A. Liam Fitzpatrick

The Effective Field Theory of Inflation

We study the effective field theory of inflation, i.e. the most general theory describing the fluctuations around a quasi de Sitter background, in the case of single field models. The scalar mode can be eaten by the metric by going to unitary gauge. In this gauge, the most general theory is built with the lowest dimension operators invariant under spatial diffeomorphisms, like g00 and Kμν, the extrinsic curvature of constant time surfaces. This approach allows us to characterize all the possible high energy corrections to simple slow-roll inflation, whose sizes are constrained by experiments. Also, it describes in a common language all single field models, including those with a small speed of sound and Ghost Inflation, and it makes explicit the implications of having a quasi de Sitter background. The non-linear realization of time diffeomorphisms forces correlation among different observables, like a reduced speed of sound and an enhanced level of non-Gaussianity.

The analytic bootstrap and AdS superhorizon locality

A bstractWe take an analytic approach to the CFT bootstrap, studying the 4-pt correlators of d > 2 dimensional CFTs in an Eikonal-type limit, where the conformal cross ratios satisfy |u| ≪ |υ| < 1. We prove that every CFT with a scalar operator ϕ must contain infinite sequences of operators

Universality of Long-Distance AdS Physics from the CFT Bootstrap

{{\mathcal{O}}_{{\tau, \ell }}}

The effective field theory of dark matter direct detection

with twist approaching τ → 2Δϕ + 2n for each integer n as ℓ → ∞. We show how the rate of approach is controlled by the twist and OPE coefficient of the leading twist operator in the ϕ × ϕ OPE, and we discuss SCFTs and the 3d Ising Model as examples. Additionally, we show that the OPE coefficients of other large spin operators appearing in the OPE are bounded as ℓ → ∞. We interpret these results as a statement about superhorizon locality in AdS for general CFTs.

On the consistency relation of the three-point function in single-field inflation

A bstractWe begin by explicating a recent proof of the cluster decomposition principle in AdS≥4 from the CFT≥3 bootstrap. The CFT argument also computes the leading interactions between distant objects in AdS≥4, and we confirm the universal agreement between the CFT bootstrap and AdS gravity in the semi-classical limit.We proceed to study the generalization to CFT2, which requires knowledge of the Virasoro conformal blocks in a lightcone OPE limit. We compute these blocks in a semiclassical, large central charge approximation, and use them to prove a suitably modified theorem. In particular, from the d = 2 bootstrap we prove the existence of large spin operators with fixed ‘anomalous dimensions’ indicative of the presence of deficit angles in AdS3. As we approach the threshold for the BTZ black hole, interpreted as a CFT2 scaling dimension, the twist spectrum of large spin operators becomes dense.Due to the exchange of the Virasoro identity block, primary states above the BTZ threshold mimic a thermal background for light operators. We derive the BTZ quasinormal modes, and we use the bootstrap equation to prove that the twist spectrum is dense. Corrections to thermality could be obtained from a more refined computation of the Virasoro conformal blocks.

Virasoro Conformal Blocks and Thermality from Classical Background Fields

We extend and explore the general non-relativistic effective theory of dark matter (DM) direct detection. We describe the basic non-relativistic building blocks of operators and discuss their symmetry properties, writing down all Galilean-invariant operators up to quadratic order in momentum transfer arising from exchange of particles of spin 1 or less. Any DM particle theory can be translated into the coefficients of an effective operator and any effective operator can be simply related to most general description of the nuclear response. We find several operators which lead to novel nuclear responses. These responses differ significantly from the standard minimal WIMP cases in their relative coupling strengths to various elements, changing how the results from different experiments should be compared against each other. Response functions are evaluated for common DM targets — F, Na, Ge, I, and Xe — using standard shell model techniques. We point out that each of the nuclear responses is familiar from past studies of semi-leptonic electroweak interactions, and thus potentially testable in weak interaction studies. We provide tables of the full set of required matrix elements at finite momentum transfer for a range of common elements, making a careful and fully model-independent analysis possible. Finally, we discuss embedding non-relativistic effective theory operators into UV models of dark matter.

Extra)ordinary gauge mediation

The consistency relation for the three-point function of the cosmic microwave background is a very powerful observational signature which is believed to be true for every inflationary model in which there is only one dynamical degree of freedom. Its importance relies on the fact that deviations from it might be detected in next generation experiments, allowing us to rule out all single-field inflationary models. After making more precise the already existing proof of the consistency relation, we use a recently developed effective field theory for inflationary perturbations to provide an alternative and very explicit proof valid at leading non-trivial order in slow roll parameters.

Unitarity and the Holographic S-Matrix

A bstractWe show that in 2d CFTs at large central charge, the coupling of the stress tensor to heavy operators can be re-absorbed by placing the CFT in a non-trivial background metric. This leads to a more precise computation of the Virasoro conformal blocks between heavy and light operators, which are shown to be equivalent to global conformal blocks evaluated in the new background. We also generalize to the case where the operators carry U(1) charges. The refined Virasoro blocks can be used as the seed for a new Virasoro block recursion relation expanded in the heavy-light limit. We comment on the implications of our results for the universality of black hole thermality in AdS3, or equivalently, the eigenstate thermalization hypothesis for CFT2 at large central charge.

Searching for the Kaluza-Klein graviton in bulk RS models

We study models of ``(extra)ordinary gauge mediation, which consist of taking ordinary gauge mediation and extending the messenger superpotential to include all renormalizable couplings consistent with SM gauge invariance and an R-symmetry. We classify all such models and find that their phenomenology can differ significantly from that of ordinary gauge mediation. Some highlights include: arbitrary modifications of the squark/slepton mass relations, small μ and Higgsino NLSPs, and the possibility of having fewer than one effective messenger. We also show how these models lead naturally to extremely simple examples of direct gauge mediation, where SUSY and R-symmetry breaking occur not in a hidden sector, but due to the dynamics of the messenger sector itself.

AdS field theory from conformal field theory

A bstractThe bulk S-Matrix can be given a non-perturbative definition in terms of the flat space limit of AdS/CFT. We show that the unitarity of the S-Matrix, ie the optical theorem, can be derived by studying the behavior of the OPE and the conformal block decomposition in the flat space limit. When applied to perturbation theory in AdS, this gives a holographic derivation of the cutting rules for Feynman diagrams. To demonstrate these facts we introduce some new techniques for the analysis of conformal field theories. Chief among these is a method for conglomerating local primary operators