Simple space-time symmetries: Generalizing conformal field theory

Galois and Simple Current Symmetries in Conformal Field Theory

Symmetries in Conformal Field Theory

Let’s begin by recalling a fact about 2d conformal field theories from Phil’s talk last week. Firstly, we can define a complex semigroup A whose objects are conformal equivalence classes of Riemann surfaces which are diffeomorphic to annuli, equipped with parameterisations of their boundary components, one incoming and one outgoing. The semigroup operation is given by gluing an outgoing to an i...

Quantum Group Symmetries in Conformal Field Theory

Quantum groups play the role of hidden symmetries of some two-dimensional field theories. We discuss how they appear in this role in the Wess-Zumino-Witten model of conformal field theory.

Continuous Space-time Symmetries in a Lattice Field Theory

For purposes of regularization as well as numerical simulation, the discretization of Lorentz invariant continuum field theories on a space-time lattice is often convenient. In general this discretization destroys the rotational or Lorentz-frame independence of the theory, which is only recovered in the continuum limit. The Baxter 8-vertex model may be regarded as a particular discretization of...

Q-structure of Conformal Field Theory with Gauge Symmetries

Introduction It is well-known that abelian conformal eld theory has rich arithmetic structure (see, for example [DKK], [KSU1], [KSU2], [KUS3]). It is natural to ask whether this is also the case for no-abelian conformal eld theory. For the rst step to study arithmetic properties of non-abelian conformal eld theory, in the present notes we shall study the eld of de nition of conformal eld theory...