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Register a new userUltraviolet properties of Maximal Supergravity
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We argue that recent results in string perturbation theory indicate that the four-graviton amplitude of four-dimensional N=8 supergravity might be ultraviolet finite up to eight loops. We similarly argue that the h-loop M-graviton amplitude might be finite for h<7+M/2.
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We compare the dynamics of maximal three-dimensional gauged supergravity in appropriate truncations with the equations of motion that follow from a one-dimensional E10/K(E10) coset model at the first few levels. The constant embedding tensor, which describes gauge deformations and also constitutes an M-theoretic degree of freedom beyond eleven-dimensional supergravity, arises naturally as an integration constant of the geodesic model. In a detailed analysis, we find complete agreement at the lowest levels. At higher levels there appear mismatches, as in previous studies. We discuss the origin of these mismatches.
We construct the most general gaugings of the maximal D=6 supergravity. The theory is (2,2) supersymmetric, and possesses an on-shell SO(5,5) duality symmetry which plays a key role in determining its couplings. The field content includes 16 vector fields that carry a chiral spinor representation of the duality group. We utilize the embedding tensor method which determines the appropriate combinations of these vectors that participate in gauging of a suitable subgroup of SO(5,5). The construction also introduces the magnetic duals of the 5 two-form potentials and 16 vector fields.
We use exceptional field theory as a tool to work out the full non-linear reduction ansaetze for the AdS$_5times S^5$ compactification of IIB supergravity and its non-compact counterparts in which the sphere $S^5$ is replaced by the inhomogeneous hyperboloidal space $H^{p,q}$. The resulting theories are the maximal 5D supergravities with gauge groups SO(p,q). They are consistent truncations in the sense that every solution of 5D supergravity lifts to a solution of IIB supergravity. In particular, every stationary point and every holographic RG flow of the scalar potentials for the compact and non-compact 5D gaugings directly lift to solutions of IIB supergravity.
The maximal supergravity theory in three dimensions, which has local SO(16) and rigid $E_8$ symmetries, is discussed in a superspace setting starting from an off-shell superconformal structure. The on-shell theory is obtained by imposing further constraints. It is essentially a non-linear sigma model that induces a Poincare supergeometry that is described in detail. The possible $p$-form field strengths, for $p=2,3,4$, are explicitly constructed using supersymmetry and $E_8$. The gauged theory is also discussed.
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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