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Kramers-wannier duality from conformal defects.

Jürg Fröhlich¹, Jürgen Fuchs, Ingo Runkel

¹Institut für Theoretische Physik, ETH Zürich, Switzerland.

Physical Review Letters

|August 25, 2004

Summary

The fusion algebra of conformal defects reveals internal symmetries in 2D conformal field theories. This framework generalizes Kramers-Wannier duality, as shown in the Ising and Potts models.

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Area of Science:

Theoretical physics
Condensed matter physics
Quantum field theory

Background:

Conformal field theories (CFTs) in two dimensions are crucial for understanding critical phenomena.
Conformal defects and their fusion algebra are key to exploring symmetries and dualities.
Kramers-Wannier duality is a fundamental concept in statistical mechanics and quantum field theory.

Purpose of the Study:

To demonstrate that the fusion algebra of conformal defects encodes internal symmetries of a 2D conformal field theory.
To show how this algebraic structure allows for the derivation of generalized Kramers-Wannier dualities.
To illustrate the proposed mechanism using specific physical models.

Main Methods:

Analysis of the fusion algebra of conformal defects in 2D conformal field theories.
Application of the fusion algebra to identify internal symmetries.
Derivation of dualities by examining the algebraic properties of defects.
Case studies using the Ising model and the three-state Potts model.

Main Results:

The fusion algebra of conformal defects directly contains information about the internal symmetries of the theory.
A general method is established to read off generalizations of Kramers-Wannier duality from the fusion algebra.
The Ising and three-state Potts models serve as concrete examples validating the developed mechanism.

Conclusions:

The fusion algebra of conformal defects is a powerful tool for uncovering hidden symmetries in 2D CFTs.
This approach provides a systematic way to generalize and understand dualities beyond traditional examples.
The findings offer new perspectives on the structure and properties of solvable models in theoretical physics.

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