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.

scholarly journals Color/kinematics duality in AdS4

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Connor Armstrong ◽  
Arthur E. Lipstein ◽  
Jiajie Mei
Keyword(s):  
Gauge Symmetry ◽  
Momentum Space ◽  
Flat Space ◽  
Yang Mills ◽  
Space Limit ◽  
Double Copy

Abstract In flat space, the color/kinematics duality states that perturbative Yang-Mills amplitudes can be written in such a way that kinematic numerators obey the same Jacobi relations as their color factors. This remarkable duality implies BCJ relations for Yang-Mills amplitudes and underlies the double copy to gravitational amplitudes. In this paper, we find analogous relations for Yang-Mills amplitudes in AdS4. In particular we show that the kinematic numerators of 4-point Yang-Mills amplitudes computed via Witten diagrams in momentum space enjoy a generalised gauge symmetry which can be used to enforce the kinematic Jacobi relation away from the flat space limit, and we derive deformed BCJ relations which reduce to the standard ones in the flat space limit. We illustrate these results using compact new expressions for 4-point Yang-Mills amplitudes in AdS4 and their kinematic numerators in terms of spinors. We also spell out the relation to 3d conformal correlators in momentum space, and speculate on the double copy to graviton amplitudes in AdS4.

scholarly journals ATTRACTOR SOLUTION IN COUPLED YANG–MILLS FIELD DARK ENERGY MODELS

2009 ◽  
Vol 18 (09) ◽  
pp. 1331-1342 ◽  
Author(s):  
WEN ZHAO
Keyword(s):  
Dark Energy ◽  
Equation Of State ◽  
De Sitter ◽  
Yang Mills ◽  
Constraint Equations ◽  
Energy Models ◽  
Big Rip ◽  
Attractor Solution ◽  
The Universe ◽  
Mills Field

We investigate the attractor solution in the coupled Yang–Mills field dark energy models with the general interaction term, and obtain the constraint equations for the interaction if the attractor solution exists. The research also shows that, if the attractor solution exists, the equation of state of dark energy must evolve from wy > 0 to wy ≤ -1, which is slightly suggested by the observation. At the same time, the total equation of state in the attractor solution is w tot = -1, the universe is a de Sitter expansion, and the cosmic big rip is naturally avoided. These features are all independent of the interacting forms.

scholarly journals MHV amplitudes and BCFW recursion for Yang-Mills theory in the de Sitter static patch

2021 ◽  
Vol 2021 (9) ◽  
Author(s):  
Emil Albrychiewicz ◽  
Yasha Neiman ◽  
Mirian Tsulaia
Keyword(s):  
Scattering Problem ◽  
The Other ◽  
Tree Level ◽  
De Sitter ◽  
Recursion Relations ◽  
Yang Mills ◽  
The Past ◽  
Infinite Set ◽  
Mills Field ◽  
Helicity Structure

Abstract 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−1MHV helicity structure, dressed by ordinary Minkowski amplitudes. We derive all the N−1MHV 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.

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.

Gibbons–Hawking temperature corrected by quantum cosmology

2017 ◽  
Vol 26 (10) ◽  
pp. 1750116 ◽  
Author(s):  
Je-An Gu ◽  
Sang Pyo Kim ◽  
Che-Min Shen
Keyword(s):  
Wave Function ◽  
Quantum Cosmology ◽  
Quantum Correction ◽  
Planck Scale ◽  
Friedmann Equation ◽  
Back Reaction ◽  
De Sitter ◽  
Pure Gravity ◽  
The Universe ◽  
Spacetime Fluctuations

We explore a quantum cosmology description of the de Sitter (dS) radiation and its back-reaction to a dS space, inherent in the wave function of the Wheeler–DeWitt equation for pure gravity with a cosmological constant. We first investigate the quantum Friedmann–Lemaitre–Robertson–Walker cosmological model and then consider the possible effects of inhomogeneities of the universe on the dS radiation. In both the cases we obtain the modified Friedmann equation, including the back-reaction from spacetime fluctuations, and the quantum-corrected Gibbons–Hawking (GH) temperature. It is shown that the quantum correction increases the GH temperature with the increment characterized by the ratio of the dS scale to the Planck scale.

scholarly journals EXACT STRING SOLUTIONS IN (2 + 1)-DIMENSIONAL DE SITTER SPACE-TIME

1994 ◽  
Vol 09 (29) ◽  
pp. 2745-2754 ◽  
Author(s):  
H. J. DE VEGA ◽  
A. V. MIKHAILOV ◽  
N. SÁNCHEZ
Keyword(s):  
Flat Space ◽  
De Sitter Space ◽  
Space Time ◽  
The Other ◽  
De Sitter ◽  
Expansion Factor ◽  
New Feature ◽  
The Universe ◽  
Time Analogy

Exact and explicit string solutions in de Sitter space-time are found. (Here, the string equations reduce to a sinh-Gordon model). A new feature without flat space-time analogy appears: starting with a single worldsheet, several (here two) strings emerge. One string is stable and the other (unstable) grows as the universe grows. Their invariant size and energy either grow as the expansion factor or tend to constant. Moreover, strings can expand (contract) for large (small) universe radius at a different rate than the universe does.

scholarly journals Exact Four-Dimensional Exploding Universe Solution in String Theory

1997 ◽  
Vol 12 (19) ◽  
pp. 1355-1360 ◽  
Author(s):  
Shin'ichi Nojiri
Keyword(s):  
String Theory ◽  
Analytic Continuation ◽  
Flat Space ◽  
Fixed Time ◽  
Space Time ◽  
Speed Of Light ◽  
Left Behind ◽  
Flat Background ◽  
The Universe

We obtain a four-dimensional exploding universe solution in string theory. The solution is obtained from the string theory in the flat background by using non-Abelian T-duality and the analytic continuation. In the solution, the radius of the universe is finite for fixed time and the universe is surrounded by the boundary consists of singularity. The boundary runs away with the speed of light and the flat space–time is left behind.

scholarly journals The Virasoro-Shapiro amplitude in AdS5 × S5 and level splitting of 10d conformal symmetry

2021 ◽  
Vol 2021 (11) ◽  
Author(s):  
F. Aprile ◽  
J. M. Drummond ◽  
H. Paul ◽  
M. Santagata
Keyword(s):  
Conformal Symmetry ◽  
Flat Space ◽  
Tree Level ◽  
Yang Mills ◽  
Anomalous Dimensions ◽  
Crossing Symmetry ◽  
String Correction ◽  
Space Limit ◽  
Fixed Order ◽  
Bootstrap Algorithm

Abstract The genus zero contribution to the four-point correlator $$ \left\langle {\mathcal{O}}_{p_1}{\mathcal{O}}_{p_2}{\mathcal{O}}_{p_3}{\mathcal{O}}_{p_4}\right\rangle $$ O p 1 O p 2 O p 3 O p 4 of half-BPS single-particle operators $$ {\mathcal{O}}_p $$ O p in $$ \mathcal{N} $$ N = 4 super Yang-Mills, at strong coupling, computes the Virasoro-Shapiro amplitude of closed superstrings in AdS5× S5. Combining Mellin space techniques, the large p limit, and data about the spectrum of two-particle operators at tree level in supergravity, we design a bootstrap algorithm which heavily constrains its α′ expansion. We use crossing symmetry, polynomiality in the Mellin variables and the large p limit to stratify the Virasoro-Shapiro amplitude away from the ten-dimensional flat space limit. Then we analyse the spectrum of exchanged two-particle operators at fixed order in the α′ expansion. We impose that the ten-dimensional spin of the spectrum visible at that order is bounded above in the same way as in the flat space amplitude. This constraint determines the Virasoro-Shapiro amplitude in AdS5× S5 up to a small number of ambiguities at each order. We compute it explicitly for (α′)5,6,7,8,9. As the order of α′ grows, the ten dimensional spin grows, and the set of visible two-particle operators opens up. Operators illuminated for the first time receive a string correction to their anomalous dimensions which is uniquely determined and lifts the residual degeneracy of tree level supergravity, due to ten-dimensional conformal symmetry. We encode the lifting of the residual degeneracy in a characteristic polynomial. This object carries information about all orders in α′. It is analytic in the quantum numbers, symmetric under an AdS5 ↔ S5 exchange, and it enjoys intriguing properties, which we explain and detail in various cases.

scholarly journals Celestial double copy from the worldsheet

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Eduardo Casali ◽  
Atul Sharma
Keyword(s):  
Hypergeometric Function ◽  
Arbitrary Number ◽  
Cohomology Theory ◽  
Tree Level ◽  
Generalized Hypergeometric Function ◽  
Yang Mills ◽  
Twisted Cohomology ◽  
Double Copy

Abstract Using the ambitwistor string, we compute tree-level celestial amplitudes for biadjoint scalars, Yang-Mills and gravity to all multiplicities. They are presented in compact CHY-like formulas with operator-valued scattering equations and numerators acting on a generalized hypergeometric function. With these we extend the celestial double copy to tree-level amplitudes with arbitrary number of external states. We also show how color-kinematics duality is implemented in celestial amplitudes and its interpretation in terms of a generalized twisted cohomology theory.

scholarly journals THE ISSUE OF CHOOSING NOTHING: WHAT DETERMINES THE LOW ENERGY VACUUM STATE OF NATURE?

2000 ◽  
Vol 15 (29) ◽  
pp. 1813-1821 ◽  
Author(s):  
T. PADMANABHAN ◽  
T. ROY CHOUDHURY
Keyword(s):  
Wave Function ◽  
Vacuum State ◽  
Flat Space ◽  
Space Time ◽  
Low Energy ◽  
Approximate Theory ◽  
Volume Limit ◽  
Low Energies ◽  
Nonrelativistic Quantum Mechanics ◽  
The Universe

Starting from an (unknown) quantum gravitational model, one can invoke a sequence of approximations to progressively arrive at quantum field theory (QFT) in curved space–time, QFT in flat space–time, nonrelativistic quantum mechanics and Newtonian mechanics. The more exact theory can put restrictions on the range of possibilities allowed for the approximate theory which are not derivable from the latter — an example being the symmetry restrictions on the wave function for a pair of electrons. We argue that the choice of vacuum state at low energies could be such a "relic" arising from combining the principles of quantum theory and general relativity, and demonstrate this result in a simple toy model. Our analysis suggests that the wave function of the universe, when describing the large volume limit of the universe, dynamically selects a vacuum state for matter fields — which in turn defines the concept of particle in the low energy limit. The result also has the potential for providing a concrete quantum mechanical version of Mach's principle.

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