Virasoro conformal bootstrap with $c>1$

Abstract

We derive new constraints on the spectrum of two-dimensional conformal field theories with central charge $c>1.$ Employing the pillow representation of the four point correlator of identical scalars with dimension ${\Delta }_{\mathcal{O}}$ and positivity of the coefficients of its expansion in the elliptic nome we place central charge dependent bounds on the dimension of the first excited Virasoro primary the scalar couples to, in the form ${\Delta }_1<f(c,{\Delta }_{\mathcal{O}}).$ We give an analytic expression for $f(c,{\Delta }_{\mathcal{O}})$ and write down transcendental equations that significantly improve the analytic bound. We numerically evaluate the stronger bounds for arbitrary fixed values of $c$ and ${\Delta }_{\mathcal{O}}.$

arXiv comment15 pages, typos corrected, wrong claim in discussion removed

References in corpus (10)

• The Conformal Bootstrap: Theory, Numerical Techniques, and Applications
• Solving the 3D Ising Model with the Conformal Bootstrap
• Conformal Four Point Functions and the Operator Product Expansion
• Precision Islands in the Ising and $O(N)$ Models
• Analytic Bounds and Emergence of ${\text{AdS}}_2$ Physics from the Conformal Bootstrap
• Constraints on 2d CFT partition functions
• TASI Lectures on the Conformal Bootstrap
• A Numerical Approach to Virasoro Blocks and the Information Paradox
• Modular crossings, OPE coefficients and black holes
• Four-point correlation modular bootstrap for OPE densities

Cited by in corpus (1)

• Analytic Bootstrap in 2D Boundary Conformal Field Theory: Towards Braneworld Holography