Publication

Quantum groups as global symmetries II. Coulomb gas construction

2025

Abstract

We study a conformal field theory that arises in the infinite-volume limit of a spin chain with U_q(sl_2) global symmetry. Most operators in the theory are defect-ending operators which allows U_q(sl_2) symmetry transformations to act on them in a consistent way. We use Coulomb gas techniques to construct correlation functions and compute all OPE coefficients of the model in closed form, as well as to prove that the properties imposed by the quantum group symmetry are indeed satisfied by the correlation functions. In particular, we treat the non-chiral operators present in the theory. Free boson realization elucidates the origin of the defects attached to the operators. We also comment on the role of quantum group in generalized minimal models.

Official source

https://infoscience.epfl.ch/entities/publication/7cda3721-7a24-4513-a007-5c52dcaf0a9b

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2025

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/7cda3721-7a24-4513-a007-5c52dcaf0a9b

About this result

Related concepts (32)

C-symmetry

In physics, charge conjugation is a transformation that switches all particles with their corresponding antiparticles, thus changing the sign of all charges: not only electric charge but also the charges relevant to other forces. The term C-symmetry is an abbreviation of the phrase "charge conjugation symmetry", and is used in discussions of the symmetry of physical laws under charge-conjugation. Other important discrete symmetries are P-symmetry (parity) and T-symmetry (time reversal).

Quantum field theory

In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines classical field theory, special relativity, and quantum mechanics. QFT is used in particle physics to construct physical models of subatomic particles and in condensed matter physics to construct models of quasiparticles. QFT treats particles as excited states (also called quanta) of their underlying quantum fields, which are more fundamental than the particles.

Conformal field theory

A conformal field theory (CFT) is a quantum field theory that is invariant under conformal transformations. In two dimensions, there is an infinite-dimensional algebra of local conformal transformations, and conformal field theories can sometimes be exactly solved or classified. Conformal field theory has important applications to condensed matter physics, statistical mechanics, quantum statistical mechanics, and string theory. Statistical and condensed matter systems are indeed often conformally invariant at their thermodynamic or quantum critical points.

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