We show that the SU(N), level-1 Wess-Zumino-Witten conformal field theory provides a natural realization of the Yangian Y(sl~) for N _> 3. We also construct a hamiltonian/-/2 which commutes with the Yangian generators and study its spectrum. Our results, which generalize work by Haldane et al. [ 1 ], provide the field theory extension of the algebraic structure of the SU(N) Haldane-Shastry spin...

This lecture note covers topics on boundary conformal field theory, modular transformations and the Verlinde formula, and boundary logarithmic CFT. An introductory review on CFT with boundary and a discussion of its applications to logarithmic cases are given. LCFT at c = −2 is mainly discussed. This article is based on the lectures at the International Summer School on Logarithmic Conformal Fi...

The presence of infinite dimensional chiral symmetries is central to the study of two dimensional conformal field theories. These symmetries, called chiral algebras, are formed by the purely holomorphic and purely anti-holomorphic fields, respectively. How the field content of a conformal field theory (CFT) is organised into representations of the chiral algebras is encoded in the fusion ring. ...

Using conformal field theory, we derive several new crossing formulae at the two-dimensional percolation point. High-precision simulation confirms these results. Integrating them gives a unified derivation of Cardy’s formula for the horizontal crossing probability h(r), Watts’ formula for the horizontal– vertical crossing probability hv(r) and Cardy’s formula for the expected number of clusters...

Relative entropy is a measure of distinguishability for quantum states, and it plays a central role in quantum information theory. The family of Renyi entropies generalizes to Renyi relative entropies that include, as special cases, most entropy measures used in quantum information theory. We construct a Euclidean path-integral approach to Renyi relative entropies in conformal field theory, the...

We reconsider the problem of deforming a conformal field theory to a neighboring theory which is again critical. An invariant formulation of this problem is important for understanding the underlying symmetry of string theory. We give a simple derivation of A. Sen’s recent formula for the change in the stress tensor and show that, when correctly interpreted, it is coordinate-invariant. We give ...

Conformal field theories with correlation functions which have logarithmic singularities are considered. It is shown that those singularities imply the existence of additional operators in the theory which together with ordinary primary operators form the basis of the Jordan cell for the operator L0. An example of the field theory possessing such correlation functions is given.

Giant gravitons in AdS5 × S5, and its orbifolds, have a dual field theory representation as states created by chiral primary operators. We argue that these operators are not single-trace operators in the conformal field theory, but rather are determinants and subdeterminants of scalar fields; the stringy exclusion principle applies to these operators. Evidence for this identification comes from...

The simplest possible noncommutative harmonic oscillator in two dimensions is used to quantize the free closed bosonic string in two flat dimensions. The partition function is not deformed by the introduction of noncommutativity, if we rescale the time and change the compactification radius appropriately. The four point function is deformed, preserving, nevertheless, the sl(2,C) invariance. Fin...