Anomaly Cancellation...



  1. String Theory: (TOE)

    Schwarz-Green Anomaly Cancellation Equasions (1984):

    [tex]S_o = \int d^o xe \left[- \left( \frac{1}{2 K^2} \right) R - \left( \frac{1}{K^2} \right) \left( \varphi^-2 \right) \vartheta_r \varphi \vartheta^n \varphi - \left( \frac{1}{4 g^2} \right) \right]...[/tex]

    [tex]... \left[ \left( \varphi^-3 \right) F_\mu ^o F^\mu - \left( \frac{ 3 K^2}{2 g^4} \right) \left( \varphi^-2 \right) H_p H^.ky \right][/tex]

    [tex]H = dB + W_y ^o - W_l ^o[/tex]
    [tex]S_a = dA + \left[ A_1 \Lambda \right][/tex]
    [tex]S_w = d \Theta + \left[ W_1 \Theta \right][/tex]
    [tex]S_b = -tr \left( A_1 d \Lambda \right) + tr \left( W d \Theta \right)[/tex]

    Gravitational Anomaly:
    [tex] \left( \frac{n496}{64} \right) \left[ \frac{1}{5870} trR^6 + \frac{ 1}{4379} trR^2 trR^4 + \frac{ 1}{10346} \left( trR^2 \right) ^3 \right]...[/tex]
    [tex]... + \frac{ 1}{864} trR^2 trR^4 + \frac{ 1}{1536} \left( trR^2 \right) ^3[/tex]

    Yang-Mills Anomaly:
    [tex]- \frac{ 1}{15} \left( p - 32 \right) trF^6 +15 \left( p - 2 \right) tr F^2 \left( \left( p - 8 \right) trF^4 + 3 \left(trF^2 \right) ^2 \right)[/tex]

    [tex]p = 32[/tex]
    [tex]n = \frac{ 1}{2} p \left( p - 1 \right) \left( for SO \left( p \right) \right)[/tex]
    [tex]n = \frac{1}{2} \left( 32 \right) \left( 31 \right)[/tex]
    [tex]n = 496[/tex]

    Note! These equasions have not been compiled completely accurately with the actual equasions. If anyone has more accurate equasions, please post them in latex format and I will amend my source code.

    These equasions contain 'anomalies'.

    Reference:
    http://www.pbs.org/wgbh/nova/elegant/program.html

     
    Last edited: Jan 3, 2004
  2. jcsd
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