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Register a new userConstruction of all N=4 conformal supergravities
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All N=4 conformal supergravities in four space-time dimensions are constructed. These are the only N=4 supergravity theories whose actions are invariant under off-shell supersymmetry. They are encoded in terms of a holomorphic function that is homogeneous of zeroth degree in scalar fields that parametrize an SU(1,1)/U(1) coset space. When this function equals a constant the Lagrangian is invariant under continuous SU(1,1) transformations. The construction of these higher-derivative invariants also opens the door to various applications for non-conformal theories.
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We consider classes of T_6 orientifolds, where the orientifold projection contains an inversion I_{9-p} on 9-p coordinates, transverse to a Dp-brane. In absence of fluxes, the massless sector of these models corresponds to diverse forms of N=4 supergravity, with six bulk vector multiplets coupled to N=4 Yang--Mills theory on the branes. They all differ in the choice of the duality symmetry corresponding to different embeddings of SU(1,1)times SO(6,6+n) in Sp(24+2n,R), the latter being the full group of duality rotations. Hence, these Lagrangians are not related by local field redefinitions. When fluxes are turned on one can construct new gaugings of N=4 supergravity, where the twelve bulk vectors gauge some nilpotent algebra which, in turn, depends on the choice of fluxes.
Based on the known non-linear transformation rules of the Weyl multiplet fields, the action of $N=4$ conformal supergravity is constructed up to terms quadratic in the fermion fields. The bosonic sector corrects a recent result in the literature.
We review the question of quantum consistency of N=4 conformal supergravity in 4 dimensions. The UV divergences and anomalies of the standard (minimal) conformal supergravity where the complex scalar $phi$ is not coupled to the Weyl graviton kinetic term can be cancelled by coupling this theory to N=4 super Yang-Mills with gauge group of dimension 4. The same turns out to be true also for the non-minimal N=4 conformal supergravity with the action (recently constructed in arXiv:1609.09083) depending on an arbitrary holomorphic function $f(phi)$. The special case of the non-minimal conformal supergravity with $f= e^{2phi}$ appears in the twistor-string theory. We show that divergences and anomalies do not depend on the form of the function $f$ and thus can be cancelled just as in the minimal $f=1$ case by coupling the theory to four N=4 vector multiplets.
For dyons in heterotic string theory compactified on a six-torus, with electric charge vector Q and magnetic charge vector P, the positive integer I = g.c.d.(Q wedge P) is an invariant of the U-duality group. We propose the microscopic theory for computing the spectrum of all dyons for all values of I, generalizing earlier results that exist only for the simplest case of I=1. Our derivation uses a combination of arguments from duality, 4d-5d lift, and a careful analysis of fermionic zero modes. The resulting degeneracy agrees with the black hole degeneracy for large charges and with the degeneracy of field-theory dyons for small charges. It naturally satisfies several physical requirements including integrality and duality invariance. As a byproduct, we also derive the microscopic (0,4) superconformal field theory relevant for computing the spectrum of five-dimensional Strominger-Vafa black holes in ALE backgrounds and count the resulting degeneracies.
We give an explicit formula for all tree amplitudes in N=4 SYM, derived by solving the recently presented supersymmetric tree-level recursion relations. The result is given in a compact, manifestly supersymmetric form and we show how to extract from it all possible component amplitudes for an arbitrary number of external particles and any arrangement of external particles and helicities. We focus particularly on extracting gluon amplitudes which are valid for any gauge theory. The formula for all tree-level amplitudes is given in terms of nested sums of dual superconformal invariants and it therefore manifestly respects both conventional and dual superconformal symmetry.
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