Boundary Conformal Field Theory and the Worldsheet Approach by Recknagel A., Schomerus V.

By Recknagel A., Schomerus V.

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P1 −1 (1) ) · · · ( k π(k) π 2 (k) . . π pm −1 (k) ) (with some k which does not occur in the previous cycles), then the corresponding term contributes tr (M p1 ) · · · tr (M pm ). Therefore, we have to count how many permutations π ∈ Sl can be written as products of m cycles of lengths p1 , . . , pm ; call that number c{pi } . We will “fill” the m cycles one after the other: for the first one, we can choose p1 out of l numbers and order them in (p1 − 1)! different ways (cyclic re-orderings within the cycles do not change π).

107) the coherent states are built over the ground states |kv, k . The boosted brane we have described here is located along a one-dimensional line x1 = b + vx0 where x0 is the time-like coordinate and x1 is space-like. Next, we want to show that a rotated D1-brane in a two-dimensional target is closely related to the boundary theory of two compactified bosons with Neumann boundary conditions and a B-field switched on. 94) for a rotated D1-brane and perform a T -duality along one of the two circles, say along the second coordinate X2 .

The only object that requires some further attention is the specific ground state |R, R (D,d) on which we act with our exponential. 65) for n = 0. 66) := √ ψ0μ ± iψ 0μ . ψ± 2 μ The only non-vanishing anti-commutators among the ψ± are given by μ ν = g μν . ψ+ , ψ− Let us now define the state |R, R to be the unique Ramond ground state that μ . From this we generate the |R, R (D,d) is annihilated by all the operators ψ+ α through application of some ψ− , a = d + 1, . . , D, D |R, R (D,d) a ψ− |R, R = a=d+1 where μ ψ+ |R, R = 0 for all μ = 1, .

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