113 research outputs found
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- 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 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 -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- and spin- 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
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 graviton four-point function in de Sitter space
We compute the tree-level late-time graviton four-point correlation function,
and the related quartic wavefunction coefficient, for Einstein gravity in de
Sitter spacetime. We derive this result in several ways: by direct calculation,
using the in-in formalism and the wavefunction of the universe; by a heuristic
derivation leveraging the flat space wavefunction coefficient; and by using the
boostless cosmological bootstrap, in particular the combination of the
cosmological optical theorem, the amplitude limit, and the manifestly local
test. We find agreement among the different methods.Comment: 46 page
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
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
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