Black Holes in String Theory [thesis] by J. Maldacena

By J. Maldacena

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Let us work out the properties of (1,5) and (5,1) strings. 1) where two of the coordinates have Neumann-Neumann boundary conditions (X 0 , X 9 ), four coordinates have Dirichlet-Dirichlet boundary conditions (X 1 , X 2 , X 3 , X 4 ) and the other four have Neumann-Dirichlet conditions (X 5 , X 6 , X 7 , X 8 ). The vacuum energy of the worldsheet bosons is E = 4(−1/24 + 1/48). Consider the NS sector for the worldsheet fermions, the 4 that are in the ND directions will end up having R-type quantization conditions.

The potential is given by V ∼ a D12 + D13 + D14 . D-terms have a † a ′ the structure D ∼ φ T φ where φ are components of the hypermultiplets and T a are the gauge group generators. As an example of D-terms let us consider the pure YM Lagrangian dimensionally reduced to six dimensions. 1) a IJ 6 a2 a2 a2 D12 + D13 + D14 The index of Q1 reminds us that in the aplication of interest these fivebranes are D-strings, hopefully this will not cause confusion. 2) one should use the Jacobi identity for the commutators.

Let us work out the properties of (1,5) and (5,1) strings. 1) where two of the coordinates have Neumann-Neumann boundary conditions (X 0 , X 9 ), four coordinates have Dirichlet-Dirichlet boundary conditions (X 1 , X 2 , X 3 , X 4 ) and the other four have Neumann-Dirichlet conditions (X 5 , X 6 , X 7 , X 8 ). The vacuum energy of the worldsheet bosons is E = 4(−1/24 + 1/48). Consider the NS sector for the worldsheet fermions, the 4 that are in the ND directions will end up having R-type quantization conditions.

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