Degenerate Operators and the $1/c$ Expansion: Lorentzian Resummations, High Order Computations, and Super-Virasoro Blocks

Abstract

One can obtain exact information about Virasoro conformal blocks by analytically continuing the correlators of degenerate operators. We argued in recent work that this technique can be used to explicitly resolve information loss problems in AdS${}_3$/CFT${}_2$. In this paper we use the technique to perform calculations in the small $1/c\propto G_N$ expansion: (1) we prove the all-orders resummation of logarithmic factors $\propto \frac{1}{c}\log z$ in the Lorentzian regime, demonstrating that $1/c$ corrections directly shift Lyapunov exponents associated with chaos, as claimed in prior work, (2) we perform another all-orders resummation in the limit of large $c$ with fixed $cz$, interpolating between the early onset of chaos and late time behavior, (3) we explicitly compute the Virasoro vacuum block to order $1/c^2$ and $1/c^3$, corresponding to $2$ and $3$ loop calculations in AdS${}_3$, and (4) we derive the heavy-light vacuum blocks in theories with $\mathcal{N}=1,2$ superconformal symmetry.

34+20 pages, 2 figures

References in corpus (8)

• Universal Spectrum of 2d Conformal Field Theory in the Large c Limit
• Entanglement Entropy at Large Central Charge
• Local bulk S-matrix elements and CFT singularities
• Chaos in the black hole S-matrix
• N=1 SUSY Conformal Block Recursive Relations
• Elliptic recurrence representation of the N=1 Neveu-Schwarz blocks
• Stringy effects in scrambling
• Semiclassical OPE coefficients from 3D gravity

Cited by in corpus (26)

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• A theory of reparameterizations for AdS${}_3$ gravity
• Shockwave S-matrix from Schwarzian Quantum Mechanics
• A Numerical Approach to Virasoro Blocks and the Information Paradox
• Probing thermality beyond the diagonal
• Entanglement Entropy, OTOC and Bootstrap in 2D CFTs from Regge and Light Cone Limits of Multi-point Conformal Block
• Clocks and Rods in Jackiw-Teitelboim Quantum Gravity
• Phases of scrambling in eigenstates
• From Conformal Blocks to Path Integrals in the Vaidya Geometry
• Many-point classical conformal blocks and geodesic networks on the hyperbolic plane
• Conformal blocks from Wilson lines with loop corrections
• Operator mixing in deformed D1D5 CFT and the OPE on the cover
• A note on the Virasoro blocks at order $1/c$
• Resurgence, Conformal Blocks, and the Sum over Geometries in Quantum Gravity
• Superconformal blocks from Wilson lines with loop corrections
• Bands and gaps in Nekrasov partition function
• Chaos in Celestial CFT
• Size and momentum of an infalling particle in the black hole interior
• More on Wilson toroidal networks and torus blocks
• Chaos in Three-dimensional Higher Spin Gravity
• Effective description of sub-maximal chaos: stringy effects for SYK scrambling
• Three point functions in higher spin AdS_3 holography with 1/N corrections
• Supersymmetric Galilean conformal blocks
• Toward Null State Equations in $d>2$
• Resummation of Multi-Stress Tensors in Higher Dimensions
• Differential equations for classical Virasoro blocks with heavy and light operators