We study the conformal boundary conditions of the dilute O(n) model in two dimensions. A pair of mutually dual solutions to the boundary Yang-Baxter equations are found. They describe anisotropic special transitions, and can be interpreted in terms of symmetry breaking interactions in the O(n) model. We identify the corresponding boundary condition changing operators, Virasoro characters, and c...

We study the mutual consistency of twisted boundary conditions in the coset conformal field theory G/H. We calculate the overlap of the twisted boundary states of G/H with the untwisted ones, and show that the twisted boundary states are consistently defined in the diagonal modular invariant. The overlap of the twisted boundary states is expressed by the branching functions of a twisted affine ...

In this work we have studied the QCD phase structure and critical dynamics related to 3-$d$ $O(4)$ $Z(2)$ symmetry universality classes in two-flavor quark-meson low energy effective theory within functional renormalization group approach. We employed expansion of Chebyshev polynomials solve flow equation for order-parameter potential. The chiral transition line limit, end points explicit break...

Discussions on the Langevin Twins ‘paradox’ are most often based on a “triangular” diagram which outlines the twins spacetime travels. It won’t be our way, avoiding what we think to be a problem at the basis of numerous controversies. Our approach relies on a fundamentally different Equivalence Principle, namely the so-called “Punctual Equivalence Principle” (GB01), from which we think that a v...

the mathematical aspect of cartographic mapping is a process which establishes a unique connection between points of the earth’s sphere and their images on a plane. it was proven in differential geometry that an isometric mapping of a sphere onto a plane with all corresponding distances on both surfaces remaining identical can never be achieved since the two surfaces do not possess the same gau...

In this work we have studied the QCD phase structure and critical dynamics related to 3-$d$ $O(4)$ $Z(2)$ symmetry universality classes in two-flavor quark-meson low energy effective theory within functional renormalization group approach. We employed expansion of Chebyshev polynomials solve flow equation for order-parameter potential. The chiral transition line limit, end points explicit break...

These pedagogical lectures present some material, classical or more recent, on (Rational) Conformal Field Theories and their general setting " in the bulk " or in the presence of a boundary. Two well posed problems are the classification of modular invariant partition functions and the determination of boundary conditions consistent with conformal invari-ance. It is shown why the two problems a...

A generalization of the Coulomb Gas model with modular SL(2, Z)symmetry allows for a discrete infinity of phases which are characterized by the condensation of dyonic pseudoparticles and the breaking of parity and time reversal. Here we study the phase diagram of such a model by using renormalization group techniques. Then the symmetry SL(2, Z) acting on the two-dimensional parameter space give...

We investigate the quantum structure of Witten’s cubic open bosonic string field theory by computing the one-loop contribution to the open string tadpole using both oscillator and conformal field theory methods. We find divergences and a breakdown of BRST invariance in the tadpole diagram arising from tachyonic and massless closed string states, and we discuss ways of treating these problems. F...