Abstract
Using Supergravity on AdS7×S4 we calculate the bulk one-loop contribution to the conformal anomaly of the (2,0) theory describing N coincident M5 branes. When this is added to the tree-level result, and an additional subleading order contribution calculated by Tseytlin, it gives an expression for the anomaly that interpolates correctly between the large N theory and the free (2,0) tensor theory corresponding to N=1. Thus we can argue that we have identified the exact N-dependence of the anomaly, which may have a simple protected form valid away from the large N limit.
Highlights
The low energy (2, 0) theory describing N coincident M5 branes is not yet well understood
For the (2, 0) theory the leading order coefficient of the Euler invariant in the type-A anomaly is related to the four-point correlator of the stress tensor, while the coefficients of Weyl invariants in the type-B anomaly depend on the two and three point correlators
If we look at the leading order result [12] for the (2, 0) conformal anomaly, we discover that the type-B anomaly is given by 4N3 times that for the free theory, while the type-A anomalies have a different ratio, 16N3/7 [1]
Summary
The low energy (2, 0) theory describing N coincident M5 branes is not yet well understood. It is given in general by a sum of type-A and type-B anomalies proportional to Euler and Weyl invariants respectively, and in the N = 4 SYM theory these are related respectively to three and two point correlators of the stress tensor. For the (2, 0) theory the leading order coefficient of the Euler invariant in the type-A anomaly is related to the four-point correlator of the stress tensor, while the coefficients of Weyl invariants in the type-B anomaly depend on the two and three point correlators. In [9,10,11] we checked the sub-leading order correction to the conformal anomaly of N = 4 SYM by a oneloop calculation in AdS5 × S5 supergravity.
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