1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Anomaly Cancellation

  1. Jan 3, 2004 #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
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you help with the solution or looking for help too?
Draft saved Draft deleted



Similar Discussions: Anomaly Cancellation
  1. Diff anomaly (Replies: 0)

  2. D!=26 anomalies (Replies: 5)

Loading...