By Recknagel A., Schomerus V.
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Additional info for Boundary Conformal Field Theory and the Worldsheet Approach to D-Branes
After sketching various approaches to ﬁrst-quantised closed strings and the route from CFT correlators to string scattering amplitudes and eﬀective actions, including supergravity, we turn to D-branes. We start with solitonic p-branes and their low-energy eﬀective action, then try to set up a dictionary between notions from target space physics and various worldsheet quantities that occurred in the ﬁrst chapter. Some more technical background material needed to build models with target space supersymmetry, and an analysis of brane-brane scattering based on CFT partition functions, are collected at the end of this chapter.
Construction of the boundary state Once more, we would like to construct a boundary state to store information about the one-point functions of our boundary theory. 57) of the gluing conditions so that all fermionic components can be considered in one go. On the other hand, we still have to distinguish between the Ramond and Neveu–Schwarz sector of the model. Once again, the boundary state for the Neveu–Schwarz sector is a bit simpler, ⎧ ⎫ ⎨ ⎬ μ ν Ωμν ψ−r ψ −r |N S ⊗ |N S . 62) Here, the ψ and ψ are left- and right-moving fermion modes acting on the bulk state space, and the whole exponential acts on the unique ground state of the NS–NS sector of the bulk theory.
The above derivation of the Moyal product from the free boson boundary CFT with non-vanishing B-ﬁeld is a special case of Kontsevich’s deformation quantisation , see also . 2 Free fermionic ﬁeld theory We are now going to extend our previous analysis of free bosonic ﬁeld theory on the upper half-plane to free two-dimensional fermions. After a brief introduction to the description of massless fermions and their boundary conditions, we shall solve the model and compute a few basic quantities.
Boundary Conformal Field Theory and the Worldsheet Approach to D-Branes by Recknagel A., Schomerus V.