DiffQFT

Differentiable Quantum Field Theory on Anti-de Sitter Spacetime

Interactive two-point Witten diagram on the Poincaré half-plane

Drag the red boundary points along the bottom edge

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Δ --
Free correlator Gfree --
MC integral IΔ --
Boundary separation --

What am I looking at?

This visualisation shows the integrand density of a two-point Witten diagram in Euclidean AdS2, computed in Poincaré upper half-plane coordinates where the metric is ds2 = (L/z)2(dz2 + dx2).

Two boundary-to-bulk propagators KΔ originate from the operator insertion points p1 and p2 on the conformal boundary (z = 0, bottom edge). The heatmap encodes the integrand

(L/z)2 · K(z,x; p1)Δ · K(z,x; p2)Δ

where K(z,x; p) = Lz / (z2 + (x−p)2) is the Poisson-type bulk-boundary kernel and the scaling dimension is Δ = ½ + √(¼ + m2L2).

The integral of this density over the bulk gives the holographic two-point function, here estimated by a simple Monte Carlo sampler. In the AdS/CFT correspondence this encodes the correlator of the dual CFT operator on the boundary.

About the project

DiffQFT implements differentiable Witten diagram computation, neural surrogates for holographic correlators, and physics-informed neural networks for Sine-Gordon theory on AdS2. The core library uses PyTorch with custom autograd ops for hypergeometric functions, enabling gradient-based optimization through QFT observables.

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