PHY2406H

Today we explain the light-front gauge incarnation of kappa-symmetry, a local fermionic symmetry on the worldline/worldsheet, which permits construction of a manifestly supersymmetric action. We start by constructing the story for the superparticle. Then we move to the superstring. In particular, we explain how fixing the light-front gauge makes the Green-Schwarz superstring action quadratic (not quartic!) in fermions. From this, we show how the equations of motion produce the familiar Klein-Gordon equation on the worldsheet for the transverse coordinates and – this is the “magic” part – the Dirac equation for their [spacetime] superpartners. This is all done in flat spacetime (the classic prototype).

Today we introduced spinors in various dimensions D=p+q. In particular, starting from the basic Dirac matrix algebra anticommutation relations, we derived the fact that Dirac spinors in D dimensions have dimensionality 2^[D/2].

Today we restarted our discussion of the superstring, and built the state space using Ramond and Neveu-Schwarz fermions.

This time we discuss

• construction of the closed bosonic string state space;
• supersymmetric string theory.

This lecture covers the physics of how the critical dimension and zero-point mass shift come about.  Here are my notes from today’s lecture.

Ahhhh, open string quantization, at last!

In light-front gauge, that is.

Next time, we prove closure of the Lorentz algebra if the critical dimension is given by (d-2)=24 and the mass-squared shift is -1 (in appropriate units).

Today’s chapter of Zwiebach, Ch.11, discusses [first] quantization for the relativistic point particle (with geometric action) in light front gauge. LF gauge leads to a number of simplifications. We also construct the Poincare symmetry generators as a prelude to open string quantization in LF gauge.

P.S.: I hope you are all suitably impressed that I am working on Waitangi Day, New Zealand‘s annual national holiday!

Here are the lecture notes for quantization of fields of spin s=0,1,2 in LF gauge.

The relevant chapter of Zwiebach is Chapter 10, which runs through light-front quantization of fields carrying intrinsic spin s=0,1,2.