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Twisted Partition Functions as Order Parameters

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arxiv 2505.16546 v2 pith:OCNJSA27 submitted 2025-05-22 hep-th cond-mat.str-el

Twisted Partition Functions as Order Parameters

Jun Maeda , Yuya Tanizaki This is my paper
classification hep-th cond-mat.str-el
keywords partitionsymmetryfunctionbehaviorcasefieldorderquantum
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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For quantum field theories with global symmetry, we can study the behavior of the partition function with the background gauge field to diagnose different quantum phases. For the case of discrete symmetries, we find that the symmetry-twisted partition function works as an order parameter that discriminates spontaneous symmetry breaking (SSB), symmetry-protected topological (SPT) states, and symmetry-enriched topological (SET) states. We then consider its application to the case of 4d Yang-Mills theory with adjoint matters to understand the relation between the twisted partition function and the Wilson-'t Hooft classification. We also study its behavior for the spontaneously broken U(1) symmetry and interpret the result from the viewpoint of the mixed anomaly with the emergent solitonic symmetry.

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Cited by 5 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

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    Proposes torus and lens-space twisted partition functions as criteria for center-vortex and monopole condensation and proves vortex condensation implies monopole condensation in gapped phases.

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    Tensor renormalization group computes symmetry-twisted partition functions to identify critical points solely from them, yielding Tc=2.2017(2) and nu=0.663(33) for the 3D O(2) model plus TBKT=0.8928(2) for the 2D O(2)...

  4. Numerical Hints for Dyon Condensation at $\theta=2\pi$ via Wilson-'t Hooft Loops in $SU(2)$ Yang-Mills Theory

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