We use the recently developed generalized double-copy construction to obtain an improved representation of the five-loop four-point integrand of N = 8 supergravity whose leading ultraviolet behavior we analyze using state-of-the-art loop-integral expansion and reduction methods. We find that the five-loop critical dimension where ultraviolet divergences first occur is D c = 24/5, corresponding to a D 8 R 4 counterterm. This ultraviolet behavior stands in contrast to the cases of four-dimensional N = 4 supergravity at three loops and N = 5 supergravity at four loops whose improved ultraviolet behavior demonstrates enhanced cancellations beyond implications from standard-symmetry considerations. We express this D c = 24/5 divergence in terms of two relatively simple positive-definite integrals reminiscent of vacuum integrals, excluding any additional ultraviolet cancellations at this loop-order. We note nontrivial relations between the integrals describing this leading ultraviolet behavior and integrals describing lower-loop behavior. This observation suggests not only a path towards greatly simplifying future calculations at higher loops, but may even allow us to directly investigate ultraviolet behavior in terms of simplified integrals, avoiding the construction of complete integrands.

We present new formulas for one-loop ambitwistor-string correlators for gauge theories in any even dimension with arbitrary combinations of gauge bosons, fermions and scalars running in the loop. Our results are driven by new all-multiplicity expressions for tree-level two-fermion correlators in the RNS formalism that closely resemble the purely bosonic ones. After taking forward limits of tree-level correlators with an additional pair of fermions/bosons, one-loop correlators become combinations of Lorentz traces in vector and spinor representations. Identities between these two types of traces manifest all supersymmetry cancellations and the power counting of loop momentum. We also obtain parity-odd contributions from forward limits with chiral fermions. One-loop numerators satisfying the Bern-Carrasco-Johansson (BCJ) duality for diagrams with linearized propagators can be extracted from such correlators using the well-established tree-level techniques in Yang-Mills theory coupled to biadjoint scalars. Finally, we obtain streamlined expressions for BCJ numerators up to seven points using multiparticle fields.

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The coefficient of the dimensionally regularized two-loop R 3 divergence of (nonsupersymmetric) gravity theories has recently been shown to change when non-dynamical three forms are added to the theory, or when a pseudo-scalar is replaced by the anti-symmetric two-form field to which it is dual. This phenomenon involves evanescent operators, whose matrix elements vanish in four dimensions, including the Gauss-Bonnet operator which is also connected to the trace anomaly. On the other hand, these effects appear to have no physical consequences in renormalized scattering processes. In particular, the dependence of the two-loop four-graviton scattering amplitude on the renormalization scale is simple. In this paper, we explain this result for any minimally-coupled massless gravity theory with renormalizable matter interactions by using unitarity cuts in four dimensions and never invoking evanescent operators.

In this paper, we develop an improved method for directly calculating double-copy-compatible tree numerators in (super-)Yang-Mills and Yang-Mills-scalar theories. Our new scheme gets rid of any explicit dependence on reference orderings, restoring a form of crossing symmetry to the numerators. This in turn improves the computational efficiency of the algorithm, allowing us to go well beyond the number of external particles accessible with the reference order based methods. Motivated by a parallel study of one-loop BCJ numerators from forward limits, we explore the generalization to include a pair of fermions. To improve the accessibility of the new algorithm, we provide a Mathematica package that implements the numerator construction. The structure of the computation also provides for a straightforward introduction of minimally-coupled massive particles potentially useful for future computations in both classical and quantum gravity.

We evaluate one-loop amplitudes of N = 4 supergravity in D dimensions using the double-copy procedure that expresses gravity integrands in terms of corresponding ones in Yang-Mills theory. We organize the calculation in terms of a set of gauge-invariant tensors, allowing us to identify evanescent contributions. Among the latter, we find the matrix elements of supersymmetric completions of curvature-squared operators. In addition, we find that such evanescent terms and the U(1)anomalous contributions to one-loop N = 4 amplitudes are tightly intertwined. The appearance of evanescent operators in N = 4 supergravity and their relation to anomalies raises the question of their effect on the known four-loop divergence in this theory. We provide bases of gauge-invariant tensors and corresponding projectors useful for Yang-Mills theories as a by-product of our analysis.Recent explicit calculations have shown that gravity theories still have perturbative secrets waiting to be revealed. We have learned a number of surprising lessons from these calculations: results in gravity theories can be obtained directly from their Yang-Mills counterparts via a double-copy procedure [1][2][3][4]; of a curious disconnect between the leading two-loop divergence of graviton amplitudes [5,6] and the corresponding renormalizationscale dependence [7,8]; and about the surprisingly tame ultraviolet behavior of certain supergravity theories [9][10][11][12]. These lessons augur more surprises to come. In this paper we investigate the role of evanescent effects in the one-loop four-point amplitude of N = 4 supergravity, along with its relation to the U(1) anomaly in the duality symmetry of this theory [13][14][15].Evanescent effects arise from operators whose matrix elements vanish when working strictly in four dimensions, but give rise to nonvanishing contributions in dimensional regularization. Such contributions originate from the cancellation of poles against small deviations in the four-dimensional limit; that is, they are due to ǫ/ǫ effects, where ǫ = (4−D)/2 is the dimensional regulator. Although such effects might at first appear to be a mere technicality, they turn out to play an important role [7] in understanding ultraviolet divergences of Einstein gravity in the context of dimensional regularization [5,6]. In particular, the Gauss-Bonnet operator is evanescent and appears as a one-loop counterterm whose insertion at two loops contaminates the ultraviolet divergence, but results in no physical consequences in the renormalized amplitude. An important question therefore is whether a supersymmetric version of the Gauss-Bonnet operator appears in the matrix elements of N = 4 supergravity. If such an operator exists it would be important to determine its effects on the known four-loop divergence [16] of the theory.On the other hand, the N = 4 supergravity theory has an anomaly in its U(1) duality symmetry [13]. The anomaly manifests itself in the failure of certain helicity amplitudes which vanish at tree level to persist in vanishing at l...

In the low-energy effective action of string theories, non-abelian gauge interactions and supergravity are augmented by infinite towers of higher-mass-dimension operators. We propose a new method to construct one-loop matrix elements with insertions of operators D2kFn and D2kRn in the tree-level effective action of type-I and type-II superstrings. Inspired by ambitwistor string theories, our method is based on forward limits of moduli-space integrals using string tree-level amplitudes with two extra points, expanded in powers of the inverse string tension α′. Similar to one-loop ambitwistor computations, intermediate steps feature non-standard linearized Feynman propagators which eventually recombine to conventional quadratic propagators. With linearized propagators the loop integrand of the matrix elements obey one-loop versions of the monodromy and KLT relations. We express a variety of four- and five-point examples in terms of quadratic propagators and formulate a criterion on the underlying genus-one correlation functions that should make this recombination possible at all orders in α′. The ultraviolet divergences of the one-loop matrix elements are crosschecked against the non-separating degeneration of genus-one integrals in string amplitudes. Conversely, our results can be used as a constructive method to determine degenerations of elliptic multiple zeta values and modular graph forms at arbitrary weight.

Color-ordered amplitudes for the scattering of n particles in the adjoint representation of SU(N ) gauge theory satisfy constraints that arise from group theory alone. These constraints break into subsets associated with irreducible representations of the symmetric group S n , which allows them to be presented in a compact and natural way. Using an iterative approach, we derive the constraints for six-point amplitudes at all loop orders, extending earlier results for n = 4 and n = 5. We then decompose the four-, five-, and six-point group-theory constraints into their irreducible S n subspaces. We comment briefly on higher-point two-loop amplitudes.