Duality rotations for interacting fields

Non-renormalization for non-supersymmetric black holes

“…Our claim generalizes a result by Gaillard and Zumino [16]. They showed that, if a Lagrangian L depends on a duality-invariant parameter α, and further that the duality…”

“…• Duality: the equations of motion of classical electrodynamics are invariant under electromagnetic duality but the corresponding classical action is not [16]. We show that duality constrains the dependence of the quantum action on the explicit field strength and, in the case of Einstein-Maxwell theory, eliminates it entirely.…”

“…In section 4.3 (and also appendix C.1) we will show that all four-derivative corrections corrections to the action (4.1) must in fact be invariant under the duality symmetry (4.4) even though, as is well-known, the two-derivative action (4.1) is not invariant under duality (4.4), but rather must transform in a very particular way in order that the equations of motion respect duality symmetry [16]. In anticipation of this result we proceed to form all possible Lorentz invariants from I µνρσ and the Riemann tensor by contraction of Lorentz indices.…”

“…A common quantitative measure of the logarithmic corrections is the contribution of these classically marginal operators to the trace of the renormalized energy momentum tensor 16) where E 4 is the Gauss-Bonnet invariant (2.8), the square of the Weyl tensor is 17) and the dots denote other four derivative operators, including those formed from matter fields. The notation is adopted from the scale anomaly of conformal field theory in nondynamical background geometries but the physical interpretation is different here.…”

“…When there are also scalars in the theory that transform under duality, such as in N = 2 supergravity, the duality symmetry can further be extended to a non-compact (sub)group of Sp(2n V + 2, R) [16]. 4 The dual field strengths G Iµν (with I = 0, .…”