Harald Ita

Recursive calculation of one-loop QCD integral coefficients

We present a new procedure, using on-shell recursion, to determine coefficients of integral functions appearing in the one-loop scattering amplitudes of gauge theories, including QCD. With this procedure, coefficients of integrals, including bubbles and triangles, can be determined without resorting to integration. We give criteria for avoiding spurious singularities and boundary terms that would invalidate the recursion. As an example where the criteria are satisfied, we obtain all cut-constructible contributions to the one-loop n-gluon scattering amplitude, Anone−loop(...−−−+++...), with split-helicity from an = 1 chiral multiplet and from a complex scalar. Using the supersymmetric decomposition, these are ingredients in the construction of QCD amplitudes with the same helicities. This method requires prior knowledge of amplitudes with sufficiently large numbers of legs as input. In many cases, these are already known in compact forms from the unitarity method.

Unexpected Cancellations in Gravity Theories

Recent computations of scattering amplitudes show that N = 8 supergravity is surprisingly well behaved in the ultraviolet and may even be ultraviolet finite in perturbation theory. The novel cancellations necessary for ultraviolet finiteness first appear at one loop in the guise of the no-triangle hypothesis. We study one-loop amplitudes in pure Einstein gravity and point out the existence of cancellations similar to those found previously in N = 8 supergravity. These cancellations go beyond those found in the one-loop effective action. Using unitarity, this suggests that generic theories of quantum gravity based on the Einstein-Hilbert action may be better behaved in the ultraviolet at higher loops than suggested by naive power counting, though without additional (supersymmetric) cancellations they diverge. We comment on future studies that should be performed to support this proposal.

MHV-Vertices for Gravity Amplitudes

We obtain a CSW-style formalism for calculating graviton scattering amplitudes and prove its validity through the use of a special type of BCFW-like parameter shift. The procedure is illustrated with explicit examples.

The no-triangle hypothesis for Script N = 8 supergravity

We study the perturbative expansion of = 8 supergravity in four dimensions from the viewpoint of the ``no-triangle hypothesis, which states that one-loop graviton amplitudes in = 8 supergravity only contain scalar box integral functions. Our computations constitute a direct proof at six-points and support the no-triangle conjecture for seven-point amplitudes and beyond.

Generalized unitarity and six-dimensional helicity

We combine the unitarity method with the six-dimensional helicity formalism of Cheung and OConnell to construct loop-level scattering amplitudes. As a first example, we construct dimensionally regularized QCD one-loop four-point amplitudes. As a nontrivial multiloop example, we confirm that the recently constructed four-loop four-point amplitude of N=4 super-Yang-Mills theory, including nonplanar contributions, is valid for dimensions D{<=}6. We comment on the connection of our approach to the recently discussed Higgs infrared regulator and on dual conformal properties in six dimensions.

Six-point one-loop N=8 supergravity NMHV amplitudes and their IR behaviour

Abstract We present compact formulas for the box coefficients of the six-graviton NMHV one-loop amplitudes in N = 8 supergravity. We explicitly demonstrate that the corresponding box integral functions, with these coefficients, have the complete IR singularities expected of the one-loop amplitude. This is strong evidence for the conjecture that N = 8 one-loop amplitudes may be expressed in terms of scalar box integral functions. This structure, although unexpected from a power counting viewpoint, is analogous to the structure of N = 4 super-Yang–Mills amplitudes. The box-coefficients match the tree amplitude terms arising from recursion relations.

Two-loop Integrand Decomposition into Master Integrals and Surface Terms

Loop amplitudes are conveniently expressed in terms of master integrals whose coefficients carry the process dependent information. Similarly before integration, the loop integrands may be expressed as a linear combination of propagator products with universal numerator-tensors. Such a decomposition is an important input for the numerical unitarity approach, which constructs integrand coefficients from on-shell tree amplitudes. We present a new method to organise multi-loop integrands into a direct sum of terms that integrate to zero (surface terms) and remaining master integrands. This decomposition facilitates a general, numerical unitarity approach for multi-loop amplitudes circumventing analytic integral reduction. Vanishing integrals are well known as integration-by-parts identities. Our construction can be viewed as an explicit construction of a complete set of integration-by-parts identities excluding doubled propagators. Interestingly, a class of horizontal identities is singled out which hold as well for altered propagator powers.

On type II strings in two dimensions

We consider type IIA/B strings in two-dimensions and their projection with respect to the nilpotent space-time supercharge. Based on the ground ring structure, we propose a duality between perturbed type II strings and the topological B-model on deformed Calabi-Yau singularities. Depending on the type II spectra, one has either the conifold or the suspended pinch point geometry. Using the corresponding quiver gauge theory, obtained by D-branes wrapping in the resolved suspended pinch point geometry, we propose the all orders perturbative partition function.

Dual conformal symmetry, integration-by-parts reduction, differential equations, and the nonplanar sector

We show that dual conformal symmetry, mainly studied in planar

Perturbative Gravity and Twistor Space

mathcal N = 4