The Parisi-Sourlas Uplift and Infinitely Many Solvable 4d CFTs

Abstract

Parisi-Sourlas (PS) supersymmetry is known to emerge in some models with random field type of disorder. When PS SUSY is present the $d$-dimensional theory allows for a $d-2$-dimensional description. In this paper we investigate the reversed question and we provide new indications that any given CFT${}_{d-2}$ can be uplifted to a PS SUSY CFT${}_d$. We show that any scalar four-point function of a CFT${}_{d-2}$ is mapped to a set of 43 four-point functions of the uplifted CFT${}_d$ which are related to each other by SUSY and satisfy all necessary bootstrap axioms. As a byproduct we find 43 non trivial relations between conformal blocks across dimensions. We test the uplift in generalized free field theory (GFF) and find that PS SUSY is a powerful tool to bootstrap an infinite class of previously unknown GFF observables. Some of this power is shown to persist in perturbation theory around GFF. We explain why all diagonal minimal models admit an uplift and we show exact results for correlators and CFT data of the $4d$ uplift of the Ising model. Despite being strongly coupled $4d$ CFTs, the uplifted minimal models contain infinitely many conserved currents and are expected to be integrable.

arXiv comment50 pages + 15 pages of appendices, 3 figures, Mathematica notebook in the ancillary files. v2: published version, added minor comments

References in corpus (27)

• The Conformal Bootstrap: Theory, Numerical Techniques, and Applications
• Conformal Four Point Functions and the Operator Product Expansion
• Conformal Partial Waves and the Operator Product Expansion
• Analyticity in Spin in Conformal Theories
• Bootstrapping the O(N) Vector Models
• Bootstrapping Mixed Correlators in the 3D Ising Model
• Radial Coordinates for Conformal Blocks
• Unitarity and the Holographic S-Matrix
• Conformal Partial Waves: Further Mathematical Results
• Analytic Bounds and Emergence of ${\text{AdS}}_2$ Physics from the Conformal Bootstrap
• Recursion Relations for Conformal Blocks
• The Analytic Functional Bootstrap I: 1D CFTs and 2D S-Matrices
• The Analytic Functional Bootstrap II: Natural Bases for the Crossing Equation
• Diagonal Limit for Conformal Blocks in d Dimensions
• The 3d Stress-Tensor Bootstrap
• Radial expansion for spinning conformal blocks
• Phase transitions in disordered systems: the example of the random-field Ising model in four dimensions
• Evidence for Supersymmetry in the Random-Field Ising Model at D = 5
• Restoration of dimensional reduction in the random-field Ising model at five dimensions
• Random Field Ising Model and Parisi-Sourlas Supersymmetry I. Supersymmetric CFT
• The fate of Parisi-Sourlas supersymmetry in Random Field models
• Mixed Scalar-Current bootstrap in three dimensions
• Random Field Ising Model and Parisi-Sourlas Supersymmetry. Part II. Renormalization Group
• Chiral correlators of the Ising conformal field theory
• Charting the space of 3D CFTs with a continuous global symmetry
• Random Field ${\varphi }^3$ Model and Parisi-Sourlas Supersymmetry
• Four Lectures on the Random Field Ising Model, Parisi-Sourlas Supersymmetry, and Dimensional Reduction