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We discuss a no-boundary proposal for a subregion of the universe. In the classical approximation, this density matrix involves finding a specific classical solution of the equations of motion with no boundary. Beyond the usual no boundary condition at early times, we also have another no boundary condition in the region we trace out. We can find the prescription by starting from the usual Hartle-Hawking proposal for the wavefunction on a full slice and tracing out the unobserved region in the classical approximation. We discuss some specific subregions and compute the corresponding solutions. These geometries lead to phenomenologically unacceptable probabilities, as expected. We also discuss how the usual Coleman de Luccia bubble solutions can be interpreted as a possible no boundary contribution to the density matrix of the universe. These geometries lead to local (but not global) maxima of the probability that are phenomenologically acceptable., Comment: 35+16 pages, 22 figures; one paragraph added and refs added

We analyze the one-loop effects of massive fields on 2-to-2 scattering processes involving gravitons. It has been suggested that in the presence of gravity, any local effective field theory description must break down at the "species scale". We first observe that unitarity and analyticity of the amplitude indeed imply a species-type bound $G\Lambda^{d-2}N\leq O(1)$, where $N$ counts parametrically light species and $\Lambda$ is an energy scale above which new unknown ingredients must modify the graviton amplitude. To clarify what happens at this scale, we contrast the partial wave decomposition of calculated amplitudes with that of some ultraviolet scenarios: string theory and strongly interacting Planck-scale physics. Observing that the latter exhibit a markedly stronger high-spin content, we define nonperturbatively the high-spin onset scale $\Lambda_{\rm o}$, which coincides with the string scale and higher-dimensional Planck scale in respective examples. We argue that, generally, no local field description can exist at distances shorter than $1/\Lambda_{\rm o}$., Comment: 44+9 pages, 17 figures; refs added, figure 12 updated

We review the effective field theory (EFT) bootstrap by formulating it as an infinite-dimensional semidefinite program (SDP), built from the crossing symmetric sum rules and the S-matrix primal ansatz. We apply the program to study the large-$N$ chiral perturbation theory ($\chi$PT) and observe excellent convergence of EFT bounds between the dual (rule-out) and primal (rule-in) methods. This convergence aligns with the predictions of duality theory in SDP, enabling us to analyze the bound states and resonances in the ultra-violet (UV) spectrum. Furthermore, we incorporate the upper bound of unitarity to uniformly constrain the EFT space from the UV scale $M$ using the primal method, thereby confirming the consistency of the large-$N$ expansion. In the end, we translate the large-$N$ $\chi$PT bounds to constrain the higher derivative corrections of holographic QCD models., Comment: 58 pages, 15 figures, 1 table, latex; refs added, typo corrected, footnote added; error of eq (2.13) and Fig 2 added fixed; typo in eq (3.14) fixed

We explore the use of the differential representation of AdS amplitudes to compute Witten diagrams. The differential representation expresses AdS amplitudes in terms of conformal generators acting on contact Witten diagrams, which allows us to construct differential equations for Witten diagrams. These differential equations can then be transformed into difference equations in Mellin space, which can be solved recursively. Using this method, we efficiently re-computed scalar four-point amplitudes and obtained new results for scalar six-point amplitudes mediated by gluons and scalars, as well as two examples of scalar eight-point amplitudes from gluon exchange., Comment: 42 pages, 13 figures, latex

We report the differential representation of three-point and four-point amplitudes for Yang-Mills fields and Einstein gravity in AdS at tree-level. The amplitudes exhibit the flat-space structures by using the weight-shifting operators with reordering, which makes the differential double copy relation at the three-point level straightforward. For four-point Yang-Mills amplitudes, we establish the differential BCJ relation, which can be useful for proving the differential doubly copy at the four-point level in the future., Comment: 13 pages; typo fixed; grammarly errors fixed including abstract; new appendices and discussions added; new refs added; proposal modified

We present the NLO electroweak radiative corrections to the ee\gamma production in \gamma\gamma collision, which is an ideal channel for calibrating the beam luminosity of a Photon Linear Collider. We analyze the dependence of the total cross section on the beam colliding energy, and then investigate the kinematic distributions of final particles at various initial photon beam polarizations at EW NLO accuracy. The numerical results indicate that the EW relative corrections to the total cross section are non-negligible and become increasingly significant as the increase of the beam colliding energy. Such EW corrections are very important and should be taken into consideration in precision theoretical and experimental studies at high-energy \gamma\gamma colliders., Comment: 32 pages, 50 figures, 3 tables

Do gravitational interactions respect the basic principles of relativity and quantum mechanics? We show that any graviton S-matrix that satisfies these assumptions cannot significantly differ from General Relativity at low energies. We provide sharp bounds on the size of potential corrections in terms of the mass M of new higher-spin states, in spacetime dimensions D>=5 where the S-matrix does not suffer from infrared ambiguities. The key novel ingredient is the full set of SO(D-1) partial waves for this process, which we show how to efficiently compute with Young tableau manipulations. We record new bounds on the central charges of holographic conformal theories., Comment: 6 pages + 6 appendices, ancillary files for partial wave data

Continuous variable quantum cryptography has developed rapidly in recent decades, but how to verify identity in the continuous variable quantum system is still an urgent issue to be solved. To solve this problem, we propose a continuous variable quantum identification (CV-QI) protocol based on the correlation of two-mode squeezed vacuum state and the continuous variable teleportation. The bidirectional identity verification between two participants of the communication can be achieved by the proposed CV-QI protocol. In order to guarantee the security, we make full use of the decoy state sequences during the whole process of the proposed CV-QI protocol. Besides, we provide the security analyses of the proposed CV-QI protocol, and analyses indicate that the security of the proposed CV-QI protocol is guaranteed., Comment: Further correction

We study constraints from causality and unitarity on $2\to2$ graviton scattering in four-dimensional weakly-coupled effective field theories. Together, causality and unitarity imply dispersion relations that connect low-energy observables to high-energy data. Using such dispersion relations, we derive two-sided bounds on gravitational Wilson coefficients in terms of the mass $M$ of new higher-spin states. Our bounds imply that gravitational interactions must shut off uniformly in the limit $G \to 0$, and prove the scaling with $M$ expected from dimensional analysis (up to an infrared logarithm). We speculate that causality, together with the non-observation of gravitationally-coupled higher spin states at colliders, severely restricts modifications to Einstein gravity that could be probed by experiments in the near future., Comment: 35 pages + appendices + refs, 14 figures

It is known that the $(a,c)$ central charges in four-dimensional CFTs are linear combinations of the three independent OPE coefficients of the stress-tensor three-point function. In this paper, we adopt the holographic approach using AdS gravity as an effect field theory and consider higher-order corrections up to and including the cubic Riemann tensor invariants. We derive the holographic central charges and OPE coefficients and show that they are invariant under the metric field redefinition. We further discover a hidden relation among the OPE coefficients that two of them can be expressed in terms of the third using differential operators, which are the unit radial vector and the Laplacian of a four-dimensional hyperbolic space whose radial variable is an appropriate length parameter that is invariant under the field redefinition. Furthermore, we prove that the consequential relation $c=1/3 \ell_{\rm eff}\partial a/\partial\ell_{\rm eff}$ and its higher-dimensional generalization are valid for massless AdS gravity constructed from the most general Riemann tensor invariants., Comment: Latex, 1 figure, 31 pages, typos corrected, a reference added, a technique issue clarified, to appear in JHEP

Different frameworks exist to describe the flat-space limit of AdS/CFT, include momentum space, Mellin space, coordinate space, and partial-wave expansion. We explain the origin of momentum space as the smearing kernel in Poincare AdS, while the origin of latter three is the smearing kernel in global AdS. In Mellin space, we find a Mellin formula that unifies massless and massive flat-space limit, which can be transformed to coordinate space and partial-wave expansion. Furthermore, we also manage to transform momentum space to smearing kernel in global AdS, connecting all existed frameworks. Finally, we go beyond scalar and verify that $\langle VV\mathcal{O}\rangle$ maps to photon-photon-massive amplitudes., Comment: 57 pages, 12 figures, latex; comments added, refs added; the version to appear on JHEP