scholarly journals Hamiltonian truncation in Anti-de Sitter spacetime

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Matthijs Hogervorst ◽  
Marco Meineri ◽  
João Penedones ◽  
Kamran Salehi Vaziri
Keyword(s):  
Arbitrary Order ◽  
Energy Levels ◽  
Quantum Field Theories ◽  
De Sitter ◽  
Conformal Boundary ◽  
Massive Scalar Field ◽  
Strongly Coupled ◽  
Sitter Spacetime ◽  
Ads Spacetime ◽  
Renormalization Group Flows

Abstract Quantum Field Theories (QFTs) in Anti-de Sitter (AdS) spacetime are often strongly coupled when the radius of AdS is large, and few methods are available to study them. In this work, we develop a Hamiltonian truncation method to compute the energy spectrum of QFTs in two-dimensional AdS. The infinite volume of constant timeslices of AdS leads to divergences in the energy levels. We propose a simple prescription to obtain finite physical energies and test it with numerical diagonalization in several models: the free massive scalar field, ϕ4 theory, Lee-Yang and Ising field theory. Along the way, we discuss spontaneous symmetry breaking in AdS and derive a compact formula for perturbation theory in quantum mechanics at arbitrary order. Our results suggest that all conformal boundary conditions for a given theory are connected via bulk renormalization group flows in AdS.

scholarly journals On the algebraic quantization of a massive scalar field in anti-de Sitter spacetime

2018 ◽  
Vol 30 (02) ◽  
pp. 1850004 ◽  
Author(s):  
Claudio Dappiaggi ◽  
Hugo R. C. Ferreira
Keyword(s):  
Scalar Field ◽  
De Sitter Spacetime ◽  
Massive Scalar ◽  
De Sitter ◽  
Functional Formalism ◽  
Arbitrary Boundary ◽  
Massive Scalar Field ◽  
Sitter Spacetime ◽  
Hadamard States ◽  
Definition Of

We discuss the algebraic quantization of a real, massive scalar field in the Poincaré patch of the [Formula: see text]-dimensional anti-de Sitter spacetime, with arbitrary boundary conditions. By using the functional formalism, we show that it is always possible to associate to such system an algebra of observables enjoying the standard properties of causality, time-slice axiom and F-locality. In addition, we characterize the wavefront set of the ground state associated to the system under investigation. As a consequence, we are able to generalize the definition of Hadamard states and construct a global algebra of Wick polynomials.

scholarly journals On the time evolution of cosmological correlators

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Sebastián Céspedes ◽  
Anne-Christine Davis ◽  
Scott Melville
Keyword(s):  
Time Evolution ◽  
Transfer Functions ◽  
Equations Of Motion ◽  
Late Time ◽  
De Sitter ◽  
Initial State ◽  
Conformal Boundary ◽  
Sitter Spacetime ◽  
Boundary Operators ◽  
Simple Equations

Abstract Developing our understanding of how correlations evolve during inflation is crucial if we are to extract information about the early Universe from our late-time observables. To that end, we revisit the time evolution of scalar field correlators on de Sitter spacetime in the Schrödinger picture. By direct manipulation of the Schrödinger equation, we write down simple “equations of motion” for the coefficients which determine the wavefunction. Rather than specify a particular interaction Hamiltonian, we assume only very basic properties (unitarity, de Sitter invariance and locality) to derive general consequences for the wavefunction’s evolution. In particular, we identify a number of “constants of motion” — properties of the initial state which are conserved by any unitary dynamics — and show how this can be used to partially fix the cubic and quartic wavefunction coefficients at weak coupling. We further constrain the time evolution by deriving constraints from the de Sitter isometries and show that these reduce to the familiar conformal Ward identities at late times. Finally, we show how the evolution of a state from the conformal boundary into the bulk can be described via a number of “transfer functions” which are analytic outside the horizon for any local interaction. These objects exhibit divergences for particular values of the scalar mass, and we show how such divergences can be removed by a renormalisation of the boundary wavefunction — this is equivalent to performing a “Boundary Operator Expansion” which expresses the bulk operators in terms of regulated boundary operators. Altogether, this improved understanding of the wavefunction in the bulk of de Sitter complements recent advances from a purely boundary perspective, and reveals new structure in cosmological correlators.

scholarly journals Analysis of scalar and fermion quantum field theory on anti-de Sitter spacetime

2018 ◽  
Vol 27 (11) ◽  
pp. 1843014 ◽  
Author(s):  
Victor E. Ambruş ◽  
Carl Kent ◽  
Elizabeth Winstanley
Keyword(s):  
Green's Functions ◽  
Green’S Functions ◽  
Vacuum Expectation ◽  
Dirac Fermion ◽  
De Sitter ◽  
Expectation Values ◽  
Sitter Spacetime ◽  
Fermion Fields ◽  
Spacetime Curvature ◽  
Ads Spacetime

We study vacuum and thermal expectation values of quantum scalar and Dirac fermion fields on anti-de Sitter (adS) spacetime. AdS spacetime is maximally symmetric and this enables expressions for the scalar and fermion vacuum Feynman Green’s functions to be derived in closed form. We employ Hadamard renormalization to find the vacuum expectation values (v.e.v.s). The thermal Feynman Green’s functions are constructed from the vacuum Feynman Green’s functions using the imaginary time periodicity/anti-periodicity property for scalars/fermions. Focusing on massless fields with either conformal or minimal coupling to the spacetime curvature (these two cases being the same for fermions) we compute the differences between the thermal expectation values and v.e.v.s. We compare the resulting energy densities, pressures and pressure deviators with the corresponding classical quantities calculated using relativistic kinetic theory.

scholarly journals CASIMIR EFFECT IN DE SITTER SPACETIME

2011 ◽  
Vol 03 ◽  
pp. 215-226 ◽  
Author(s):  
A. A. SAHARIAN
Keyword(s):  
Energy Momentum Tensor ◽  
Coupling Parameter ◽  
Momentum Tensor ◽  
Curvature Radius ◽  
De Sitter Spacetime ◽  
Parallel Plates ◽  
De Sitter ◽  
Casimir Forces ◽  
Massive Scalar Field ◽  
Sitter Spacetime

The vacuum expectation value of the energy-momentum tensor and the Casimir forces are investigated for a massive scalar field with an arbitrary curvature coupling parameter in the geometry of two parallel plates, on the background of de Sitter spacetime. The field is prepared in the Bunch–Davies vacuum state and is constrained to satisfy Robin boundary conditions on the plates. The vacuum energy-momentum tensor is non-diagonal, with the off-diagonal component corresponding to the energy flux along the direction normal to the plates. It is shown that the curvature of the background spacetime decisively influences the behavior of the Casimir forces at separations larger than the curvature radius of de Sitter spacetime. In dependence of the curvature coupling parameter and the mass of the field, two different regimes are realized, which exhibit monotonic or oscillatory behavior of the forces. The decay of the Casimir force at large plate separation is shown to be power-law, with independence of the value of the field mass.

scholarly journals CASIMIR EFFECT IN DE SITTER SPACETIME

2011 ◽  
Vol 26 (22) ◽  
pp. 3833-3844 ◽  
Author(s):  
A. A. SAHARIAN
Keyword(s):  
Energy Momentum Tensor ◽  
Coupling Parameter ◽  
Momentum Tensor ◽  
Curvature Radius ◽  
De Sitter Spacetime ◽  
Parallel Plates ◽  
De Sitter ◽  
Casimir Forces ◽  
Massive Scalar Field ◽  
Sitter Spacetime

The vacuum expectation value of the energy-momentum tensor and the Casimir forces are investigated for a massive scalar field with an arbitrary curvature coupling parameter in the geometry of two parallel plates, on the background of de Sitter spacetime. The field is prepared in the Bunch–Davies vacuum state and is constrained to satisfy Robin boundary conditions on the plates. The vacuum energy-momentum tensor is non-diagonal, with the off-diagonal component corresponding to the energy flux along the direction normal to the plates. It is shown that the curvature of the background space-time decisively influences the behavior of the Casimir forces at separations larger than the curvature radius of de Sitter spacetime. In dependence of the curvature coupling parameter and the mass of the field, two different regimes are realized, which exhibit monotonic or oscillatory behavior of the forces. The decay of the Casimir force at large plate separation is shown to be power-law, with independence of the value of the field mass.

scholarly journals Isospin-1/2 Dπ scattering and the lightest $$ {D}_0^{\ast } $$ resonance from lattice QCD

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Luke Gayer ◽  
Nicolas Lang ◽  
Sinéad M. Ryan ◽  
David Tims ◽  
Christopher E. Thomas ◽  
...  
Keyword(s):  
Scattering Amplitudes ◽  
Lattice Qcd ◽  
Quark Mass ◽  
Light Quark ◽  
Energy Levels ◽  
Experimental Result ◽  
Infinite Volume ◽  
Resonance Pole ◽  
Strongly Coupled ◽  
Light Quark Mass

Abstract Isospin-1/2 Dπ scattering amplitudes are computed using lattice QCD, working in a single volume of approximately (3.6 fm)3 and with a light quark mass corresponding to mπ ≈ 239 MeV. The spectrum of the elastic Dπ energy region is computed yielding 20 energy levels. Using the Lüscher finite-volume quantisation condition, these energies are translated into constraints on the infinite-volume scattering amplitudes and hence enable us to map out the energy dependence of elastic Dπ scattering. By analytically continuing a range of scattering amplitudes, a $$ {D}_0^{\ast } $$ D 0 ∗ resonance pole is consistently found strongly coupled to the S-wave Dπ channel, with a mass m ≈ 2200 MeV and a width Γ ≈ 400 MeV. Combined with earlier work investigating the $$ {D}_{s0}^{\ast } $$ D s 0 ∗ , and $$ {D}_0^{\ast } $$ D 0 ∗ with heavier light quarks, similar couplings between each of these scalar states and their relevant meson-meson scattering channels are determined. The mass of the $$ {D}_0^{\ast } $$ D 0 ∗ is consistently found well below that of the $$ {D}_{s0}^{\ast } $$ D s 0 ∗ , in contrast to the currently reported experimental result.

scholarly journals Unimodular vs nilpotent superfield approach to pure dS supergravity

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Sukruti Bansal ◽  
Silvia Nagy ◽  
Antonio Padilla ◽  
Ivonne Zavala
Keyword(s):  
String Theory ◽  
General Framework ◽  
Recent Progress ◽  
High Energy ◽  
De Sitter Spacetime ◽  
De Sitter ◽  
New Approach ◽  
Sitter Spacetime ◽  
Novel Approach ◽  
De Sitter Vacua

Abstract Recent progress in understanding de Sitter spacetime in supergravity and string theory has led to the development of a four dimensional supergravity with spontaneously broken supersymmetry allowing for de Sitter vacua, also called de Sitter supergravity. One approach makes use of constrained (nilpotent) superfields, while an alternative one couples supergravity to a locally supersymmetric generalization of the Volkov-Akulov goldstino action. These two approaches have been shown to give rise to the same 4D action. A novel approach to de Sitter vacua in supergravity involves the generalisation of unimodular gravity to supergravity using a super-Stückelberg mechanism. In this paper, we make a connection between this new approach and the previous two which are in the context of nilpotent superfields and the goldstino brane. We show that upon appropriate field redefinitions, the 4D actions match up to the cubic order in the fields. This points at the possible existence of a more general framework to obtain de Sitter spacetimes from high-energy theories.

scholarly journals Wavefunctions in dS/CFT revisited: principal series and double-trace deformations

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Hiroshi Isono ◽  
Hoiki Madison Liu ◽  
Toshifumi Noumi
Keyword(s):  
Principal Series ◽  
Light Fields ◽  
Quadratic Term ◽  
De Sitter Spacetime ◽  
Cosmological Horizon ◽  
De Sitter ◽  
Complementary Series ◽  
Point Function ◽  
Sitter Spacetime ◽  
Simple Scaling

Abstract We study wavefunctions of heavy scalars on de Sitter spacetime and their implications to dS/CFT correspondence. In contrast to light fields in the complementary series, heavy fields in the principal series oscillate outside the cosmological horizon. As a consequence, the quadratic term in the wavefunction does not follow a simple scaling and so it is hard to identify it with a conformal two-point function. In this paper, we demonstrate that it should be interpreted as a two-point function on a cyclic RG flow which is obtained by double-trace deformations of the dual CFT. This is analogous to the situation in nonrelativistic AdS/CFT with a bulk scalar whose mass squared is below the Breitenlohner-Freedman (BF) bound. We also provide a new dS/CFT dictionary relating de Sitter two-point functions and conformal two-point functions in the would-be dual CFT.

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