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arXiv · 2607.03534

Fixed-point tensor network for compactified boson conformal field theory

Gong Cheng·Dong-Yu Bao·Zheng-Cheng Gu
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Abstract

Fixed-point (FP) tensor networks provide a discrete spacetime representation of conformal field theories (CFTs), offering a new route toward understanding holographic duality, generalized symmetries, and even quantum gravity. In this work, we construct FP tensors for the 2D compactified boson theory at a generic compactification radius, an archetypal irrational CFT, using boundary (open-string) data with conformal boundary conditions. We show that the resulting tensors reproduce the closed-string spectrum with high accuracy and generate stable renormalization-group (RG) flows under the tensor complex renormalization algorithm. Moreover, we identify a controllable exactly marginal deformation at the level of a single tensor, enabling flows that move continuously along the $c=1$ moduli space. This framework establishes a concrete lattice-level route toward describing a broad class of 2D irrational CFTs.

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Gong Cheng, Dong-Yu Bao, Zheng-Cheng Gu. 2026-07-03. Fixed-point tensor network for compactified boson conformal field theory. https://arxiv.org/abs/2607.03534

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