacena, Silviu Pufu, Nati Seiberg, and Edward Witten for discussions. BB thanks Princeton University, XY thanks University of Amsterdam, for hospitality during the course of this work. This work is supported in part by a Simons Investigator Award from the Simons Foundation, by the Simons Collaboration Grant on the Non-Perturbative Bootstrap, and by DOE grant DE-SC00007870. BB is supported by the Bolsa de Doutoramento FCT fellowship. VR is supported by the Harvard University Graduate Prize Fellowship.
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Balthazar, B., Rodriguez, V.A. & Yin, X. Multi-instanton calculus in c = 1 string theory. J. High Energ. Phys. 2023, 50 (2023). https://doi.org/10.1007/JHEP05(2023)050
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DOI: https://doi.org/10.1007/JHEP05(2023)050