On-shell amplitudes are invariant under field redefinitions. Nonderivative field redefinitions have a natural interpretation as coordinate transformations on the target manifold. General field redefinitions, which may involve derivatives, can be viewed as coordinate transformations on the field configuration manifold. We present a unified perspective for the geometry of both the target manifold and the field configuration manifold for scalar effective field theories. In both cases, we identify vertices that can be used to build the tree-level amplitudes, with the property that they transform covariantly in the vacuum and on-shell limits. We identify a choice of metric on the field configuration manifold, for which amplitude expressions on the target manifold can be easily reproduced from their counterparts on the field configuration manifold. This clarifies the relation between the well-established framework of field space geometry and recent proposals for functional geometry.

United States

Switzerland

Timothy Cohen

Xu-Xiang Li

Zhengkang Zhang

Geometric building blocks of effective field theory amplitudes

We revisit the lore establishing the allowed space of field redefinitions and show that there are essentially no restrictions. Our conclusions hold to all orders in perturbation theory and for any dispersion relation. Field redefinitions can be nonlocal, symmetry breaking, or in certain cases have explicit dependence on spacetime. We address field redefinitions that can be resummed into the propagator, which demonstrates how to perform perturbative calculations away from the minimum in field space. Field redefinitions are used to derive higher-order Schwinger-Dyson equations, which imply multiparticle soft theorems. Non-standard field redefinitions are showcased using both relativistic and nonrelativistic examples.

Matthew Forslund

Andreas Helset

Field redefinitions can be nonlocal

We extend the soft theorems for scattering amplitudes of scalar effective field theories to one-loop order. Our analysis requires carefully accounting for the fact that the soft limit is not guaranteed to commute with evaluating IR-divergent loop integrals; new results for the soft limit of general scalar one-loop integrals are presented. The geometric soft theorem remains unmodified for any derivatively-coupled scalar effective field theory, and we conjecture that this statement holds to all orders. In contrast, the soft theorem receives nontrivial corrections in the presence of potential interactions, analogous to the case of non-Abelian gauge theories. We derive the universal leading-order correction to the scalar soft theorem arising from potential interactions at one loop. Explicit examples are provided that illustrate the general results.

Italy

Ipak Fadakar

Filippo Nardi

Geometry of soft scalars at one loop

The weak gravity conjecture has been invoked to conjecture that the dimensions of charged operators in a CFT should obey a superadditivity relation (sometimes referred to as convexity). In this paper, we study superadditivity of the operator spectrum in theories expanded about the semi-classical saddle point that dominates correlators of large charge operators. We explore this in two contexts. The first is a model with two scalar fields that carry different charges, at a non-trivial Wilson-Fisher fixed point. A careful analysis of the semi-classics for this two field model demonstrates that ‘quantum’ violations of superadditivity (those not forbidden by the conjecture) persist in the large charge regime. We then turn to study the general properties of CFTs at large charge as bottom-up EFTs. By a trial and error procedure we come up with a seemingly consistent family of examples violating the conjecture. In so doing the presence of a genuine dilaton field appears necessary. On the one hand our result demonstrates that the superadditivity conjecture cannot be proven purely on the basis of a bottom-up analysis. On the other hand, the need for a dilaton, with the corresponding infinite fine tuning, indicates the conjecture-violating EFTs are unlikely to be UV completable.

Andrew Gomes

Alexander Monin

Riccardo Rattazzi

Superadditivity at large charge

<p>The late-time limit of the power spectrum for heavy (principal series) fields in de Sitter (dS) space yields a series of polynomial terms with complex scaling dimensions. Such scaling behavior is expected to result from an associated operator with a complex dimension. In a free theory, these complex dimensions are known to match the constraints imposed by unitarity on the space of states. Yet, perturbative corrections to the scaling behavior of operators are naively inconsistent with unitary evolution of the quantum fields in dS space. This paper demonstrates how to compute one-loop corrections to the scaling dimensions that appear in the two-point function from the field theory description in terms of local operators. We first show how to evaluate these anomalous dimensions using Mellin space, which has the feature that it naturally accommodates a scaleless regulator. We then explore the consequences for the soft de Sitter effective theory (SdSET) description that emerges in the long wavelength limit. Carefully matching between the UV and SdSET descriptions requires the introduction of novel nondynamical “operators” in the effective theory. This is not only necessary to reproduce results extracted from the Källén-Lehmann representation (that use the space of unitary states directly), but it is also required by general arguments that invoke positivity.</p>

CERN

Daniel Green

Yiwen Huang

Operator origin of anomalous dimensions in de Sitter space

<p>We elaborate on a recently proposed geometric framework for scalar effective field theories. Starting from the action, a metric can be identified that enables the construction of geometric quantities on the associated functional manifold. These objects transform covariantly under general field redefinitions that relate different operator bases, including those involving derivatives. We present a novel geometric formula for the amplitudes of the theory, where the vertices in Feynman diagrams are replaced by their geometrized counterparts. This makes the on-shell covariance of amplitudes manifest, providing the link between functional geometry and effective field theories.</p>

Xiaochuan Lu

What is the geometry of effective field theories?

Matrix elements of Wilson-line dressed operators play a central role in the factorization of soft and collinear modes in gauge theories. When expressed using spinor helicity variables, these so-called form factors admit a classification starting from a Maximally Helicity Violating configuration, in close analogy with gauge theory amplitudes. We show that a single-line complex momentum shift can be used to derive recursion relations that efficiently compute these helicity form factors at tree-level: a combination of lower point form factors and on-shell amplitudes serve as the input building blocks. We obtain novel compact expressions for the 1 → 2 and 1 → 3 splitting functions in QCD, which also serves to validate our methods.

Marc Riembau

Recursion for Wilson-line form factors

We derive an off-shell recursion relation for correlators that holds at all loop orders. This allows us to prove how generalized amplitudes transform under generic field redefinitions, starting from an assumed behavior of the one-particle-irreducible effective action. The form of the recursion relation resembles the operation of raising the rank of a tensor by acting with a covariant derivative. This inspires a geometric interpretation, whose features and flaws we investigate.

United Kingdom

Dave Sutherland

On amplitudes and field redefinitions

We study confining dark sectors where the lightest hadrons are glueballs. Such models can provide viable dark matter candidates and appear in some neutral naturalness scenarios. In this work, we introduce a new phenomenological model of dark glueball hadronization inspired by the Lund string model. This enables us to make the most physically-motivated predictions for dark glueball phenomenology at the LHC to date. Our model approximately reproduces the expected thermal distribution of hadron species as an emergent consequence of hadronization dynamics. The ability to predict the production of glueball states heavier than the lightest species significantly expands the reach of long-lived glueball searches in MATHUSLA compared to previous simplified estimates. We also characterize regions of parameter space where emerging and/or semivisible jets could arise from pure-glue dark sectors, thereby providing new benchmark models that motivate searches for these signatures.

Austin Batz

Canada

David Curtin

Caleb Gemmell

Graham Kribs

Dark sector glueballs at the LHC

Recently, an increasing interest in UV/IR mixing phenomena has drawn attention to the range of validity of standard quantum field theory. Here we explore the consequences of such a limited range of validity in the context of radiative models for neutrino mass generation. We adopt an argument first published by Cohen, Kaplan and Nelson that gravity implies both UV and IR cutoffs, apply it to the loop integrals describing radiative corrections, and demonstrate that this effect has significant consequences for the parameter space of radiative neutrino mass models.