# String Theory

## Notation

• Greek letters, e.g. , for variables or indices of variables
• Std. leteters, e.g. , for indices of target space
• denotes how the Lagrangian changes wrt

## Just notes

• Gauge theories are used to obtain a "larger" space in which the symmetries (e.g. Lorentz invariance) becomes linear transforms

where is some constant (mass), and is the arclength

• Nambu-Goto action:

where

with , i.e. a matrix.

• We are pulling back the metric of the target space
• Symmetries
• Gauge symmetries:
• Reparametrizations \$δ σα = - ζα(z, σ)

• Std. parametrization:

where is called the string length, and is called tension (energy of unit of length of the string)

• Global symmetries:
• (where are the Killing coefficients)
• Polyakov action:

where

and is a symmetric metric.

1. No kinetic term implies the equations of motion are , thus the symmetries become algebraic!
• Note

for some function , which we can solve for if we know the action, but in general it can be any , and so this is an example of a non-trivial Gauge symmetry

2. Symmetries of
1. Global: