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Register a new userConformal Wave Expansions for Flat Space Amplitudes
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The extended BMS algebra contains a conformal subgroup that acts on the celestial sphere as SO(3,1). It is of interest to perform mode expansions of free fields in Minkowski spacetime that realize this symmetry in a simple way. In the present work we perform such a mode expansion for massive scalar fields using the unitary principal series representations of SO(3,1) with a view to developing a holographic approach to gravity in asymptotically flat spacetime. These mode expansions are also of use in studying holography in three-dimensional de Sitter spacetime.
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The extended-BMS algebra of asymptotically flat spacetime contains an SO(3,1) subgroup that acts by conformal transformations on the celestial sphere. It is of interest to study the representations of this subgroup associated with gravitons. To reduce the equation of motion to a Schrodinger-like equation it is necessary to impose a non-covariant gauge condition. Using these solutions, leading-order gauge invariant Weyl scalars are then computed and decomposed into families of unitary principal series representations. An invertible holographic mapping is constructed between these unitary principal series operators and massless spin-2 perturbations of flat spacetime.
Conformal supergravity amplitudes are obtained from the double-copy construction using gauge-theory amplitudes, and compared to direct calculations starting from conformal supergravity Lagrangians. We consider several different theories: minimal ${cal N}=4$ conformal supergravity, non-minimal ${cal N}=4$ Berkovits-Witten conformal supergravity, mass-deform
We present new closed-form expressions for 4-point scalar conformal blocks in the s- and t-channel lightcone expansions. Our formulae apply to intermediate operators of arbitrary spin in general dimensions. For physical spin $ell$, they are composed of at most $(ell+1)$ Gaussian hypergeometric functions at each order.
We compute the leading-color contribution to four-particle scattering amplitude in four-dimensional conformal fishnet theory that arises as a special limit of $gamma$-deformed $mathcal N=4$ SYM. We show that the single-trace partial amplitude is protected from quantum corrections whereas the double-trace partial amplitude is a nontrivial infrared finite function of the ratio of Mandelstam invariants. Applying the Lehmann--Symanzik--Zimmerman reduction procedure to the known expression of a four-point correlation function in the fishnet theory, we derive a new representation for this function that is valid for arbitrary coupling. We use this representation to find the asymptotic behavior of the double-trace amplitude in the high-energy limit and to compute the corresponding exact Regge trajectories. We verify that at weak coupling the expressions obtained are in agreement with an explicit five-loop calculation.
We explore and exploit the relation between non-planar correlators in ${cal N}=4$ super-Yang-Mills, and higher-genus closed string amplitudes in type IIB string theory. By conformal field theory techniques we construct the genus-one, four-point string amplitude in AdS$_5times S^5$ in the low-energy expansion, dual to an ${cal N}=4$ super-Yang-Mills correlator in the t Hooft limit at order $1/c^2$ in a strong coupling expansion. In the flat space limit, this maps onto the genus-one, four-point scattering amplitude for type II closed strings in ten dimensions. Using this approach we reproduce several results obtained via string perturbation theory. We also demonstrate a novel mechanism to fix subleading terms in the flat space limit of AdS amplitudes by using string/M-theory.
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