• Like in QFT, where we see the particles as point-like objects, in string theory we regard strings as two-dimensional objects. Therefore, we would talk about the world sheet in string theory, which is a two-dim surface where the string propagates. And for Branes, it is world-volume. And so the string action is given by the Nambu-Goto action, which is an integral over the world-sheet coordinates.

• Symmetries in Bosonic String theory: Poincare, Reparametrization, and Weyl Scaling.

• While solving the equation of motion of N-G action: boundary conditions will appear:

1. Closed string: periodic conditions.

2. Open string: Dirichlet Conditions(this will give rise to the Dp-brane, where "D" is for Dirichlet) and Neumann conditions.

• Bosonic String state: bosonic string includes tachyon state(the mass is negative when D>2), and excited states. By requiring the first excited state to be massless, we need to determine the critical dimension as D=26.

• Superstring: 

1. Rammond-Neveu-Schwarz(RNS) formalism: make world-sheet SUSY manifest.

2. Green-Schwarz(GS) formalism: make space-time SUSY manifest.

• RNS: By introducing supersymmetry on the world sheet, we include fermions naturally.

• Five different superstring theories are dual to each other.

• Low energy effective field theory: Type IIB supergravity, which cannot be compactified from 11-dimension supergravity (the low energy effective theory of M theory). IIB supergravity has SL(2, R) symmetry, and IIB superstring has SL(2, Z) symmetry.

• The conformal transformation includes Lorentz, translation, scaling, and special conformal transformations.

• In D-dimensional Minkowski space, the conformal group is SO(D,2), a finite group. (or SO(D+1, 1) as a rotation group like Lorentz)

• On the string world sheet, it is a 2-dimensional conformal field theory. The generators are Virasoro Operators that satisfy the Virasoro Algebra.

• As for primary and descendant operators, they are covered in my research note.

• State-Operator Correspondence and Operator Product Expansion.

• Conformal symmetry completely constrains the two-point and three-point correlation function, but not the four-point.

• The pros of Spinor Helicity Formulism can be understood better in all massless particle scattering. The redundancy of the gauge is still preserved in amplitudes using traditional Feynman rules. We can go to the little group of Lorentz for the massless cases. We can then calculate the so-called helicity amplitude by indicating the helicity of each particle.

• Gluon-scattering. All positive or negative helicity amplitudes vanish. Only one negative or one positive helicity amplitude also vanishes. So the first non-vanishing one is the so-called MHV amplitudes ("MHV "is maximal helicity violating, which means only two negative helicity gluons).

This construction of traversable wormhole is introduced by Gao-Jafferies-Wall. 

There are several conjectures so far that can be used to compute the holographic complexity.  Complexity=Volume,   Complexity=Action,   Complexity=Volume(version 2),   and a more generalized Complexity=(almost)Anything.