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By Recknagel A., Schomerus V.
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Additional resources for Boundary Conformal Field Theory and the Worldsheet Approach 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. 1 A very brief reminder of closed string theory In the following few subsections, we shall describe the Polyakov action of bosonic string theory and discuss various approaches to its quantisation.
100), but built over the highest weights |k ≡ |k1 , k2 = |k sin φ, k cos φ . e. Zφφ (q) = Z00 (q). The rotation is a symmetry of the target R2 – in contrast to the two-torus, where a rotation does inﬂuence the boundary ﬁeld content. 104), the parameter x0 gives the minimal distance of the rotated brane from the origin. It is sometimes preferable to describe the same state in terms of the coordinate β = β(x0 , φ) = x0 / cos φ at which the brane intersects the 2-axis. 105) || φ; x0 = dk˜ eiβ k |k φ, cos φ where |k φ is built on the highest weight states |k˜ tan φ, k˜ .
2. e. z) G(z) = G(¯ z=¯ z >0 , G(z) = G(¯ z) z=¯ z <0 . 74) The case = 1 corresponds to the Neveu–Schwarz sector, = −1 to the Ramond sector. 74) to hold. 64), namely || D, d; x0 || D, d; x0 (N S) = || D, d; x0 ⊗ || D, d (N S) (R) = || D, d; x0 ⊗ || D, d (R) , . More speciﬁcally, || D, d; x0 is the boundary state of the bosonic system with B = 0. A non-zero B-ﬁeld may be admitted, but must then be accompanied by the corresponding gluing condition in the fermionic sector in order to preserve supersymmetry.
Boundary Conformal Field Theory and the Worldsheet Approach to D-Branes by Recknagel A., Schomerus V.