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Torus one-point correlation numbers in minimal Liouville gravity

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arxiv 2210.14568 v2 pith:M7VRRLI3 submitted 2022-10-26 hep-th

classification hep-th
keywords amplitudesliouvilletorusapproachcalculationsequationsgravitymethod
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abstract

We present a method for the first principles calculation of tachyon one-point amplitudes in $(2,2p+1)$ minimal Liouville gravity defined on a torus. The method is based on the higher equations of motion in the Liouville CFT. These equations were earlier successfully applied for analytic calculations of the amplitudes in the spherical topology. We show that this approach allows to reduce the moduli integrals entering the definition of the torus amplitudes to certain boundary contributions, which can be calculated explicitly. The results agree with the calculations performed in the matrix models approach.

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  1. $x-y$ swap for $(2,2p+1)$ minimal string

    hep-th 2025-06 conditional novelty 6.0 of 10

    An x-y swapped spectral curve is conjectured to reproduce (2,2p+1) minimal string tachyon correlators without resonance transformations; verified at low genus, with a ground-ring extension that does not match HEM.

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