# Anomaly Cancellation...

by Orion1
Tags: anomaly, cancellation
 P: 989 String Theory: (TOE) Schwarz-Green Anomaly Cancellation Equasions (1984): $$S_o = \int d^o xe \left[- \left( \frac{1}{2 K^2} \right) R - \left( \frac{1}{K^2} \right) \left( \varphi^-2 \right) \vartheta_r \varphi \vartheta^n \varphi - \left( \frac{1}{4 g^2} \right) \right]...$$ $$... \left[ \left( \varphi^-3 \right) F_\mu ^o F^\mu - \left( \frac{ 3 K^2}{2 g^4} \right) \left( \varphi^-2 \right) H_p H^.ky \right]$$ $$H = dB + W_y ^o - W_l ^o$$ $$S_a = dA + \left[ A_1 \Lambda \right]$$ $$S_w = d \Theta + \left[ W_1 \Theta \right]$$ $$S_b = -tr \left( A_1 d \Lambda \right) + tr \left( W d \Theta \right)$$ Gravitational Anomaly: $$\left( \frac{n496}{64} \right) \left[ \frac{1}{5870} trR^6 + \frac{ 1}{4379} trR^2 trR^4 + \frac{ 1}{10346} \left( trR^2 \right) ^3 \right]...$$ $$... + \frac{ 1}{864} trR^2 trR^4 + \frac{ 1}{1536} \left( trR^2 \right) ^3$$ Yang-Mills Anomaly: $$- \frac{ 1}{15} \left( p - 32 \right) trF^6 +15 \left( p - 2 \right) tr F^2 \left( \left( p - 8 \right) trF^4 + 3 \left(trF^2 \right) ^2 \right)$$ $$p = 32$$ $$n = \frac{ 1}{2} p \left( p - 1 \right) \left( for SO \left( p \right) \right)$$ $$n = \frac{1}{2} \left( 32 \right) \left( 31 \right)$$ $$n = 496$$ 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