High energy scattering in Einstein–Cartan gravity

We consider Riemann–Cartan gravity with minimal Palatini action, which is classically equivalent to Einstein gravity. Following the ideas of Lipatov (Nucl Phys B 365:614–632, 1991, Phys Part Nucl 44:391–413, 2013, Subnucl Ser 49:131, 2013, Subnucl Ser 50:213–225, 2014, Int J Mod Phys A 31(28/29):1645011, 2016, EPJ Web Conf 125:01010, 2016) and Bartels et al. (JHEP 07:056, 2014) 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. We add to the Palatini action the new terms. These terms are responsible for the interaction of gravitational quanta with gravitational reggeons. The latter 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. It contains interaction between the ordinary quanta of spin connection and vielbein with the gravitational reggeons.

Reggeon field theory and self duality: making ends meet

Motivated by the question of unitarity of Reggeon Field Theory, we use the effective field theory philosophy to find possible Reggeon Field Theory Hamiltonians HRFT. We require that HRFT is self dual, reproduce all known limits (dilute-dense and dilute-dilute) and exhibits all the symmetries of the JIMWLK Hamiltonian. We find a family of Hamiltonians which satisfy all the above requirements. One of these is identical in form to the so called “diamond action” discussed in [67, 68]. However we show by explicit calculation that the so called “diamond condition” is not satisfied beyond leading perturbative order.

The JIMWLK evolution and the s-channel unitarity

Further developing ideas set forth in [1], we discuss QCD Reggeon Field Theory (RFT) and formulate restrictions imposed on its Hamiltonian by the unitarity of underlying QCD. We identify explicitly the QCD RFT Hilbert space, provide algebra of the basic degrees of freedom (Wilson lines and their duals) and the algorithm for calculating the scattering amplitudes. We formulate conditions imposed on the “Fock states” of RFT by unitary nature of QCD, and explain how these constraints appear as unitarity constraints on possible RFT hamiltonians that generate energy evolution of scattering amplitudes. We study the realization of these constraints in the dense-dilute limit of RFT where the appropriate Hamiltonian is the JIMWLK Hamiltonian HJIMWLK. We find that the action HJIMWLK on the dilute projectile states is unitary, but acting on dense “target” states it violates unitarity and generates states with negative probabilities through energy evolution.

Strong Interactions in the Regge Limit and Infrared Region

In this talk, we encode the perturbative BFKL leading logarithmic resummation, relevant for the Regge limit behavior of QCD scattering amplitudes, in the IR regulated effective action, which satisfies exact functional renormalization group equations. The goal is to use this framework to study, in the high-energy limit and at larger transverse distances the transition to a much simpler effective local Reggeon field theory, whose critical properties were recently investigated in the same framework. We perform a numerical analysis of the spectrum of the BFKL Pomeron by the introduction of a Wilsonian infrared regulator to understand the properties of the leading poles (Pomeron states) contributing to the high-energy scattering