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Register a new userTwo-loop supersymmetric QCD and half-maximal supergravity 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.
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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.
We find a large class of supersymmetric domain wall solutions from six-dimensional $N=(2,2)$ gauged supergravity with various gauge groups. In general, the embedding tensor lives in $mathbf{144}_c$ representation of the global symmetry $SO(5,5)$. We explicitly construct the embedding tensors in $mathbf{15}^{-1}$ and $overline{mathbf{40}}^{-1}$ representations of $GL(5)sim mathbb{R}^+times SL(5)subset SO(5,5)$ leading to $CSO(p,q,5-p-q)$ and $CSO(p,q,4-p-q)ltimesmathbb{R}^4_{boldsymbol{s}}$ gauge groups, respectively. These gaugings can be obtained from $S^1$ reductions of seven-dimensional gauged supergravity with $CSO(p,q,5-p-q)$ and $CSO(p,q,4-p-q)$ gauge groups. As in seven dimensions, we find half-supersymmetric domain walls for purely magnetic or purely electric gaugings with the embedding tensors in $mathbf{15}^{-1}$ or $overline{mathbf{40}}^{-1}$ representations, respectively. In addition, for dyonic gauge groups with the embedding tensors in both $mathbf{15}^{-1}$ and $overline{mathbf{40}}^{-1}$ representations, the domain walls turn out to be $frac{1}{4}$-supersymmetric as in the seven-dimensional analogue. By the DW/QFT duality, these solutions are dual to maximal and half-maximal super Yang-Mills theories in five dimensions. All of the solutions can be uplifted to seven dimensions and further embedded in type IIB or M-theories by the well-known consistent truncation of the seven-dimensional $N=4$ gauged supergravity.
We continue the study of supersymmetric domain wall solutions in six-dimensional maximal gauged supergravity. We first give a classification of viable gauge groups with the embedding tensor in $mathbf{5}^{+7}$, $bar{mathbf{5}}^{+3}$, $mathbf{10}^{-1}$, $mathbf{24}^{-5}$, and $overline{mathbf{45}}^{+3}$ representations of the off-shell symmetry $GL(5)subset SO(5,5)$. We determine an explicit form of the embedding tensor for gauge groups arising from each representation together with some examples of possible combinations among them. All of the resulting gauge groups are of a non-semisimple type with abelian factors and translational groups of different dimensions. We find $frac{1}{2}$- and $frac{1}{4}$-supersymmetric domain walls with $SO(2)$ symmetry in $SO(2)ltimes mathbb{R}^8$ and $SO(2)ltimes mathbb{R}^6$ gauge groups from the embedding tensor in $mathbf{24}^{-5}$ representation and in $CSO(2,0,2)ltimes mathbb{R}^4$, $CSO(2,0,2)ltimes mathbb{R}^2$, and $CSO(2,0,1)ltimes mathbb{R}^4$ gauge groups with the embedding tensor in $overline{mathbf{45}}^{+3}$ representations. These gauge groups are parametrized by a traceless matrix and electrically and magnetically embedded in $SO(5,5)$ global symmetry, respectively.
This is a personal recollection of several results related to the study of the high energy limit of scattering amplitudes in gravitational theories. They would not have been possible without the encouragement and constant support from Lev Nikolaevich Lipatov.
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.
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