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In structural engineering, the stability of columns under compressive axial loads is a critical consideration, described as buckling. A typical example involves a column PQ, which is pin-connected at both ends and subjected to a centric axial load F applied at one end, with a reaction force of F' = -F at the other end. Here, it is crucial to understand that when an applied load exceeds the critical load, buckling occurs as the system becomes unstable.
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Factorizing Defects from Generalized Pinning Fields.

Fedor K Popov1, Yifan Wang2

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|November 30, 2025
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Summary
This summary is machine-generated.

We introduce generalized pinning fields in conformal field theory to model critical impurities. These fields factorize spacetime on surfaces, constraining factorization channels by bulk symmetries and solving critical impurities in 2D minimal models.

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Area of Science:

  • Theoretical Physics
  • Quantum Field Theory
  • Condensed Matter Physics

Background:

  • Conformal field theory (CFT) describes critical phenomena and is crucial for understanding universal behaviors in many-body systems.
  • Universality classes in CFT typically capture the macroscopic properties of systems near critical points.
  • Critical impurities can significantly alter the behavior of physical systems, but their modeling remains challenging.

Purpose of the Study:

  • Introduce generalized pinning fields in CFT to model critical impurities at large distances.
  • Provide a rigorous mathematical definition for these defects as unbounded operators.
  • Investigate the consequences of inserting these defects on codimension-one surfaces.

Main Methods:

  • Definition of generalized pinning fields as unbounded operators on the Hilbert space.
  • Analysis of spacetime factorization when these defects are inserted on codimension-one surfaces.
  • Application of bulk symmetries to constrain the factorization channels.

Main Results:

  • Demonstrated that generalized pinning fields model a broad class of critical impurities, extending known universality classes.
  • Proved that insertion of these defects on codimension-one surfaces leads to spacetime factorization.
  • Established that bulk symmetries constrain the possible factorization channels.

Conclusions:

  • Successfully solved critical impurities in 2D minimal models using the generalized pinning field framework.
  • Confirmed and established the factorization phenomena for critical impurities, linking it to localized mass deformations in the 3D O(N) model.