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Register a new userRelationship Between Gravity and Gauge Scattering in the High Energy Limit
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Investigations of high-energy graviton-graviton and gluon-gluon scattering are performed in the leading eikonal approximation for the kinematic regime of large center of mass energy and low momentum transfer. We find a double copy relation between the amplitudes of the two theories to all loop orders when, on the gauge theory side, we retain only the set of diagrams at each loop order for which the collinear divergences cancel amongst themselves. For this to happen the color structure of all diagrams in the set must be identical. Using standard field theoretic methods, it is shown that this relation is reflected in a similar double copy relationship between the classical shockwaves of the two theories as well.
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We consider Riemann-Cartan gravity with minimal Palatini action, which is classically equivalent to Einstein gravity. Following the ideas of L.Lipatov cite{LipGrav} we propose the effective action for this theory aimed at the description of the high-energy scattering of gravitating particles in the multi - Regge kinematics. For that purpose we add to the Palatini action the new terms responsible for the interaction of gravitational quanta with certain collective excitations that replace exchange by multiple gravitational excitations. We propose the heuristic explanation of its particular form based on an analogy to the reggeon field theory of QCD. We argue that Regge kinematics assumes the appearance of an effective two - dimensional model describing the high - energy scattering similar to that of QCD. Such a model may be formulated in a way leading to our final effective theory, which contains interaction between the ordinary quanta of spin connection and vielbein with their effective counterparts that pretend to the role of the gravitational reggeons.
We analyse the high-energy limit of the gluon-gluon scattering amplitude in QCD, and display an intriguing relation between the finite parts of the one-loop gluon impact factor and the finite parts of the two-loop Regge trajectory.
We consider the relativistic scattering of unequal-mass scalar particles through graviton exchange in the small-angle high-energy regime. We show the self-consistency of expansion around the eikonal limit and compute the scattering amplitude up to the next-to-leading power correction of the light particle energy, including gravitational effects of the same order. The first power correction is suppressed by a single power of the ratio of momentum transfer to the energy of the light particle in the rest frame of the heavy particle, independent of the heavy particle mass. We find that only gravitational corrections contribute to the exponentiated phase in impact parameter space in four dimensions. For large enough heavy-particle mass, the saddle point for the impact parameter is modified compared to the leading order by a multiple of the Schwarzschild radius determined by the mass of the heavy particle, independent of the energy of the light particle.
In the AdS/CFT description of four-dimensional QCD matter undergoing Bjorken expansion, does the holographic energy-momentum tensor contain a Casimir-type contribution that should not be attributed to thermal matter? When the bulk isometry ansatz that yielded such a Casimir term for (1+1)-dimensional boundary matter is generalised to a four-dimensional boundary, we show that a Casimir term does not arise, owing to singularities in the five-dimensional bulk solution. The geometric reasons are traced to a difference between the isometries of AdS_3 and AdS_{d+1} for d>=3.
In the high energy limit of scattering amplitudes in Quantum Chromodynamics and supersymmetric theories the dominant Feynman diagrams are characterized by a hidden integrability. A well-known example is that of Odderon exchange, which can be described as a bound state of three reggeized gluons and corresponds to a closed spin chain with periodic boundary conditions. In the $N=4$ supersymmetric Yang-Mills theory a similar spin chain arises in the multi-Regge asymptotics of the eight-point amplitude in the planar limit. We investigate the associated open spin chain in transverse momentum and rapidity variables solving the corresponding effective Feynman diagrams. We introduce the concept of complexity in the high energy effective field theory and study its emerging scaling laws.
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