1. Brief review of basic string theory Bosonic string Superstring three different formulations of superstring (depending on how to deal with the fermionic coordinates): Ramond-Neveu-Schwarz (RNS), Green-Schwarz (GS), Pure spinor Vertex operators D-brane: boundary condition (directly imposing Dirichlet boundary condition, Neumann and then T-duality), boundary state representation, supergravity solution T-duality (target-space duality) closed, open string context (our focus), supergravity context Creation and annihilation operator techniques vs conformal field theory techniques

2. Bosonic string Bosonic coordinate M=0,…,25

3. Superstring: RNS formulation M=0,…,9, a=1,2 flat space action quadratic, simple for tree computation, minimal initial input In general, loop computations are complicated due to necessity to take “spin structure” into account Two loop amplitude was done first in RNS (later in pure spinor) : complicated! Not known how to write down a curved space action in general: not suitable for our purpose

4. Superstring: GS formulation M=0,…,9,  =1,…,32 we will mostly use this formulation Manifestly space-time supersymmetric Known how to write down an action in a curved background, will provide a guide how to construct the counter vertex operator Flat space action quadratic only in the light-cone gauge (otherwise quartic in  ), past attempts of covariant gauge fixing led to infinite tower of ghosts

5. Superstring: Pure spinor formulation (and some other fields) Variation of conventional GS formulation Covariant gauge fixing of GS without infinite tower of ghosts : pure spinor variable Higher loop amplitudes are much simpler Later we will quote two loop amplitudes three loop amplitudes must be done in this formulation (I believe)

6. Vertex operator Quantum mechanics (1 st quantization): convenient for two particle interaction, bra- and ket- representation Multi-particle scattering QFT String theory: relativistic QM of strings (1 st quantization), still consider multi-string scattering (QFT of strings, i.e., string field theory, is hard) states (including bra- and ket states) are often represented by vertex operators: “state-operator mapping”, computation of scattering amplitudes are most commonly formulated in terms of vertex operators

7. Vertex operators: examples Bosonic string theory

8. D-brane: string description Will be the main topic of the lectures

9. D-brane: also appears as a solution supergravity field eqs h For D3 brane

10. At the heart of AdS/CFT : two descriptions of a D-brane Dirichlet boundary conditions (open string) Supergravity solution (closed string)