On completeness and generalized symmetries in quantum field theory
Abstract
We review a notion of completeness in QFT arising from the analysis of basic properties of the set of operator algebras attached to regions. In words, this completeness asserts that the physical observable algebras produced by local degrees of freedom are the maximal ones compatible with causality. We elaborate on equivalent statements to this completeness principle such as the nonexistence of generalized symmetries and the uniqueness of the net of algebras. We clarify that for noncomplete theories, the existence of generalized symmetries is unavoidable and further that they always come in dual pairs with precisely the same “size”. Moreover, the dual symmetries are always broken together, be it explicitly or effectively. Finally, we comment on several issues raised in recent literature, such as the relationship between completeness and modular invariance, dense sets of charges, and absence of generalized symmetries in the bulk of holographic theories.
 Publication:

Modern Physics Letters A
 Pub Date:
 November 2021
 DOI:
 10.1142/S0217732321300251
 arXiv:
 arXiv:2110.11358
 Bibcode:
 2021MPLA...3630025C
 Keywords:

 Quantum field theory;
 generalized symmetries;
 02.10.v;
 02.30.Tb;
 03.65.Fd;
 03.65.Ud;
 03.67.a;
 03.70.+k;
 11.10.z;
 11.10.Cd;
 11.15.q;
 11.30.j;
 11.30.Ly;
 Logic set theory and algebra;
 Operator theory;
 Algebraic methods;
 Entanglement and quantum nonlocality;
 Quantum information;
 Theory of quantized fields;
 Field theory;
 Axiomatic approach;
 Gauge field theories;
 Symmetry and conservation laws;
 Other internal and higher symmetries;
 High Energy Physics  Theory
 EPrint:
 Invited Review for Mod. Phys. Lett. A. 15 pages