• DOI:10.1090/fic/030/20
• Corpus ID: 16599790

Conformal field theory and Doplicher-Roberts reconstruction

@inproceedings{Mueger2000ConformalFT,
  title={Conformal field theory and Doplicher-Roberts reconstruction},
  author={Michael Mueger},
  year={2000}
}

• Michael Mueger
• Published 21 August 2000
• Mathematics

After a brief review of recent rigorous results concerning the representation theory of rational chiral conformal field theories (RC- QFTs) we focus on pairs (A, F) of conformal field theories, where F has a finite group G of global symmetries and A is the fixpoint theory. The comparison of the representation categories of A and F is strongly intertwined with various issues related to braided tensor categories. We explain that, given the representation category of A, the representation category of F can be computed (up to equivalence) by a purely cate- gorical construction. The latter is of considerable independent interest since it amounts to a Galois theory for braided tensor categories. We emphasize the characterization of modular categories as braided tensor categories with trivial center and we state a double commutant theo- rem for subcategories of modular categories. The latter implies that a modular category M which has a replete full modular subcategory M1 factorizes as M ≃ M1 ⊗C M2 where M2 = M ∩ Mis another mod- ular subcategory. On the other hand, the representation category of A is not determined completely by that of F and we identify the needed additional data in terms of soliton representations. We comment on 'holomorphic orbifold' theories, i.e. the case where F has trivial repre- sentation theory, and close with some open problems. We point out that our approach permits the proof of many conjec- tures and heuristic results on 'simple current extensions' and 'holomor- phic orbifold models' in the physics literature on conformal field theory.