Abstract
We consider the basic radius changing conformal interface for a free compact boson. After investigating different theoretical aspects of this object we focus on the fusion of this interface with conformal boundary conditions. At fractions of the self-dual radius there exist exceptional D-branes. It was argued in [1] that changing the radius in the bulk induces a boundary RG flow. Following [2] we conjecture that fusing the basic radius changing interface (that changes the radius from a fraction of the self-dual radius) with the exceptional boundary conditions gives the boundary condition which is the end point of the RG flow considered in [1]. By studying the fusion singularities we recover RG logarithms and see, in particular instances, how they get resummed into power singularities. We discuss what quantities need to be calculated to gain full non-perturbative control over the fusion.
Highlights
Where L(ni) and L(ni) are the left and right Virasoro algebra modes in the corresponding theories
Following [2] we conjecture that fusing the basic radius changing interface with the exceptional boundary conditions gives the boundary condition which is the end point of the renormalisation group (RG) flow considered in [1]
By studying the fusion singularities we recover RG logarithms and see, in particular instances, how they get resummed into power singularities
Summary
We consider a free compact boson φ(x, τ ) in two-dimensional space-time with action. 8π dσ dt((∂tφ)2 − (∂xφ)). Zn, z corresponds to the original surface Σ with punctures at zi and with an additional puncture at z = 0, and the integration is taken over Σ minus the unit discs cut out in the zi coordinates around the punctures pi Associated with this deformation formula is a canonical flat connection Γon the deformation moduli space [33, 34] which can be used to construct parallel transport of states between the undeformed and deformed state spaces. We note that it is the same as the leading order linear divergence in the g-factor of perturbation interfaces (defects) discussed in [35], it is associated with the boundary identity field that lives on the boundary of the integration region It was shown in [33] that the Bogolyubov transformation (2.10), (2.12) is infinitesimally equivalent to the transport associated with the connection Γfor the radius changing deformation of a free boson. In CFT language each primary is mapped into an infinite combination of descendants
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