72 research outputs found
Late-time structure of the Bunch-Davies de Sitter wavefunction
We examine the late time behavior of the Bunch-Davies wavefunction for interacting light fields in a de Sitter background. We use perturbative techniques developed in the framework of AdS/CFT, and analytically continue to compute tree and loop level contributions to the Bunch-Davies wavefunction. We consider self-interacting scalars of general mass, but focus especially on the massless and conformally coupled cases. We show that certain contributions grow logarithmically in conformal time both at tree and loop level. We also consider gauge fields and gravitons. The four-dimensional Fefferman-Graham expansion of classical asymptotically de Sitter solutions is used to show that the wavefunction contains no logarithmic growth in the pure graviton sector at tree level. Finally, assuming a holographic relation between the wavefunction and the partition function of a conformal field theory, we interpret the logarithmic growths in the language of conformal field theory
The discreet charm of the discrete series in dS2
We study quantum field theories placed on a two-dimensional de Sitter spacetime (dS2) with an eye on the group-theoretic organization of single and multiparticle states. We explore the distinguished role of the discrete series unitary irreducible representation (UIR) in the Hilbert space. By employing previous attempts to realize these states in free tachyonic scalar field theories, we propose how the discrete series may contribute to the Källén-Lehmann decomposition of an interacting scalar two-point function. We also study BF gauge theories with SL(N, R) gauge group in dS2 and establish a relation between the discrete series UIRs and the operator content of these theories. Although present at the level of the operators, states carrying discrete series quantum numbers are projected out of the gauge-invariant Hilbert space. This projection is reminiscent of what happens for quantum field theories coupled to semiclassical de Sitter gravity, where we must project onto the subspace of de Sitter invariant states. We discuss how to impose the diffeomorphism constraints on local field-theory operators coupled to two-dimensional gravity in de Sitter, with particular emphasis on the role of contact terms. Finally, we discuss an SYK-type model with a random two-body interaction that encodes an infinite tower of discrete series operators. We speculate on its potential microscopic connection to the SL(N, R) BF theory in the large-N limit.</p
OPE statistics from higher-point crossing
We present new asymptotic formulas for the distribution of OPE coefficients in conformal field theories. These formulas involve products of four or more coefficients and include light-light-heavy as well as heavy-heavy-heavy contributions. They are derived from crossing symmetry of the six and higher point functions on the plane and should be interpreted as non-Gaussianities in the statistical distribution of the OPE coefficients. We begin with a formula for arbitrary operator exchanges (not necessarily primary) valid in any dimension. This is the first asymptotic formula constraining heavy-heavy-heavy OPE coefficients in d > 2. For two-dimensional CFTs, we present refined asymptotic formulas stemming from exchanges of quasi-primaries as well as Virasoro primaries.We present new asymptotic formulas for the distribution of OPE coefficients in conformal field theories. These formulas involve products of four or more coefficients and include light-light-heavy as well as heavy-heavy-heavy contributions. They are derived from crossing symmetry of the six and higher point functions on the plane and should be interpreted as non-Gaussianities in the statistical distribution of the OPE coefficients. We begin with a formula for arbitrary operator exchanges (not necessarily primary) valid in any dimension. This is the first asymptotic formula constraining heavy-heavy-heavy OPE coefficients in . For two-dimensional CFTs, we present refined asymptotic formulas stemming from exchanges of quasi-primaries as well as Virasoro primaries
Areas and entropies in BFSS/gravity duality
The BFSS matrix model provides an example of gauge-theory / gravity duality
where the gauge theory is a model of ordinary quantum mechanics with no spatial
subsystems. If there exists a general connection between areas and entropies in
this model similar to the Ryu-Takayanagi formula, the entropies must be more
general than the usual subsystem entanglement entropies. In this note, we first
investigate the extremal surfaces in the geometries dual to the BFSS model at
zero and finite temperature. We describe a method to associate regulated areas
to these surfaces and calculate the areas explicitly for a family of surfaces
preserving symmetry, both at zero and finite temperature. We then
discuss possible entropic quantities in the matrix model that could be dual to
these regulated areas.Comment: 29 pages, 3 figures. v2 Examples in section 6 moved to appendix.
Minor comments adde
de Sitter Supersymmetry Revisited
We present the basic superconformal field theories in
four-dimensional de Sitter space-time, namely the non-abelian super Yang-Mills
theory and the chiral multiplet theory with gauge interactions or cubic
superpotential. These theories have eight supercharges and are invariant under
the full group of conformal symmetries, which includes the de Sitter
isometry group as a subgroup. The theories are ghost-free and the
anti-commutator is positive. SUSY
Ward identities uniquely select the Bunch-Davies vacuum state. This vacuum
state is invariant under superconformal transformations, despite the fact that
de Sitter space has non-zero Hawking temperature. The theories
are classically invariant under the superconformal group, but this
symmetry is broken by radiative corrections. However, no such difficulty is
expected in the theory, which is presented in appendix B.Comment: 21 pages, 2 figure
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