Hi I'm trying to understand very basic aspects of the WZW model, and would appreciate any help. The main thing i don't get is how you replace(adsbygoogle = window.adsbygoogle || []).push({});

[tex]

I = \frac{1}

{2}\int\limits_0^1 {\gamma _{\alpha \beta } } \frac{{dx^\alpha }}

{{d\tau }}\frac{{dx^\beta }}

{{d\tau }}d\tau

[/tex]

with

[tex]

I = \frac{{ - k}}

{4}\int\limits_0^1 {tr} (g^{ - 1} \frac{d}

{{d\tau }}g)^2 d\tau

[/tex]

for some group g

My thoughts are I don't know how the metric enters and the connection doesn't. For example consider

[tex]

{\mathbf{g}} = P\exp \int\limits_0^1 {\frac{{dx^\mu }}

{{d\tau }}} {\mathbf{A}}_\mu d\tau

[/tex]

then

[tex]

{\mathbf{g}}^{ - {\mathbf{1}}} \frac{d}

{{d\tau }}{\mathbf{g}} = - \frac{{dx^\mu }}

{{d\tau }}{\mathbf{A}}_\mu

[/tex]

so the connection enters but not sure how the metric does cos I'm not familiar with any identity that says

[tex]

tr\left( {{\mathbf{A}}_\mu {\mathbf{A}}_\tau } \right) = \gamma _{\mu \tau }

[/tex]

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# WZW model

Can you offer guidance or do you also need help?

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