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Abstract We obtain the perturbative expansion of the free energy on S 4 for four dimensional Lagrangian N $$ \mathcal{N} $$ = 2 superconformal field theories, to all orders in the ’t Hooft coupling, in the planar limit. We do so by using supersymmetric localization, after rewriting the 1-loop factor as an effective action involving an infinite number of single and double trace terms. The answer we obtain is purely combinatorial, and involves a sum over tree graphs. We also apply these methods to the perturbative expansion of the free energy at finite N , and to the computation of the vacuum expectation value of the 1/2 BPS circular Wilson loop, which in the planar limit involves a sum over rooted tree graphs.

Abstract We discuss radiation in theories with scalar fields. Our key observation is that even in flat spacetime, the radiative fields depend qualitatively on the coupling of the scalar field to the Ricci scalar: for non-minimally coupled scalars, the radiative energy density is not positive definite, the radiated power is not Lorentz invariant and it depends on the derivative of the acceleration. We explore implications of this observation for radiation in conformal field theories. First, we find a relation between two coefficients that characterize radiation, that holds in all the conformal field theories we consider. Furthermore, we find evidence that for a 1/2-BPS probe coupled to N $$ \mathcal{N} $$ = 4 super Yang-Mills, and following an arbitrary trajectory, the spacetime dependence of the one-point function of the energy momentum tensor is independent of the Yang-Mills coupling.

Abstract We derive an expression for the vacuum expectation value (vev) of the 1/2 BPS circular Wilson loop of N = 4 $$ \mathcal{N}=4 $$ super Yang Mills in terms of color invariants, valid for any representation R of any gauge group G. This expression allows us to discuss various exact relations among vevs in different representations. We also display the reduction of these color invariants to simpler ones, up to seventh order in perturbation theory, and verify that the resulting expression is considerably simpler for the logarithm of 〈W〉 R than for 〈W〉 R itself. We find that in the particular case of the symmetric and antisymmetric representations of SU(N), the logarithm of 〈W〉 R satisfies a quadratic Casimir factorization up to seventh order, and argue that this property holds to all orders. Finally, we derive the large N expansion of 〈W〉 R for an arbitrary, but fixed, representation of SU(N), up to order 1/N 2.