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Register a new userTwo-loop $mathcal{N}=2$ SQCD amplitudes with external matter from iterated cuts
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We develop an iterative method for constructing four-dimensional generalized unitarity cuts in $mathcal{N} = 2$ supersymmetric Yang-Mills (SYM) theory coupled to fundamental matter hypermultiplets ($mathcal{N} = 2$ SQCD). For iterated two-particle cuts,specifically those involving only four-point amplitudes, this implies simple diagrammatic rules for assembling the cuts to any loop order, reminiscent of the rung rule in $mathcal{N} = 4$ SYM. By identifying physical poles, the construction simplifies the task of extracting complete integrands. In combination with the duality between color and kinematics we construct all four-point massless MHV-sector scattering amplitudes up to two loops in $mathcal{N} = 2$ SQCD, including those with matter on external legs. Our results reveal chiral infrared-finite integrands closely related to those found using loop-level BCFW recursion. The integrands are valid in $Dleq 6$ dimensions with external states in a four-dimensional subspace; the upper bound is dictated by our use of six-dimensional chiral $mathcal{N} = (1,0)$ SYM as a means of dimensionally regulating loop integrals.
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Using four-dimensional unitarity and MHV-rules we calculate the one-loop MHV amplitudes with all external particles in the adjoint representation for N=2 supersymmetric QCD with N_f fundamental flavours. We start by considering such amplitudes in the superconformal N=4 gauge theory where the N=4 supersymmetric Ward identities (SWI) guarantee that all MHV amplitudes for all types of external particles are given by the corresponding tree-level result times a universal helicity- and particle-type-independent contribution. In N=2 SQCD the MHV amplitudes differ from those for N=4 for general values of N_f and N_c. However, for N_f=2N_c where the N=2 SQCD is conformal, the N=2 MHV amplitudes (with all external particles in the adjoint representation) are identical to the N=4results. This factorisation at one-loop motivates us to pose a question if there may be a BDS-like factorisation for these amplitudes which also holds at higher orders of perturbation theory in superconformal N=2 theory.
We show that one-loop amplitudes in massless gauge theories can be determined from single cuts. By cutting a single propagator and putting it on-shell, the integrand of an n-point one-loop integral is transformed into an (n+2)-particle tree level amplitude. The single-cut approach described here is complementary to the double or multiple unitarity cut approaches commonly used in the literature. In common with these approaches, if the cut is taken in four dimensions, one finds only the cut-constructible parts of the amplitude, while if the cut is in D=4-2 epsilon dimensions, both rational and cut-constructible parts are obtained. We test our method by reproducing the known results for the fully rational all-plus and mostly-plus QCD amplitudes A^{(1)}_4(1^+,2^+,3^+,4^+) and A^{(1)}_5(1^+,2^+,3^+,4^+,5^+). We also rederive expressions for the scalar loop contribution to the four-gluon MHV amplitude, A_4^{(1,N=0)}(-,-,+,+) which has both cut-constructible and rational contributions, and the fully cut-constructible n-gluon MHV amplitude in N=4 Supersymetric Yang-Mills, A_4^{(1,N=4)}(-,-,+,...,+).
We present the fully integrated form of the two-loop four-gluon amplitude in $mathcal{N} = 2$ supersymmetric quantum chromodynamics with gauge group SU$(N_c)$ and with $N_f$ massless supersymmetric quarks (hypermultiplets) in the fundamental representation. Our result maintains full dependence on $N_c$ and $N_f$, and relies on the existence of a compact integrand representation that exhibits the duality between color and kinematics. Specializing to the $mathcal{N} = 2$ superconformal theory, where $N_f = 2N_c$ , we obtain remarkably simple amplitudes that have an analytic structure close to that of $mathcal{N} = 4$ super-Yang-Mills theory, except that now certain lower-weight terms appear. We comment on the corresponding results for other gauge groups.
We study dualities for 3d $mathcal{N} = 2$ $SU(N_c)$ SQCD at Chern-Simons level $k$ in presence of an adjoint with polynomial superpotential. The dualities are dubbed chiral because there is a different amount of fundamentals $N_f$ and antifundamentals $N_a$. We build a complete classification of such dualities in terms of $ |N_f - N_a| $ and $k$. The classification is obtained by studying the flow from the non-chiral case, and we corroborate our proposals by matching the three-sphere partition functions. Finally, we revisit the case of $SU(N_c)$ SQCD without the adjoint, comparing our results with previous literature.
We study $mathcal{N} = 3$ supersymmetric Chern-Simons-matter theory coupled to matter in the fundamental representation of $SU(N)$. In the t Hooft large $N$ limit, we compute the exact $2 to 2$ scattering amplitudes of the fundamental scalar superfields to all orders in the t Hooft coupling $lambda$. Our computations are presented in $mathcal{N} = 1$ superspace and make significant use of the residual $SO(2)_R$ symmetry in order to solve for the exact four-point correlator of the scalar superfields. By taking the on-shell limit, we are able to extract the exact $2 to 2$ scattering amplitudes of bosons/fermions in the symmetric, anti-symmetric and adjoint channels of scattering. We find that the scattering amplitude of the $mathcal{N} = 3$ theory in the planar limit is tree-level exact to all orders in the t Hooft coupling $lambda$. The result is consistent with the conjectured bosonization duality and is expected to have enhanced symmetry structures such as dual superconformal symmetry and Yangian symmetry.
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