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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Lectures on 2D gravity and 2D string theory (TASI 1992)
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abstract
Emphasis is on 2d target space (c=1 coupled to gravity). Contents: 0. Introduction, Overview, and Purpose 1. Loops and States in Conformal Field Theory 2. 2D Euclidean Quantum Gravity I: Path Integral Approach 3. Brief Review of the Liouville Theory 4. 2D Euclidean Quantum Gravity II: Canonical Approach 5. 2D Critical String Theory 6. Discretized surfaces, matrix models, and the continuum limit 7. Matrix Model Technology I: Method of Orthogonal Polynomials 8. Matrix Model Technology II: Loops on the Lattice 9. Matrix Model Technology III: Free Fermions from the Lattice 10. Loops and States in Matrix Model Quantum Gravity 11. Loops and States in the $c=1$ Matrix Model 12. Fermi Sea Dynamics and Collective Field Theory 13. String scattering in two spacetime dimensions 14. Vertex Operator Calculations and Continuum Methods 15. Achievements, Disappointments, Future Prospects "if you read only one set of lecture notes this year, don't read these."
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The free energy of a D-dimensional matrix model with Gaussian heat-kernel propagator equals the Einstein-Hilbert action with cosmological constant, constants fixed by graph invariants of ribbon graphs.
The charge-p Schwinger model on de Sitter space has p distinct, locally indistinguishable, de Sitter-invariant Hadamard vacuum states produced by spontaneously broken discrete Z_p symmetries.
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.
Full parametric solution of the 7vMM spectral curve via Jacobi theta functions, with phase diagram and scaling asymptotics of the dense-massive tricritical point.
Generic sum rules express arbitrary traces through convolutions of a single Laguerre polynomial for group character averages in Gaussian matrix models.
In gapped random matrix systems with parametrically many degenerate ground states, the spectral form factor at low temperatures is dominated by the disconnected contribution at all times, while the connected form factor depends only on the non-degenerate eigenvalues.
Binary relations on random networks constitute the universe, with space and matter as phases of a statistical model whose Ollivier-Ricci curvature produces emergent 3D geometry, Einstein equations, and relativistic quantum mechanics at large scales.
Disk path integrals of timelike Liouville theory yield one-loop Hartle-Hawking-like wavefunctions in a fixed extrinsic-curvature representation, with a conjectured all-loop form and a K-independent pairing that may define a cosmological inner product.
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.
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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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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From Matrix Models to Gaussian Molecules and the Einstein-Hilbert Action
The free energy of a D-dimensional matrix model with Gaussian heat-kernel propagator equals the Einstein-Hilbert action with cosmological constant, constants fixed by graph invariants of ribbon graphs.
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de Sitter Vacua & pUniverses
The charge-p Schwinger model on de Sitter space has p distinct, locally indistinguishable, de Sitter-invariant Hadamard vacuum states produced by spontaneously broken discrete Z_p symmetries.
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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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Exact solution of the Seven-Vertex Model on a dynamical lattice
Full parametric solution of the 7vMM spectral curve via Jacobi theta functions, with phase diagram and scaling asymptotics of the dense-massive tricritical point.
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Group character averages via a single Laguerre
Generic sum rules express arbitrary traces through convolutions of a single Laguerre polynomial for group character averages in Gaussian matrix models.
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Spectral Form Factor of Gapped Random Matrix Systems
In gapped random matrix systems with parametrically many degenerate ground states, the spectral form factor at low temperatures is dominated by the disconnected contribution at all times, while the connected form factor depends only on the non-degenerate eigenvalues.
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Networks as the fundamental constituents of the universe
Binary relations on random networks constitute the universe, with space and matter as phases of a statistical model whose Ollivier-Ricci curvature produces emergent 3D geometry, Einstein equations, and relativistic quantum mechanics at large scales.
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Quantum Liouville Cosmology
Disk path integrals of timelike Liouville theory yield one-loop Hartle-Hawking-like wavefunctions in a fixed extrinsic-curvature representation, with a conjectured all-loop form and a K-independent pairing that may define a cosmological inner product.
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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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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.