A genus zero Lefschetz fibration on the Akbulut cork

Abstract We study two-dimensional Liouville gravity and minimal string theory on spaces with fixed length boundaries. We find explicit formulas describing the gravitational dressing of bulk and boundary correlators in the disk. Their structure has a striking resemblance with observables in 2d BF (plus a boundary term), associated to a quantum deformation of SL(2, ℝ), a connection we develop in some detail. For the case of the (2, p) minimal string theory, we compare and match the results from the continuum approach with a matrix model calculation, and verify that in the large p limit the correlators match with Jackiw-Teitelboim gravity. We consider multi-boundary amplitudes that we write in terms of gluing bulk one-point functions using a quantum deformation of the Weil-Petersson volumes and gluing measures. Generating functions for genus zero Weil-Petersson volumes are derived, taking the large p limit. Finally, we present preliminary evidence that the bulk theory can be interpreted as a 2d dilaton gravity model with a sinh Φ dilaton potential.

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NEW EXAMPLES OF CALABI–YAU 3-FOLDS AND GENUS ZERO SURFACES

Communications in Contemporary Mathematics ◽

10.1142/s0219199713500107 ◽

2014 ◽

Vol 16 (02) ◽

pp. 1350010 ◽

Cited By ~ 5

Author(s):

GILBERTO BINI ◽

FILIPPO F. FAVALE ◽

JORGE NEVES ◽

ROBERTO PIGNATELLI

Keyword(s):

Fundamental Group ◽

Moduli Space ◽

General Type ◽

Picard Number ◽

Surfaces Of General Type ◽

Geometric Genus ◽

Genus Zero ◽

New Family ◽

Hodge Numbers ◽

Projective Lines

We classify the subgroups of the automorphism group of the product of four projective lines admitting an invariant anticanonical smooth divisor on which the action is free. As a first application, we describe new examples of Calabi–Yau 3-folds with small Hodge numbers. In particular, the Picard number is 1 and the number of moduli is 5. Furthermore, the fundamental group is nontrivial. We also construct a new family of minimal surfaces of general type with geometric genus zero, K2 = 3 and fundamental group of order 16. We show that this family dominates an irreducible component of dimension 4 of the moduli space of the surfaces of general type.

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VIRASORO CORRELATION FUNCTIONS FOR VERTEX OPERATOR ALGEBRAS

International Journal of Mathematics ◽

10.1142/s0129167x12501066 ◽

2012 ◽

Vol 23 (10) ◽

pp. 1250106 ◽

Cited By ~ 3

Author(s):

DONNY HURLEY ◽

MICHAEL P. TUITE

Keyword(s):

Graph Theory ◽

Vertex Operator ◽

Generating Functions ◽

Operator Algebra ◽

Correlation Functions ◽

Vertex Operator Algebra ◽

Operator Algebras ◽

Vertex Operator Algebras ◽

Genus Zero ◽

Genus One

We consider all genus zero and genus one correlation functions for the Virasoro vacuum descendants of a vertex operator algebra. These are described in terms of explicit generating functions that can be combinatorially expressed in terms of graph theory related to derangements in the genus zero case and to partial permutations in the genus one case.

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