Journal of High Energy Physics最新文献

The time-ordered multilayer integrals have long been cited as major challenges in the analytical study of cosmological correlators and wavefunction coefficients. The recently proposed family tree decomposition technique solved these time integrals in terms of canonical objects called family trees, which are multivariate hypergeometric functions with energies as variables and twists as parameters. In this work, we provide a systematic study of the analytical properties of family trees. By exploiting the great flexibility of Mellin representations of family trees, we identify and characterize all their singularities in both variables and parameters and find their exact series representations around all singularities with finite convergent domains. These series automatically generate analytical continuation of arbitrary family trees over many distinct regions in the energy space. As a corollary, we show the factorization of family trees at zero partial-energy singularities to all orders. Our findings offer essential analytical data for further understanding and computing cosmological correlators.

Cosmological correlation functions of inflaton and graviton perturbations are the fundamental observables of early universe cosmology and remain a primary target for observations. In this work, we ask the following question: are these observables independent of one another? We find that in the parity-odd sector of inflationary perturbation theory, the answer is a resounding no! In earlier work we derived a correlator-to-correlator factorisation formula which states that parity-odd correlators factorise into lower-point correlators under some mild assumptions on the underlying theory. In this work, we show that these assumptions are satisfied in dynamical Chern-Simons gravity where the action of minimal inflation is augmented by a coupling between the inflaton and the gravitational Chern-Simons term. Such a theory gives rise to a parity-odd trispectrum of curvature perturbations, and we show that such a trispectrum can be expressed solely in terms of the bispectrum that arises due to the minimal coupling between the inflaton and graviton, and the graviton power spectrum which receives a parity-odd correction in this theory. The trispectrum is quadratic in this mixed inflaton-graviton bispectrum and can therefore be interpreted as a “double copy”. Our final expression for the parity-odd trispectrum is a relatively simple function of the external momenta that is rational and factorised.

We revisit the holographic symmetry algebra in the MHV sector. We find an infinite dimensional Abelian symmetry algebra whose generators are the conformally soft negative helicity gravitons and gluons. So the complete symmetry algebra in the MHV graviton sector is a semideirect product of the w_1+∞ algebra and the infinite dimensional Abelian algebra. Similarly in the MHV gluon sector the symmetry algebra is a semidirect product of the S algebra and the infinite dimensional Abelian algebra. The extended symmetry algebra has some use. For example, it is known for sometime that an n point MHV amplitude satisfies (n − 2) Knizhnik-Zamolodchikov (KZ) type equations. So two equations are missing. We show that the extended symmetry algebra has additional null states whose decoupling give rise to the two missing equations.

We develop a framework based on modern amplitude techniques to analyze emission and absorption effects in black hole physics, including Hawking radiation. We first discuss quantum field theory on a Schwarzschild background in the Boulware and the Unruh vacua, and introduce the corresponding S-matrices. We use this information to determine on-shell absorptive amplitudes describing processes where a black hole transitions to a different mass state by absorbing or emitting quanta, to all orders in gravitational coupling. This on-shell approach allows for a universal description of black holes, with their intrinsic differences encapsulated in the discontinuities of the amplitudes, without suffering from off-shell ambiguities such as gauge freedom. Furthermore, the absorptive amplitudes serve as building blocks to describe physics beyond that of isolated black holes. As applications, we find that the Hawking thermal spectrum is well understood by three-point processes. We also consider a binary system and compute the mass shift of a black hole induced by the motion of a companion object, including quantum effects. We show that the mean value of the mass shift is classical and vacuum-independent, while its variance differs depending on the vacuum choice. Our results provide confirmation of the validity of the on-shell program in advancing our understanding of black hole physics.

This paper develops a framework for the Hamiltonian quantization of complex Chern-Simons theory with gauge group (text{SL}(2,{mathbb{C}})) at an even level (kin {mathbb{Z}}_{+}). Our approach follows the procedure of combinatorial quantization to construct the operator algebras of quantum holonomies on 2-surfaces and develop the representation theory. The *-representation of the operator algebra is carried by the infinite dimensional Hilbert space ({mathcal{H}}_{overrightarrow{lambda }}) and closely connects to the infinite-dimensional *-representation of the quantum deformed Lorentz group ({mathcal{U}}_{text{q}}left(s{l}_{2}right)otimes {mathcal{U}}_{widetilde{text{q}}}left(s{l}_{2}right)). The quantum group ({mathcal{U}}_{text{q}}left(s{l}_{2}right)otimes {mathcal{U}}_{widetilde{text{q}}}left(s{l}_{2}right)) also emerges from the quantum gauge transformations of the complex Chern-Simons theory. Focusing on a m-holed sphere Σ_0,m, the physical Hilbert space ({mathcal{H}}_{text{phys}}) is identified by imposing the gauge invariance and the flatness constraint. The states in ({mathcal{H}}_{text{phys}}) are the ({mathcal{U}}_{text{q}}left(s{l}_{2}right)otimes {mathcal{U}}_{widetilde{text{q}}}left(s{l}_{2}right))-invariant linear functionals on a dense domain in ({mathcal{H}}_{overrightarrow{lambda }}). Finally, we demonstrate that the physical Hilbert space carries a Fenchel-Nielsen representation, where a set of Wilson loop operators associated with a pants decomposition of Σ_0,m are diagonalized.

An important insight from the study of AdS/CFT is that bulk locality can be derived from crossing symmetry of the boundary CFT. In this paper, we take the first steps in extending this statement to de Sitter background by demonstrating how to reconstruct a conformally coupled scalar effective field theory (EFT) with higher derivative interactions in four-dimensional de Sitter space from its in-in correlators. The latter can be computed from a certain EFT in Euclidean Anti-de Sitter space involving two scalar fields, which we derive from crossing symmetry of boundary correlators along with two novel constraints arising from unmixing anomalous dimensions of degenerate operators and equating them in different OPE channels. To facilitate the analysis, we work in Mellin space and apply dispersion relations to extract anomalous dimensions more efficiently.

In this work, we investigate the finite basis topologies of two-loop dimensionally regularized Feynman integrals in the ‘t Hooft-Veltman scheme in the Standard Model. We present a functionally distinct finite basis of Master Integrals that spans the whole transcendental space of all two-loop Feynman integrals with external momenta in four dimensions. We also indicate that all the two-loop Master Integrals, in an appropriate basis, with more than 8 denominators, do not contribute to the finite part of any two-loop scattering amplitude. In addition, we elaborate on the application of the ‘t Hooft-Veltman decomposition to improve the performance of numerical evaluation of Feynman integrals using AMFlow and DCT packages. Moreover, we analyze the spectrum of special functions and the corresponding geometries appearing in any two-loop scattering amplitude. Our work will allow for a reduction in the computational complexity required for providing high-precision predictions for future high-multiplicity collider observables, both analytically and numerically, as we exemplify on the two-loop QCD correction relevant to the pp → H + 3j process.

We investigate conformal field theories with gauge group U(N) at arbitrary rank N, focusing on the role of trace relations in determining the structure of the Hilbert space. Working in the free trace algebra without imposing relations, we identify a class of evanescent states that vanish at finite N. Using the Koszul complex of [1], we implement trace relations systematically via ghosts and a fermionic charge Q_b. This framework allows us to define and compute transition amplitudes between evanescent and physical states, which we show correspond precisely to ordinary CFT amplitudes analytically continued in N. Our results provide a direct algebraic realization of the proposals which realize trace relations in the bulk as over-maximal giant gravitons [1–3] and establish analytic continuation in N as a powerful tool for understanding finite-N effects.

Scalar fields interacting with the primordial curvature perturbation during inflation may communicate their statistics to the latter. This situation motivates the study of how the probability density function (PDF) of a light spectator field φ in a pure de Sitter space-time, becomes non-Gaussian under the influence of a scalar potential ( mathcal{V}left(varphi right) ). One approach to this problem is offered by the stochastic formalism introduced by Starobinsky and Yokoyama. It results in a Fokker-Planck equation for the time-dependent PDF ρ(φ, t) describing the statistics of φ which, in the limit of equilibrium gives one back the solution ρ(φ) ∝ exp ( left[-frac{8{pi}^2}{3{H}^4}mathcal{V}left(varphi right)right] ). We study the derivation of ρ(φ, t) using quantum field theory tools. Our approach yields an almost Gaussian distribution function, distorted by minor corrections comprised of terms proportional to powers of ( {mathcal{O}}_{varphi}mathcal{V}left(varphi right) ), where ( {mathcal{O}}_{varphi } ) stands for a derivative operator acting on ( mathcal{V}left(varphi right) ) proportional to ∆N, the number of e-folds succeeding the Hubble-horizon crossing of φ’s wavelengths. This general form is obtained perturbatively and remains valid even with loop corrections. Our solution satisfies a Fokker-Planck equation that receives corrections with respect to the one found within the stochastic approach, allowing us to comment on the validity of the standard equilibrium solution for generic potentials. We posit that higher order corrections to the Fokker-Planck equation may become important towards the equilibrium.

Besides solving the spectral problem of (mathcal{N}=4) Super-Yang-Mills (SYM) theory, integrability also provides us with tools to compute the structure constants of the theory, most prominently through the hexagon formalism. We show that, with minor modifications, this formalism can also be applied to orbifolds of (mathcal{N}=4) SYM theory, which are integrable theories in their own right. To substantiate this claim, we test our results against a direct gauge-theory calculation at tree-level. We focus here on a family of (mathcal{N}=2) supersymmetric ({mathbb{Z}}_{M})-orbifold theories. BPS correlators in these theories have recently been investigated with independent localisation techniques and a structural matching with wrapping corrections in the hexagon formalism was observed. Together with our weak-coupling evidence, this suggests that a full determination of the structure constants of orbifold theories at finite coupling may be within reach.