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Register a new userMHV amplitudes and BCFW recursion for Yang-Mills theory in the de Sitter static patch
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We study the scattering problem in the static patch of de Sitter space, i.e. the problem of field evolution between the past and future horizons of a de Sitter observer. We formulate the problem in terms of off-shell fields in Poincare coordinates. This is especially convenient for conformal theories, where the static patch can be viewed as a flat causal diamond, with one tip at the origin and the other at timelike infinity. As an important example, we consider Yang-Mills theory at tree level. We find that static-patch scattering for Yang-Mills is subject to BCFW-like recursion relations. These can reduce any static-patch amplitude to one with N^{-1}MHV helicity structure, dressed by ordinary Minkowski amplitudes. We derive all the N^{-1}MHV static-patch amplitudes from self-dual Yang-Mills field solutions. Using the recursion relations, we then derive from these an infinite set of MHV amplitudes, with arbitrary number of external legs.
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We study the scattering problem in the static patch of de Sitter space, i.e. the problem of field evolution between the past and future horizons of a de Sitter observer. We calculate the leading-order scattering for a conformally massless scalar with cubic interaction, as both the simplest case and a warmup towards Yang-Mills and gravity. Our strategy is to decompose the static-patch evolution problem into a pair of more symmetric evolution problems in two Poincare patches, sewn together by a spatial inversion. To carry this out explicitly, we end up developing formulas for the momentum-space effect of
In this work, our prime objective is to study non-locality and long-range effects of two-body correlation using quantum entanglement from the various information-theoretic measures in the static patch of de Sitter space using a two-body Open Quantum System (OQS). The OQS is described by a system of two entangled atoms, surrounded by a thermal bath, which is modelled by a massless probe scalar field. Firstly, we partially trace over the bath field and construct the Gorini Kossakowski Sudarshan Lindblad (GSKL) master equation, which describes the time evolution of the reduced subsystem density matrix. This GSKL master equation is characterized by two components, these are-Spin chain interaction Hamiltonian and the Lindbladian. To fix the form of both of them, we compute the Wightman functions for probe massless scalar field. Using this result along with the large time equilibrium behaviour we obtain the analytical solution for reduced density matrix. Further using this solution we evaluate various entanglement measures, namely Von-Neumann entropy, R$e$nyi entropy, logarithmic negativity, entanglement of formation, concurrence and quantum discord for the two atomic subsystems on the static patch of De-Sitter space. Finally, we have studied the violation of Bell-CHSH inequality, which is the key ingredient to study non-locality in primordial cosmology.
We study the empirical realisation of the memory effect in Yang-Mills theory, especially in view of the classical vs. quantum nature of the theory. Gauge invariant analysis of memory in classical U(1) electrodynamics and its observation by total change of transverse momentum of a charge is reviewed. Gauge fixing leads to a determination of a gauge transformation at infinity. An example of Yang-Mills memory then is obtained by reinterpreting known results on interactions of a quark and a large high energy nucleus in the theory of Color Glass Condensate. The memory signal is again a kick in transverse momentum, but it is only obtained in quantum theory after fixing the gauge, after summing over an ensemble of classical processes.
We consider Yang--Mills theory with a compact structure group $G$ on four-dimensional de Sitter space dS$_4$. Using conformal invariance, we transform the theory from dS$_4$ to the finite cylinder ${cal I}times S^3$, where ${cal I}=(-pi/2, pi/2)$ and $S^3$ is the round three-sphere. By considering only bundles $Pto{cal I}times S^3$ which are framed over the boundary $partial{cal I}times S^3$, we introduce additional degrees of freedom which restrict gauge transformations to be identity on $partial{cal I}times S^3$. We study the consequences of the framing on the variation of the action, and on the Yang--Mills equations. This allows for an infinite-dimensional moduli space of Yang--Mills vacua on dS$_4$. We show that, in the low-energy limit, when momentum along ${cal I}$ is much smaller than along $S^3$, the Yang--Mills dynamics in dS$_4$ is approximated by geodesic motion in the infinite-dimensional space ${cal M}_{rm vac}$ of gauge-inequivalent Yang--Mills vacua on $S^3$. Since ${cal M}_{rm vac}cong C^infty (S^3, G)/G$ is a group manifold, the dynamics is expected to be integrable.
We study the dS/CFT duality between minimal type-A higher-spin gravity and the free Sp(2N) vector model. We consider the bulk spacetime as elliptic de Sitter space dS_4/Z_2, in which antipodal points have been identified. We apply a technique from arXiv:1509.05890, which extracts the quantum-mechanical commutators (or Poisson brackets) of the linearized bulk theory in an *observable patch* of dS_4/Z_2 directly from the boundary 2-point function. Thus, we construct the Lorentzian commutators of the linearized bulk theory from the Euclidean CFT. In the present paper, we execute this technique for the entire higher-spin multiplet, using a higher-spin-covariant language, which provides a promising framework for the future inclusion of bulk interactions. Aside from its importance for dS/CFT, our construction of a Hamiltonian structure for a bulk causal region should be of interest within higher-spin theory itself. The price we pay is a partial symmetry breaking, from the full dS group (and its higher-spin extension) to the symmetry group of an observable patch. While the boundary field theory plays a role in our arguments, the results can be fully expressed within a boundary *particle mechanics*. Bulk fields arise from this boundary mechanics via a version of second quantization.
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