<math>\begin{align}   & \left\{ \begin{align}   & m{\alpha }'\tau \hbar \varepsilon \mu \alpha \mathbf{T}ic\varsigma  \\   & \text{      }\And  \\   & \text{  }\mathsf{\mathcal{P}}\pi y\sigma \mathbf{I}\subset \mathbf{S} \\  \end{align} \right\} \\   & \text{    }Wikia \\  \end{align}</math>

Pure Spinor Formalism

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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

The Pure Spinor Formalism is a modification to the GS Formalism invented by Nathan Berkovits, in which the Ghosts are pure spinors. Unlike the GS Formalism, the Pure Spinor Formalism is manifestly spacetime-supersymmetric.

Action PrincipleEdit this section

According to equation 3.1 in [1], the action for a superstring in flat space is

S = \int \mbox{d} ^2  z (\frac{1}{2} \partial X^m \overline{\partial} X_m + p_{\alpha} \overline{\partial} \theta^{\alpha} + \omega_{\alpha} \overline{\partial} \lambda^{\alpha} + \hat{p}_{\bar{\alpha}} \partial \hat{\theta}^{\bar{\alpha}} + \hat{\omega}_{\bar{\alpha}} \partial \hat{\lambda}^{\bar{\alpha}} )

where \lambda is a bosonic pure spinor ghost and \omega its conjugate momentum (see equation 2.7 in [1]), with unhatted (\lambda, \omega) being left-moving and hatted (\hat{\lambda}, \hat{\omega}) being right-moving (see remark beneath equation 2.1 in [2]).

Mathematical OriginEdit this section

Berkovits has recently[3] obtained the pure spinor formalism for the superstring by starting with purely bosonic variables (10 space-time dimensions, and a 10-dimensional bosonic pure spinor). The fermions of the superstring arise as Ghosts in this construction.

ReferencesEdit this section

  1. 1.0 1.1 Bedoya, Oscar., Berkovits, Nathan..
  2. Berkovits, Nathan..
  3. Berkovits, Nathan..

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