Two-loop supersymmetric QCD and half-maximal supergravity amplitudes

Abstract

Using the duality between color and kinematics, we construct two-loop four-point scattering amplitudes in $\mathcal{N}=2$ super-Yang-Mills (SYM) theory coupled to $N_f$ fundamental hypermultiplets. Our results are valid in $D\le 6$ dimensions, where the upper bound corresponds to six-dimensional chiral $\mathcal{N}=(1,0)$ SYM theory. By exploiting a close connection with $\mathcal{N}=4$ SYM theory - and, equivalently, six-dimensional $\mathcal{N}=(1,1)$ SYM theory - we find compact integrands with four-dimensional external vectors in both the maximally-helicity-violating (MHV) and all-chiral-vector sectors. Via the double-copy construction corresponding $D$-dimensional half-maximal supergravity amplitudes with external graviton multiplets are obtained in the MHV and all-chiral sectors. Appropriately tuning $N_f$ enables us to consider both pure and matter-coupled supergravity, with arbitrary numbers of vector multiplets in $D=4$. As a bonus, we obtain the integrands of the genuinely six-dimensional supergravities with $\mathcal{N}=(1,1)$ and $\mathcal{N}=(2,0)$ supersymmetry. Finally, we extract the potential ultraviolet divergence of half-maximal supergravity in $D=5-2\epsilon$ and show that it non-trivially cancels out as expected.

53 pages, 5 figures, 1 table + appendices, ancillary files; v2 published version

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Cited by in corpus (48)

• Inelastic Black Hole Scattering from Charged Scalar Amplitudes
• Ultraviolet Properties of N = 8 Supergravity at Five Loops
• The Kerr-Schild double copy in curved spacetime
• Double copy for massive quantum particles with spin
• Gravitational Radiation from Color-Kinematics Duality
• Type D Spacetimes and the Weyl Double Copy
• The Five-Loop Four-Point Integrand of N=8 Supergravity as a Generalized Double Copy
• Heterotic and bosonic string amplitudes via field theory
• Two-loop supersymmetric QCD and half-maximal supergravity amplitudes
• A new gauge-invariant double copy for heavy-mass effective theory
• Double Copy from Homotopy Algebras
• BRST-Lagrangian Double Copy of Yang-Mills Theory
• Gluons and gravitons at one loop from ambitwistor strings
• On the kinematic algebra for BCJ numerators beyond the MHV sector
• The pure BRST Einstein-Hilbert Lagrangian from the double-copy to cubic order
• On the Double Copy for Spinning Matter
• Off-Shell Color-Kinematics Duality for Chern-Simons
• Gauged supergravities and spontaneous SUSY breaking from the double copy
• Unraveling conformal gravity amplitudes
• $D=6$, $\mathcal{N}=(2,0)$ and $\mathcal{N}=(4,0)$ theories
• The Double Copy of Massive Scalar-QCD
• Efficient Calculation of Crossing Symmetric BCJ Tree Numerators
• Two-Loop Scattering Amplitudes: Double-Forward Limit and Colour-Kinematics Duality
• Amplitudes, Hopf algebras and the colour-kinematics duality
• Gauge $\times$ Gauge on Spheres
• Two-loop $\mathcal{N}=2$ SQCD amplitudes with external matter from iterated cuts
• One-loop monodromy relations on single cuts
• Non-planar form factors of generic local operators via on-shell unitarity and color-kinematics duality
• String Correlators: Recursive Expansion, Integration-by-Parts and Scattering Equations
• Full-color three-loop three-point form factors in N=4 SYM
• $\text{Tr}(F^3)$ supersymmetric form factors and maximal transcendentality Part II: $0<\mathcal{N}<4$ super Yang-Mills
• Positive helicity Einstein-Yang-Mills amplitudes from the Double Copy
• Perfecting one-loop BCJ numerators in SYM and supergravity
• One-loop Amplitudes for N=2 Homogeneous Supergravities
• Gauge $\times$ Gauge $=$ Gravity on Homogeneous Spaces using Tensor Convolutions
• Spin-four N=7 W-Supergravity: S-fold and Double Copy Construction
• Color-kinematics duality, double copy and the unitarity method for higher-derivative QCD and quadratic gravity
• Spinor-helicity formalism for massive and massless amplitudes in five dimensions
• Unified Formalism for 6D Superamplitudes Based on a Symplectic Grassmannian
• The Full-Color Two-Loop Four-Gluon Amplitude in $\mathcal{N}=2$ Super-QCD
• On Positive Geometry and Scattering Forms for Matter Particles
• Cyclic Mario Worlds -- Color-Decomposition for One-Loop QCD
• Color-Kinematics Duality for Sudakov Form Factor in Non-Supersymmetric Pure Yang-Mills Theory
• Loop-level double-copy for massive fermions in the fundamental
• Scattering Amplitudes and BCFW in $\mathcal{N}=2^{\ast }$ Theory
• Next-to-MHV Yang-Mills kinematic algebra
• Infrared and transcendental structure of two-loop supersymmetric QCD amplitudes
• Three-loop color-kinematics duality: A 24-dimensional solution space induced by new generalized gauge transformations