An introduction to conformal field theory (hep-th 9910156) by Gaberdiel M.R. PDF

By Gaberdiel M.R.

Show description

Read or Download An introduction to conformal field theory (hep-th 9910156) PDF

Similar quantum physics books

New PDF release: Quantum integrability of bosonic massive Thirring model in

By utilizing a variation of the quantum inverse scattering approach, commutation relationsbetween all parts of the quantum monodromy matrix of the bosonic massiveThirring (BMT) version are got. utilizing these relatives, the quantum integrabilityof BMT version is demonstrated and the S-matrix of two-body scatteringbetween the corresponding quasiparticles has been received.

Additional resources for An introduction to conformal field theory (hep-th 9910156)

Sample text

If the number of irreducible representations is infinite. However, this does not seem to be correct since the triplet algebra [150] has only finitely many irreducible representations, but contains indecomposable representations in their fusion products that lead to logarithmic correlation functions [151]. Logarithmic conformal field theories are not actually pathological; as was shown in [41] a consistent local conformal field theory that satisfies all conditions of a local theory (including modular invariance of the partition function) can be associated to this triplet algebra.

We therefore define, more precisely, the fusion rule Nijk to be the multiplicity with which the representation conjugate to φk appears in φi (u1 )φj (u2). The action of the meromorphic fields (or rather their modes) on the product of the two fields can actually be described rather explicitly using the comultiplication formula [40, 125, 126]:† let us denote by A the algebra of modes of the meromorphic fields. A comultiplication is a homomorphism ∆ : A → A ⊗ A, Vn (ψ) → ∆(1)(Vn (ψ)) ⊗ ∆(2)(Vn (ψ)) , (224) and it defines an action on the product of two fields as Vn (ψ) φi (u1 )φj (u2) = ∆(1)(Vn (ψ))φi (u1) ∆(2)(Vn (ψ))φj (u2) .

The equation that comes from the coefficient of xs−1 , s(s − 1) + s = s2 = 0 . (241) Generically, the indicial equation has two distinct roots (that do not differ by an integer), and for each solution of the indicial equation there is a solution of the original differential equation that is of the form (240). However, if the two roots coincide (as in our case), only one solution of the differential equation is of the form (240), and the general solution to (239) is F (x) = AG(x) + B [G(x) log(x) + H(x)] , (242) where G and H are regular at x = 0 (since s = 0 solves (241)), and A and B are constants.

Download PDF sample

An introduction to conformal field theory (hep-th 9910156) by Gaberdiel M.R.


by Jeff
4.2

Rated 4.95 of 5 – based on 13 votes