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Register a new userInfrared and transcendental structure of two-loop supersymmetric QCD amplitudes
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Using a careful choice of infrared (IR) subtraction scheme, we demonstrate the cancellation of all terms with transcendental weights 0,1,2 from the finite part of the full-color two-loop four-gluon $mathcal{N}=2$ supersymmetric QCD amplitude, with $N_f$ massless supersymmetric quarks. This generalizes the previously observed cancellation of weight-2 terms in the superconformal theory, where $N_f=2N_c$ for gauge group SU$(N_c)$. The subtraction scheme follows naturally both from general IR factorization principles and from an integrand-level analysis of divergences in this amplitude. The divergences are written in terms of scalar triangle integrals whose expressions are known to all orders in the dimensional regulator $epsilon=(4-D)/2$. We also present integrated expressions for the full-color two-loop four-point amplitudes with both matter and vectors on external legs in which lower-weight terms also cancel using an appropriate IR scheme. This provides us with values for the two-loop cusp, gluonic, and quark anomalous dimensions in $mathcal{N}=2$ supersymmetric QCD, which are cross-checked between the three different amplitudes.
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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 $Dle 6$ 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 $D=5-2epsilon$ and show that it non-trivially cancels out as expected.
Using the Gelfand-Kapranov-Zelevinsku{i} system for the primitive cohomology of an infinite series of complete intersection Calabi-Yau manifolds, whose dimension is the loop order minus one, we completely clarify the analytic structure of all banana amplitudes with arbitrary masses. In particular, we find that the leading logarithmic structure in the high energy regime, which corresponds to the point of maximal unipotent monodromy, is determined by a novel $widehat Gamma$-class evaluation in the ambient spaces of the mirror, while the imaginary part of the amplitude in this regime is determined by the $widehat Gamma$-class of the mirror Calabi-Yau manifold itself. We provide simple closed all loop formulas for the former as well as for the Frobenius $kappa$-constants, which determine the behaviour of the amplitudes, when the momentum square equals the sum of the masses squared, in terms of zeta values. We extend our previous work from three to four loops by providing for the latter case a complete set of (inhomogenous) Picard-Fuchs differential equations for arbitrary masses. This allows to evaluate the amplitude as well as other master integrals with raised powers of the propagators in very short time to very high numerical precision for all values of the physical parameters. Using a recent $p$-adic analysis of the periods we determine the value of the maximal cut equal mass four-loop amplitude at the attractor points in terms of periods of modular weight two and four Hecke eigenforms and the quasiperiods of their meromorphic cousins.
In this talk we review the recent computation of the five- and six-gluon two-loop amplitudes in Yang-Mills theory using local integrands which make the infrared pole structure manifest. We make some remarks on the connection with BCJ relations and the all-multiplicity structure.
The infrared structure of (multi-loop) scattering amplitudes is determined entirely by the identities of the external particles participating in the scattering. The two-loop infrared structure of pure qcd amplitudes has been known for some time. By computing the two-loop amplitudes for $bar{f},flongrightarrow X$ and $bar{f},flongrightarrow V_1,V_2$ scattering in an $SU(N)times SU(M)times U(1)$ gauge theory, I determine the anomalous dimensions which govern the infrared structure for any massless two-loop amplitude.
We study the self energies of all particles which appear in a lattice regularization of supersymmetric QCD (${cal N}=1$). We compute, perturbatively to one-loop, the relevant two-point Greens functions using both the dimensional and the lattice regularizations. Our lattice formulation employs the Wilson fermion acrion for the gluino and quark fields. The gauge group that we consider is $SU(N_c)$ while the number of colors, $N_c$ and the number of flavors, $N_f$, are kept as generic parameters. We have also searched for relations among the propagators which are computed from our one-loop results. We have obtained analytic expressions for the renormalization functions of the quark field ($Z_psi$), gluon field ($Z_u$), gluino field ($Z_lambda$) and squark field ($Z_{A_pm}$). We present here results from dimensional regularization, relegating to a forthcoming publication our results along with a more complete list of references. Part of the lattice study regards also the renormalization of quark bilinear operators which, unlike the non-supersymmetric case, exhibit a rich pattern of operator mixing at the quantum level.
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