An Algebraic Classification of Exceptional EFTs Part II: Supersymmetry

We present a novel approach to classify supersymmetric effective field theories (EFTs) whose scattering amplitudes exhibit enhanced soft limits. These enhancements arise due to non-linearly realised symmetries on the Goldstone modes of such EFTs and we classify the algebras that these symmetries can form. Our main focus is on so-called exceptional algebras which lead to field-dependent transformation rules and EFTs with the maximum possible soft enhancement at a given derivative power counting. We adapt existing techniques for Poincar\'{e} invariant theories to the supersymmetric case, and introduce superspace inverse Higgs constraints as a method of reducing the number of Goldstone modes while maintaining all symmetries. Restricting to the case of a single Goldstone supermultiplet in four dimensions, we classify the exceptional algebras and EFTs for a chiral, Maxwell or real linear supermultiplet. Moreover, we show how our algebraic approach allows one to read off the soft weights of the different component fields from superspace inverse Higgs trees, which are the algebraic cousin of the on-shell soft data one provides to soft bootstrap EFTs using on-shell recursion. Our Lie-superalgebraic approach extends the results of on-shell methods and provides a complementary perspective on non-linear realisations

An Algebraic Classification of Exceptional EFTs

We classify four-dimensional effective field theories (EFTs) with enhanced soft limits, which arise due to non-linearly realised symmetries on the Goldstone modes of such theories. We present an algorithm for deriving all possible algebras that can be non-linearly realised on a set of Goldstone modes with canonical propagators, linearly realised Poincar\'{e} symmetries and interactions at weak coupling. We then perform a full classification of the cases with multiple scalars or multiple spin-$1/2$ fermions as the Goldstone modes. In each case there are only a small number of algebras consistent with field-dependent transformation rules, leading to the class of exceptional EFTs including the scalar sector of Dirac-Born-Infeld, Special Galileon and Volkov-Akulov theories. We also discuss the coupling of a $U(1)$ gauge vector to the exceptional scalar theories, showing that there is a Special Galileon version of the full Dirac-Born-Infeld theory. This paper is part I in a series of two papers, with the second providing an algebraic classification of supersymmetric theories

Cosmological Correlators Through the Looking Glass: Reality, Parity, and Factorisation

We consider the evolution of quantum fields during inflation, and show that the total-energy singularities appearing in the perturbative expansion of the late-time Wavefunction of the Universe are purely real when the external states are massless scalars and massless gravitons. Our proof relies on the tree-level approximation, Bunch-Davies initial conditions, and exact scale invariance (IR-convergence), but without any assumptions on invariance under de Sitter boosts. We consider all $n$-point functions and allow for the exchange of additional states of any mass and integer spin. Our proof makes use of a decomposition of the inflationary bulk-bulk propagator of massive spinning fields which preserves UV-convergence and ensures that the time-ordered contributions are purely real after we rotate to Euclidean time. We use this reality property to show that the maximally-connected parts of wavefunction coefficients, from which total-energy singularities come from, are purely real. In a theory where all states are in the complementary series, this reality extends to the full wavefunction coefficient. We then use our reality theorem to show that parity-odd correlators (correlators that are mirror asymmetric) are factorised and do not diverge when the total-energy is conserved. We pay special attention to the parity-odd four-point function (trispectrum) of inflationary curvature perturbations and use our reality/factorisation theorems to show that this observable is factorised into a product of cubic diagrams thereby enabling us to derive exact shapes. We present examples of couplings between the inflaton and massive spin-$1$ and spin-$2$ fields, with the parity-violation in the trispectrum driven by Chern-Simons corrections to the spinning field two-point function, or from parity-violating cubic interactions which we build within the Effective Field Theory of Inflation.Comment: 67 pages, 7 figure

The cosmological constant problem and gravity in the infrared

In this thesis we explore low energy extensions of Einstein's theory of General Relativity (GR). Initially our motivation will be the cosmological constant problem where large radiative corrections due to quantum field theories minimally coupled to the dynamical metric in GR leads to unacceptably large space-time curvatures. We will discuss the cosmological constant problem in detail, paying special attention to how it affects the global structure of a space-time whose dynamics are dictated by GR. With this in mind we will present and discuss recently proposed global modifications of GR which in the semi-classical limit sequester the radiatively unstable loop corrections to the cosmological constant from the space-time curvature. This is achieved by supplementing the local dynamics of GR with highly non-trivial global constraints, and we demonstrate how this can be achieved in a theory which is manifestly local. In this theory we will also consider the effects of an early universe phase transition on the late time dynamics. Away from global modifications of GR we will also consider local modifications which necessarily involve the propagation of new degrees of freedom. We outline the possible screening mechanisms which, since no new gravitational degrees of freedom have been observed in local environments, are an important feature of any local modification of GR. For one of these mechanisms, namely, the Vainshtein mechanism, we will consider the regime of validity of theories which make use of the Vainshtein mechanism and assess suggestions that one can trust these theories beyond the scale we would naively expect them to become strongly coupled. Following this we will move onto the chameleon mechanism, another example of a screening mechanism, and present a high energy extension motivated by the breakdown in the original chameleon theory in the early universe. The interactions of the resulting DBI chameleon theory will be motivated by our discussion of the Vainshtein mechanism

Spontaneously broken spacetime symmetries and the role of inessential Goldstones

In contrast to internal symmetries, there is no general proof that the coset construction for spontaneously broken spacetime symmetries leads to universal dynamics. One key difference lies in the role of Goldstone bosons, which for spacetime symmetries includes a subset which are inessential for the non- linear realisation and hence can be eliminated. In this paper we address two important issues that arise when eliminating inessential Goldstones.The first concerns the elimination itself, which is often performed by imposing socalledinverse Higgs constraints. Contrary to claims in the literature, there are a series of conditions on the structure constants which must be satisfied to employ the inverse Higgs phenomenon, and we discuss which parametrisation of the coset element is the most effective in this regard. We also consider generalisations of the standard inverse Higgs constraints, which can include integrating out inessential Goldstones at low energies, and prove that under certain assumptions these give rise to identical effective field theories for the essential Goldstones.Secondly, we consider mappings between non- linear realisations that differ both in the coset element and the algebra basis. While these can always be related to each other by a point transformation, remarkably, the inverse Higgs constraints are not necessarily mapped onto each other under this transformation. We discuss the physical implications of this non- mapping, with a particular emphasis on the coset space corresponding to the spontaneous breaking of the Anti-De Sitter isometries by a Minkowski probe brane.</p

The cosmological constant problem and gravity in the infrared

In this thesis we explore low energy extensions of Einstein's theory of General Relativity (GR). Initially our motivation will be the cosmological constant problem where large radiative corrections due to quantum field theories minimally coupled to the dynamical metric in GR leads to unacceptably large space-time curvatures. We will discuss the cosmological constant problem in detail, paying special attention to how it affects the global structure of a space-time whose dynamics are dictated by GR. With this in mind we will present and discuss recently proposed global modifications of GR which in the semi-classical limit sequester the radiatively unstable loop corrections to the cosmological constant from the space-time curvature. This is achieved by supplementing the local dynamics of GR with highly non-trivial global constraints, and we demonstrate how this can be achieved in a theory which is manifestly local. In this theory we will also consider the effects of an early universe phase transition on the late time dynamics. Away from global modifications of GR we will also consider local modifications which necessarily involve the propagation of new degrees of freedom. We outline the possible screening mechanisms which, since no new gravitational degrees of freedom have been observed in local environments, are an important feature of any local modification of GR. For one of these mechanisms, namely, the Vainshtein mechanism, we will consider the regime of validity of theories which make use of the Vainshtein mechanism and assess suggestions that one can trust these theories beyond the scale we would naively expect them to become strongly coupled. Following this we will move onto the chameleon mechanism, another example of a screening mechanism, and present a high energy extension motivated by the breakdown in the original chameleon theory in the early universe. The interactions of the resulting DBI chameleon theory will be motivated by our discussion of the Vainshtein mechanism

On Graviton non-Gaussianities in the Effective Field Theory of Inflation

We derive parity-even graviton bispectra in the Effective Field Theory of Inflation (EFToI) to all orders in derivatives. Working in perturbation theory, we construct all cubic interactions that can contribute to tree-level graviton bispectra, showing that they all come from EFToI operators containing two or three powers of the extrinsic curvature and its covariant derivatives: all other operators can be removed by field redefinitions or start at higher-order in perturbations. For operators cubic in the extrinsic curvature, where the single-clock consistency relations are satisfied without a correction to the graviton two-point function, we use the Manifestly Local Test (MLT) to efficiently extract the effects of evolving graviton fluctuations to the end of inflation. Despite the somewhat complicated nature of the bulk interactions, the final boundary correlators take a very compact form. For operators quadratic in the extrinsic curvature, the leading order bispectra are a sum of contact and single exchange diagrams, which are tied together by spatial diffeomorphisms, and to all orders in derivatives we derive these bispectra by computing the necessary bulk time integrals. For single exchange diagrams we exploit factorisation properties of the bulk-bulk propagator for massless gravitons and write the result as a finite sum over residues. Perhaps surprisingly, we show these single exchange contributions have only total-energy poles and also satisfy the MLT

The boostless bootstrap and BCFW momentum shifts

In a recent paper [1], three-particle interactions without invariance under Lorentz boosts were constrained by demanding that they yield tree-level four-particle scattering amplitudes with singularities as dictated by unitarity and locality. In this brief note, we show how to obtain an independent verification and consistency check of these boostless bootstrap results using BCFW momentum shifts. We point out that the constructibility criterion, related to the behaviour of the deformed amplitude at infinite BCFW parameter z, is not strictly necessary to obtain non-trivial constraints for the three-particle interactions

Symmetric superfluids

Abstract: We present a complete classification of symmetric superfluids, namely shift-symmetric and Poincaré invariant scalar field theories that have an enlarged set of classically conserved currents at leading order in derivatives. These theories arise in the decoupling limit of the effective field theory of shift-symmetric, single-clock cosmologies and our results pick out all models with couplings fixed by additional symmetry. Remarkably, in D ≥ 2 spacetime dimensions there are only two possibilities: the Dirac-Born-Infeld theory and Scaling Superfluids with Lagrangian (−∂μϕ∂μϕ)α, for some real α. The scaling symmetry present for any α is further enhanced to the full conformal group only for α = D/2, and to infinitely many additional generators for the cuscuton, namely α = 1/2. We discuss the stability of Scaling Superfluids and point out that all coupling constants are determined by the speed of sound