By Mohaupt T.

We supply a pedagogical creation to thread idea, D-branes and p-branesolutions.

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A paedagogical treatment of the relation between the GSO projection and boundary conditions in the path integral can be found in [6]. 54 5 Thomas Mohaupt p-Branes in type II string theories In this section we discuss a class of solitons of the type II string theories, which turn out to be alternative descriptions of the D-branes introduced earlier. 1 Effective actions of type II string theories The effective actions for the massless states of type IIA/B superstring theory are the corresponding type IIA/B supergravity actions.

127) Therefore shifting the dilaton by a constant a, Φ(X) → Φ(X) + a (128) has the effect of shifting the total action (124) by a constant proportional to the Euler number: S → S + aχ(g) . (129) For the corresponding partition function this is equivalent to rescaling the coupling by ea : ∞ Z= κ g=0 −χ(g) DXDhe −S −→ ∞ (κea )−χ(g) DXDhe−S . (130) g=0 This shows that the coupling constant κ and vacuum expectation value Φ of the dilaton are not independent. To clarify the physical meaning of both quantities, we now investigate the effective action of the massless modes.

197) Spectrum and GSO projection for closed strings. Let us next study the spectrum of closed RNS strings. The masses of states are determined by ˜ −a α M 2 = 2(N − ax + N ˜x ) , ˜ N − ax = N − a ˜x , with normal ordering constants aR = 0 = a ˜R and aN S = (198) 1 2 =a ˜N S . 48 Thomas Mohaupt We start by listing the first states in the NS-NS sector: Occupation Mass States ˜ = 0 α M 2 = −2 |k N =N ˜= N =N 1 2 α M2 = 0 ˜ = 1 α M2 = 2 N =N bµ−1/2˜bν−1/2|k αµ−1α ˜ ν−1|k (199) αµ−1˜bν−1/2˜bρ−1/2|k bµ−1/2bν−1/2α ˜ ρ−1|k bµ−1/2bν−1/2˜bρ−1/2˜bσ−1/2|k All these states are bosons, and at the massless level we recognize the graviton, the dilaton and the antisymmetric tensor.