The current algebra on the circle as a germ of local field theories

How to Remove the Boundary in CFT – An Operator Algebraic Procedure

“…It is then easily seen that 2 , because in these cases the anyonic phase factors cancel. It also commutes with…”

“…is a neutral combination of charged primary fields of dimension 1 4 , transforming in the spin- 1 2 representation of SU (2), localized at t + x and t − x. The description of this model in terms of smooth Weyl operators is rather straightforward, see e.g., [2]: Weyl operators with integer multiples of the charge √ 2 belong to A(I ), while operators with half-integer multiples of the charge √ 2 in I and in J belong to…”

A new rational conformal field theory extension of the fully degenerate W1+∞(m)

“…Then, the irreducible A Zm -representations of the twisted sector are generated by applying to the untwisted irreducible A Zm -characters the modular transformations 9 , T j S ∈ P SL(2, Z) with j ∈ {0, ..., m − 1}. 9 In our case, the theory to which is applied the orbifold is a Γ θ -RCFT and m is a prime number, so we apply…”

“…RCFT extensions [9] of it are defined compactifying the free boson field on a circle of rational square radius and correspondingly introducing an extension of the Heisenberg algebra A( u(1)). More explicitly, the compactification condition on the circle with radius r = √ 2p, p positive integer, is:…”

On the KMS condition for the critical Ising model

“…In this letter we tackle this problem by exploiting the Kubo-Martin-Schwinger (KMS) condition [3] in the context of conformal field theory [4] and the exchange algebra of the chiral conformal field theories [5] to compute the chiral KMS states for the critical Ising model. We compare the KMS boundary condition and the action of the center of the conformal group with the derived monodromy properties of the chiral KMS states.…”