Two-loop chiral anomalies in open superstrings

Abstract

We partially analyze the two-loop box and hexagon chiral gauge anomalies in D=6 and 10 dimensions for super-Yang-Mills theories. We apply these results to the SO(32) open superstring and show that the leading gauge'anomaly vanishes at two-loop order while the subleading gauge anomalies, the mixed anomalies, and the subleading chiral gravitational anomalies may all be canceled with appropriate counterterms. To do this in field theory it is necessary to include a term Z?(TrF 2 ) 2 which is absent at one-loop order in the zero-slope limit of the SO(32) superstring.

SO(8) and G2×G2 N=1 supergravities in D=6

“…First we observe that the leading one-loop gauge anomaly in D = 6 is proportional to N − 8 for SO(N) gauge groups. (Likewise one can show that the leading 2-loop [11] and 3-loop [12]perturbative gauge anomalies also have factors of N − 8.) The SO(8) that cancels this anomaly has 28 generators, and one might expect this fact to play a prominent role in the cancellation of both the leading perturbative gravitational anomaly and the global gravitational anomaly.…”