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Hyperbolic three-string vertex

Atakan Hilmi Fırat
(
- MIT, Cambridge, CTP
)

Feb 7, 2021

37 pages

Published in:

JHEP 08 (2021) 035

Published: Aug 9, 2021

e-Print:

2102.03936 [hep-th]

DOI:

10.1007/JHEP08(2021)035

Report number:

MIT-CTP/5282

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Abstract: (Springer)

We begin developing tools to compute off-shell string amplitudes with the recently proposed hyperbolic string vertices of Costello and Zwiebach. Exploiting the relation between a boundary value problem for Liouville’s equation and a monodromy problem for a Fuchsian equation, we construct the local coordinates around the punctures for the generalized hyperbolic three-string vertex and investigate their various limits. This vertex corresponds to the general pants diagram with three boundary geodesics of unequal lengths. We derive the conservation laws associated with such vertex and perform sample computations. We note the relevance of our construction to the calculations of the higher-order string vertices using the pants decomposition of hyperbolic Riemann surfaces.

Note:

37 pages, 6 figures, v2: minor typos corrected, version published in JHEP

String Field Theory
Differential and Algebraic Geometry
string
conservation law
Riemann surface
Liouville
monodromy
off-shell

References(43)

Figures(0)

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