scholarly journals The inflationary wavefunction from analyticity and factorization

2021 ◽  
Vol 2021 (12) ◽  
pp. 018
Author(s):  
David Meltzer
Keyword(s):  
Analytic Continuation ◽  
De Sitter Space ◽  
Conformal Group ◽  
Tree Level ◽  
Late Time ◽  
De Sitter ◽  
Scale Invariant ◽  
Arbitrary Mass ◽  
Lower Point ◽  
Finite Sum

Abstract We study the analytic properties of tree-level wavefunction coefficients in quasi-de Sitter space. We focus on theories which spontaneously break dS boost symmetries and can produce significant non-Gaussianities. The corresponding inflationary correlators are (approximately) scale invariant, but are not invariant under the full conformal group. We derive cutting rules and dispersion formulas for the late-time wavefunction coefficients by using factorization and analyticity properties of the dS bulk-to-bulk propagator. This gives a unitarity method which is valid at tree-level for general n-point functions and for fields of arbitrary mass. Using the cutting rules and dispersion formulas, we are able to compute n-point functions by gluing together lower-point functions. As an application, we study general four-point, scalar exchange diagrams in the EFT of inflation. We show that exchange diagrams constructed from boost-breaking interactions can be written as a finite sum over residues. Finally, we explain how the dS identities used in this work are related by analytic continuation to analogous identities in Anti-de Sitter space.

scholarly journals LECTURE NOTES ON INTERACTING QUANTUM FIELDS IN DE SITTER SPACE

2014 ◽  
Vol 23 (01) ◽  
pp. 1430001 ◽  
Author(s):  
E. T. AKHMEDOV
Keyword(s):  
De Sitter Space ◽  
The Self ◽  
Field Theories ◽  
Tree Level ◽  
Main Concern ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Quantum Fields ◽  
De Sitter ◽  
Invariant States

We discuss peculiarities of quantum fields in de Sitter (dS) space on the example of the self-interacting massive real scalar, minimally coupled to the gravity background. Nonconformal quantum field theories (QFTs) in dS space show very special infrared behavior, which is not shared by quantum fields neither in flat nor in anti-dS space: in dS space loops are not suppressed in comparison with tree level contributions because there are strong infrared corrections. That is true even for massive fields. Our main concern is the interrelation between these infrared effects, the invariance of the QFT under the dS isometry and the (in)stability of dS invariant states (and of dS space itself) under nonsymmetric perturbations.

scholarly journals TACHYONS IN DE SITTER SPACE AND ANALYTICAL CONTINUATION FROM dS/CFT TO AdS/CFT

2004 ◽  
Vol 19 (29) ◽  
pp. 4985-5001 ◽  
Author(s):  
M. CADONI ◽  
P. CARTA
Keyword(s):  
Analytic Continuation ◽  
De Sitter Space ◽  
Space Time ◽  
Analytical Continuation ◽  
Green Functions ◽  
De Sitter ◽  
Field Equations ◽  
Scalar Particles

We discuss analytic continuation from d-dimensional Lorentzian de Sitter ( dS d) to d-dimensional Lorentzian anti-de Sitter ( AdS d) space–time. We show that AdS d, with opposite signature of the metric, can be obtained as analytic continuation of a portion of dS d. This implies that the dynamics of (positive square-mass) scalar particles in AdS d can be obtained from the dynamics of tachyons in dS d. We discuss this correspondence both at the level of the solution of the field equations and of the Green functions. The AdS / CFT duality is obtained as analytic continuation of the dS / CFT duality.

scholarly journals FUBINI VACUA AS A CLASSICAL DE SITTER VACUA

2007 ◽  
Vol 22 (29) ◽  
pp. 2217-2235 ◽  
Author(s):  
F. LORAN
Keyword(s):  
Einstein Field Equation ◽  
Minkowski Spacetime ◽  
Vacuum State ◽  
Information Geometry ◽  
Conformal Group ◽  
De Sitter ◽  
Frw Universe ◽  
Scale Invariant ◽  
Scalar Theory ◽  
De Sitter Vacua

The Fubini's idea to introduce a fundamental scale of hadron phenomena by means of dilatation non-invariant vacuum state in the framework of a scale invariant Lagrangian field theory is recalled. The Fubini vacua is invariant under the de Sitter subgroup of the full conformal group. We obtain a finite entropy for the quantum state corresponding to the classical Fubini vacua in Euclidean spacetime resembling the entropy of the de Sitter vacua. In Minkowski spacetime it is shown that the Fubini vacua is mainly a bath of radiation with Rayleigh–Jeans distribution for the low energy radiation. In four dimensions, the critical scalar theory is shown to be equivalent to the Einstein field equation in the ansatz of conformally flat metrics and to the SU(2) Yang–Mills theory in the 't Hooft ansatz. In D dimensions, the Hitchin formula for the information geometry metric of the moduli space of instantons is used to obtain the information geometry of the free-parameter space of the Fubini vacua which is shown to be a (D+1)-dimensional AdS space. Considering the Fubini vacua as a de Sitter vacua, the corresponding cosmological constant is shown to be given by the coupling constant of the critical scalar theory. In Minkowski spacetime it is shown that the Fubini vacua are equivalent to an open FRW universe.

Tree-level scattering amplitudes in de Sitter space diverge

1987 ◽  
Vol 197 (3) ◽  
pp. 373-378 ◽  
Author(s):  
E.G. Floratos ◽  
J. Iliopoulos ◽  
T.N. Tomaras
Keyword(s):  
Scattering Amplitudes ◽  
De Sitter Space ◽  
Tree Level ◽  
De Sitter

scholarly journals On duality of color and kinematics in (A)dS momentum space

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Soner Albayrak ◽  
Savan Kharel ◽  
David Meltzer
Keyword(s):  
Wave Function ◽  
Analytic Continuation ◽  
Momentum Space ◽  
Spectral Representation ◽  
Flat Space ◽  
Tree Level ◽  
De Sitter ◽  
Yang Mills ◽  
The Universe ◽  
Double Copy

Abstract We explore color-kinematic duality for tree-level AdS/CFT correlators in momentum space. We start by studying the bi-adjoint scalar in AdS at tree-level as an illustrative example. We follow this by investigating two forms of color-kinematic duality in Yang-Mills theory, the first for the integrated correlator in AdS4 and the second for the integrand in general AdSd+1. For the integrated correlator, we find color-kinematics does not yield additional relations among n-point, color-ordered correlators. To study color-kinematics for the AdSd+1 Yang-Mills integrand, we use a spectral representation of the bulk-to-bulk propagator so that AdS diagrams are similar in structure to their flat space counterparts. Finally, we study color KLT relations for the integrated correlator and double-copy relations for the AdS integrand. We find that double-copy in AdS naturally relates the bi-adjoint theory in AdSd+3 to Yang-Mills in AdSd+1. We also find a double-copy relation at three-points between Yang-Mills in AdSd+1 and gravity in AdSd−1 and comment on the higher-point generalization. By analytic continuation, these results on AdS/CFT correlators can be translated into statements about the wave function of the universe in de Sitter.

SCALAR FIELD THEORY IN THE AdS/CFT CORRESPONDENCE: AN OPERATOR FORMULATION

2007 ◽  
Vol 22 (30) ◽  
pp. 2287-2295 ◽  
Author(s):  
G. A. KERIMOV
Keyword(s):  
Field Theory ◽  
Scalar Field ◽  
Scalar Fields ◽  
De Sitter Space ◽  
De Sitter ◽  
Point Function ◽  
Scalar Field Theory ◽  
Arbitrary Mass ◽  
Boundary Limit ◽  
Operator Formulation

Starting with a scalar field theory in Euclidean anti-de Sitter space constructed in an earlier paper, we examine the boundary limit of the quantized bulk field. Our AdS/CFT correspondence is generally valid for interacting fields, and is illustrated by a treatment of three-point function for scalar fields of arbitrary mass.

scholarly journals A derivation of AdS/CFT for vector models

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Ofer Aharony ◽  
Shai M. Chester ◽  
Erez Y. Urbach
Keyword(s):  
High Spin ◽  
Path Integral ◽  
De Sitter Space ◽  
Conformal Group ◽  
Local Fields ◽  
Local Action ◽  
De Sitter ◽  
Gauge Fixing ◽  
Spin Fields ◽  
Non Local

Abstract We explicitly rewrite the path integral for the free or critical O(N) (or U(N)) bosonic vector models in d space-time dimensions as a path integral over fields (including massless high-spin fields) living on (d + 1)-dimensional anti-de Sitter space. Inspired by de Mello Koch, Jevicki, Suzuki and Yoon and earlier work, we first rewrite the vector models in terms of bi-local fields, then expand these fields in eigenmodes of the conformal group, and finally map these eigenmodes to those of fields on anti-de Sitter space. Our results provide an explicit (non-local) action for a high-spin theory on anti-de Sitter space, which is presumably equivalent in the large N limit to Vasiliev’s classical high-spin gravity theory (with some specific gauge-fixing to a fixed background), but which can be used also for loop computations. Our mapping is explicit within the 1/N expansion, but in principle can be extended also to finite N theories, where extra constraints on products of bulk fields need to be taken into account.

scholarly journals Time dependent couplings as observables in de Sitter space

2014 ◽  
Vol 29 (08) ◽  
pp. 1430016 ◽  
Author(s):  
Hiroyuki Kitamoto ◽  
Yoshihisa Kitazawa
Keyword(s):  
Physical Mechanism ◽  
Quantum Effect ◽  
De Sitter Space ◽  
Time Dependent ◽  
General Covariance ◽  
De Sitter ◽  
Scale Invariant ◽  
Logarithmic Corrections ◽  
Slow Roll ◽  
The One

We summarize and expand our investigations concerning the soft graviton effects on microscopic matter dynamics in de Sitter space. The physical couplings receive IR logarithmic corrections which are sensitive to the IR cutoff at the one-loop level. The scale invariant spectrum in the gravitational propagator at the super-horizon scale is the source of the de Sitter symmetry breaking. The quartic scalar, Yukawa and gauge couplings become time dependent and diminish with time. In contrast, the Newton's constant increases with time. We clarify the physical mechanism behind these effects in terms of the conformal mode dynamics in analogy with 2d quantum gravity. We show that they are the inevitable consequence of the general covariance and lead to gauge invariant predictions. We construct a simple model in which the cosmological constant is self-tuned to vanish due to UV–IR mixing effect. We also discuss phenomenological implications such as decaying Dark Energy and SUSY breaking at the inflation era. The quantum effect alters the classical slow roll picture in general, if the tensor-to-scalar ratio r is as small as 0.01.

scholarly journals An invitation to the principal series

2020 ◽  
Vol 9 (3) ◽  
Author(s):  
Tarek Anous ◽  
Jim Skulte
Keyword(s):  
Isometry Group ◽  
Hamiltonian Formulation ◽  
Series Representation ◽  
Principal Series ◽  
Scalar Fields ◽  
De Sitter Space ◽  
Late Time ◽  
De Sitter ◽  
Principal Series Representation ◽  
Massive Scalar Field

Scalar unitary representations of the isometry group of dd-dimensional de Sitter space SO(1,d)SO(1,d) are labeled by their conformal weights \DeltaΔ. A salient feature of de Sitter space is that scalar fields with sufficiently large mass compared to the de Sitter scale 1/\ell1/ℓ have complex conformal weights, and physical modes of these fields fall into the unitary continuous principal series representation of SO(1,d)SO(1,d). Our goal is to study these representations in d=2d=2, where the relevant group is SL(2,\mathbb{R})SL(2,ℝ). We show that the generators of the isometry group of dS_22 acting on a massive scalar field reproduce the quantum mechanical model introduced by de Alfaro, Fubini and Furlan (DFF) in the early/late time limit. Motivated by the ambient dS_22 construction, we review in detail how the DFF model must be altered in order to accommodate the principal series representation. We point out a difficulty in writing down a classical Lagrangian for this model, whereas the canonical Hamiltonian formulation avoids any problem. We speculate on the meaning of the various de Sitter invariant vacua from the point of view of this toy model and discuss some potential generalizations.

scholarly journals On the consistency of (partially-)massless matter couplings in de Sitter space

2021 ◽  
Vol 2021 (10) ◽  
Author(s):  
Charlotte Sleight ◽  
Massimo Taronna
Keyword(s):  
Gauge Invariance ◽  
Point Processes ◽  
Scalar Fields ◽  
Flat Space ◽  
De Sitter Space ◽  
Tree Level ◽  
De Sitter ◽  
Scalar Matter ◽  
Carry Over ◽  
Massless Fields

Abstract We study the consistency of the cubic couplings of a (partially-)massless spinning field to two scalars in (d + 1)-dimensional de Sitter space. Gauge invariance of observables with external (partially)-massless spinning fields translates into Ward-Takahashi identities on the boundary. Using the Mellin-Barnes representation for boundary correlators in momentum space, we give a systematic study of Ward-Takahashi identities for tree-level 3- and 4-point processes involving a single external (partially-)massless field of arbitrary integer spin-J. 3-point Ward-Takahashi identities constrain the mass of the scalar fields to which a (partially-)massless spin-J field can couple. 4-point Ward-Takahashi identities then constrain the corresponding cubic couplings. For massless spinning fields, we show that Weinberg’s flat space results carry over to (d+1)-dimensional de Sitter space: for spins J = 1, 2 gauge-invariance implies charge-conservation and the equivalence principle while, assuming locality, higher-spins J > 2 cannot couple consistently to scalar matter. This result also applies to anti-de Sitter space. For partially-massless fields, restricting for simplicity to those of depth-2, we show that there is no consistent coupling to scalar matter in local theories. Along the way we also give a detailed account of how contact amplitudes with and without derivatives are represented in the Mellin-Barnes representation. Various new explicit expressions for 3- and 4-point functions involving (partially-)massless fields and conformally coupled scalars in dS4 are given.

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