Simulations of the self-avoiding walk (SAW) are performed in a half-plane and a cutplane (the complex plane with the positive real axis removed) using the pivot algorithm. We test the conjecture of Lawler, Schramm and Werner that the scaling limit of the two-dimensional SAW is given by Schramm’s Stochastic Loewner Evolution (SLE). The agreement is found to be excellent. The simulations also tes...

We analyze the conformal invariance of submanifold observables associated with k-branes in the AdS/CFT correspondence. For odd k, the resulting observables are conformally invariant, and for even k, they transform with a conformal anomaly that is given by a local expression which we analyze in detail for k = 2.

The conformal invariance of unimodular gravity survives quantum corrections, even in the presence of conformal matter. Unimodular gravity can actually be understood as a certain truncation of the full Einstein-Hilbert theory, where in the Einstein frame the metric tensor has unit determinant. Our result is compatible with the idea that the corresponding restriction in the functional integral is...

Several aspects of fusion rings and fusion rule algebras, and of their manifestations in two-dimensional (conformal) field theory, are described: diagonalization and the connection with modular invariance; the presentation in terms of quotients of polynomial rings; fusion graphs; various strategies that allow for a partial classification; and the role of the fusion rules in the conformal bootst...