A First Course in String Theory

Count the number of graviton, Kalb-Ramond, and dilation states in ten dimensions. Add these numbers up and confirm you get 64.

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Equation (13.69):

p.292 “… the states (13.69) represent one-particle graviton states … ”

Equation (13.64):

In the closed string state space, the general state of fixed momentum at the massless level is

Equation (13.68):

Equation (10.108):

For the symmetric traceless part, (with the size ), the number of independent components is

The at the end reflects the fact that if the trace is zero, the last component of the trace is not independent anymore.

In ten dimensions (),

p.292 For (a skew-symmetric matrix), the number of independent components is

p.293 “The oscillator part of (13.71) has no free indices ( is summed over), so it represents one state. It corresponds to [an] one-particle state of a massless scalar field. This field is called the *dilation*.”

— Me@2015-06-29

2015.06.29 Monday (c) All rights reserved by ACHK