String Theory
All Roads Lead to String Theory (Polchinski)
Prior to the First Superstring Revolution
Early History S-Matrix Theory
Regge Trajectory
Bosonic String Theory Worldsheet
Bosonic String Theory
String Perturbation Theory
Tachyon Condensation
Supersymmetric Revolution Supersymmetry
RNS Formalism
GS Formalism
Superstring Revolutions
First Superstring Revolution GSO Projection
Type II String Theory
Type IIB String Theory
Type IIA String Theory
Type I String Theory
Type H String Theory
Type HO String Theory
Type HE String Theory
Second Superstring Revolution T-Duality
Horava-Witten String Theory
Holographic Principle
N=4 Super-Yang-Mills Theory
BFSS Matrix Theory
Matrix String Theory
(2,0) Theory
Twistor String Theory
String Field Theory
Pure Spinor Formalism
After the Revolutions
Phenomenology String Theory Landscape
Minimal Supersymmetric Standard Model
String Phenomenology


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String Perturbation Theory (or Perturbative String Theory) is a method for calculating the S-Matrix of a String Theory vacuum - the asymptotic scattering behavior of weakly coupled strings moving on that geometric background - as a sum over string histories of different topologies, analogous to the sum over Feynman diagrams employed in perturbative quantum field theory.

Also as in QFT, these scattering amplitudes only describe transitions from a state in the distant past to a state in the distant future. For the finite-time evolution of strings, one needs a more advanced formalism like String Field Theory.

BasicsEdit this section

Schematically, the scattering amplitude to start with strings in a state $ |a\rangle $ and to finish with strings in a state $ |b\rangle $ is[1]

$ \langle b|S|a\rangle = \sum_{\mathrm{topology}} \int \mathcal D X \mbox{ } e^{-S[X]} O_a[X] O_b[X] $

where $ DX $ stands for a Measure on the Moduli Space of a particular topological class of Riemann Surfaces, $ S[X] $ is the action of a particular history from that class, and $ O[X] $ is a set of Vertex Operators encoding the initial state $ |a\rangle $ or final state $ |b\rangle $.

ReferencesEdit this section

  1. After equation 2.6, Uranga, "Introduction to String Theory"[1].