Mellin averaging over N reproduces the ensemble-like randomness of wormhole physics in the gravitational path integral when the dual theory admits analytic continuation in N and observables fluctuate superpolynomially small in N.
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Invariants of algebraic curves and topological expansion
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abstract
For any arbitrary algebraic curve, we define an infinite sequence of invariants. We study their properties, in particular their variation under a variation of the curve, and their modular properties. We also study their limits when the curve becomes singular. In addition we find that they can be used to define a formal series, which satisfies formally an Hirota equation, and we thus obtain a new way of constructing a tau function attached to an algebraic curve. These invariants are constructed in order to coincide with the topological expansion of a matrix formal integral, when the algebraic curve is chosen as the large N limit of the matrix model's spectral curve. Surprisingly, we find that the same invariants also give the topological expansion of other models, in particular the matrix model with an external field, and the so-called double scaling limit of matrix models, i.e. the (p,q) minimal models of conformal field theory. As an example to illustrate the efficiency of our method, we apply it to the Kontsevitch integral, and we give a new and extremely easy proof that Kontsevitch integral depends only on odd times, and that it is a KdV tau-function.
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UNVERDICTED 16representative citing papers
The super Virasoro minimal string arises from quantizing 3d supergravity, with 0A+ and 0B+ dual to the bosonic minimal string matrix integral, 0B- to one with inverse square root singularity, and 0A- having vanishing non-trivial perturbative amplitudes.
The Stanford-Witten-Norbury volume recursion is shown to be directly derivable from a spectral curve that computes the Laplace transforms of the volumes using topological recursion.
A random matrix model is built to compute the WP volumes V^{(2m)}_{g,n}({b_i}) for super-Riemann surfaces with NS boundaries and 2m R-punctures, yielding the previously missing spectral curve and closed-form expressions via topological recursion.
Presents a seam-graded recursive algebraic method that converts the closed string tachyon vacuum equation into a sequence of matrix inversions in the zero-momentum Lorentz-scalar sector.
Non-orientable topological gravity produces a resummed topological expansion whose late-time behavior matches the GOE universality class of random matrix theory for time-reversal invariant chaotic systems.
Tropicalized massive scalar QFT is exactly solvable via a non-linear recursion for effective action coefficients that computes graph moduli space volumes, enabling a polynomial-time sampling algorithm for high-order perturbative contributions.
The perturbative c=1 string S-matrix equals a double-scaled matrix integral on the spectral curve x=2√2 cos(z), y=sin(z), establishing a worldsheet–MQM–matrix-integral triality.
Correlators of many integrable models are specializations of universal formulae built from one defining function via KdV/Gel'fand–Dikii structure, including a new closed form for V_{4,n}.
Schwinger-Dyson equations for 2D Euclidean pure gravity are reformulated as Chekhov-Eynard-Orantin topological recursion for basic-type, strip-type, and continuum dynamical triangulation models.
Introduces cap amplitude ψ(b) in one-matrix models and interprets the dilaton equation for discrete volumes N_{g,n} as boundary gluing that reduces n by one.
Introduces RMT surgery to relate off-shell 3D gravity partition functions to CFT spectral statistics via Euclidean wormholes with four-punctured sphere and trumpet boundaries.
Negative-tension ZZ-branes are required by resurgence to build complete transseries for minimal-string free energies, with analytic Stokes data and extensions to JT gravity and other string models.
Topological recursion solves Schwinger-Dyson equations for multicritical and causal dynamical triangulations in 2D quantum gravity, yielding explicit amplitudes.
Spectral curve for Eynard-Orantin recursions on dessins d'enfants is related to Narayana numbers.
A review of the chaos-assisted holographic correspondence linking the SYK model to 2D JT gravity, including the need for string theory corrections at fine quantum scales.
citing papers explorer
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Wormholes and Averaging over N
Mellin averaging over N reproduces the ensemble-like randomness of wormhole physics in the gravitational path integral when the dual theory admits analytic continuation in N and observables fluctuate superpolynomially small in N.
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The Super Virasoro Minimal String from 3d Supergravity
The super Virasoro minimal string arises from quantizing 3d supergravity, with 0A+ and 0B+ dual to the bosonic minimal string matrix integral, 0B- to one with inverse square root singularity, and 0A- having vanishing non-trivial perturbative amplitudes.
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$N=1$ Supersymmetry, Weil-Petersson Volume Recursion, and a Spectral Curve
The Stanford-Witten-Norbury volume recursion is shown to be directly derivable from a spectral curve that computes the Laplace transforms of the volumes using topological recursion.
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Ramond from Random: Weil-Petersson Volumes for Super-Riemann surfaces with NS Boundaries and R Punctures
A random matrix model is built to compute the WP volumes V^{(2m)}_{g,n}({b_i}) for super-Riemann surfaces with NS boundaries and 2m R-punctures, yielding the previously missing spectral curve and closed-form expressions via topological recursion.
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Recursive-algebraic solution of the closed string tachyon vacuum equation
Presents a seam-graded recursive algebraic method that converts the closed string tachyon vacuum equation into a sequence of matrix inversions in the zero-momentum Lorentz-scalar sector.
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Mind the crosscap: $\tau$-scaling in non-orientable gravity and time-reversal-invariant systems
Non-orientable topological gravity produces a resummed topological expansion whose late-time behavior matches the GOE universality class of random matrix theory for time-reversal invariant chaotic systems.
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Tropicalized quantum field theory and global tropical sampling
Tropicalized massive scalar QFT is exactly solvable via a non-linear recursion for effective action coefficients that computes graph moduli space volumes, enabling a polynomial-time sampling algorithm for high-order perturbative contributions.
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$c=1$ strings as a matrix integral
The perturbative c=1 string S-matrix equals a double-scaled matrix integral on the spectral curve x=2√2 cos(z), y=sin(z), establishing a worldsheet–MQM–matrix-integral triality.
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Universal formulae for correlators of a broad class of models
Correlators of many integrable models are specializations of universal formulae built from one defining function via KdV/Gel'fand–Dikii structure, including a new closed form for V_{4,n}.
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Dynamical Triangulations for 2D Pure Gravity and Topological Recursion
Schwinger-Dyson equations for 2D Euclidean pure gravity are reformulated as Chekhov-Eynard-Orantin topological recursion for basic-type, strip-type, and continuum dynamical triangulation models.
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Cap amplitudes in random matrix models
Introduces cap amplitude ψ(b) in one-matrix models and interprets the dilaton equation for discrete volumes N_{g,n} as boundary gluing that reduces n by one.
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Surgery and statistics in 3d gravity
Introduces RMT surgery to relate off-shell 3D gravity partition functions to CFT spectral statistics via Euclidean wormholes with four-punctured sphere and trumpet boundaries.
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All the D-Branes of Resurgence
Negative-tension ZZ-branes are required by resurgence to build complete transseries for minimal-string free energies, with analytic Stokes data and extensions to JT gravity and other string models.
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Multicritical Dynamical Triangulations and Topological Recursion
Topological recursion solves Schwinger-Dyson equations for multicritical and causal dynamical triangulations in 2D quantum gravity, yielding explicit amplitudes.
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Grothendieck's Dessins d'Enfants in a Web of Dualities. II
Spectral curve for Eynard-Orantin recursions on dessins d'enfants is related to Narayana numbers.
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Quantum chaos and the holographic principle
A review of the chaos-assisted holographic correspondence linking the SYK model to 2D JT gravity, including the need for string theory corrections at fine quantum scales.