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By S. Vongehr

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Additional resources for Black Hole Thermodynamics in Semiclassical, Superstring Theory

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If the (say) two colliding open strings are a bosonic one and a fermionic one the emitted particle will be a fermion. Then the calculation of the D-brane decay to lowest order in string coupling means calculation of the disc amplitude where one bosonic and one fermionic Vertex operator are on the boundary of the disc and a fermionic closed string vertex operator is put into the bulk of the disc. On fermionic decay see [Gubser,97] and [Das et al,97]. ,96]. Denoting the emission process for the configuration of branes as |i >→ |f > one may write: dΓD ∝ dd−1 k δ[k0 − 2nL ] | < f |Hint |i > |2 Ref f k0 (191) If the initial state is not known an averaging over initial states will be required.

Et al,96]. ,97]. 4 Hawking Decay Charges and anti charges can annihilate each other. For example two D-strings combine with a D-¯ 1-brane (↑ + ↑ + ↓) resulting in one D-string with left and right moving momentum. Open strings with nR units of momentum 1/Ref f can combine with left moving strings carrying nL = nR units of momentum resulting in closed strings with P9 = 0 and total mass M = R2nefLf which in turn can leave the D-branes and tunnel through the outer horizon in case of a black hole. The 49 emission of charged particles (P9 = 0) is suppressed because their momentum has to be quantised in units of 1/R9 which needs the right numbers nL and nR of momentum units that happen to combine and results in a quite massive particle (1/R9 ) anyway.

But on the D-brane side of the comparison between D-brane configuration and supergravity effective theory one has a very clear topological picture with the entropy coming from the degeneracy of possible numbers of branes and possible windings — especially for BPS states that have nm = 0 where n is the momentum quantum number and m counts the winding because T-duality is (n ↔ m)-duality. Cranking up the coupling there is no reason to assume this topological picture will change as long as one does not encounter phase transitions.

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