arXiv subjects

Kurt Hinterbichler

Publications and source records attributed to Kurt Hinterbichler.

At least 19 recordsLinked to original sources

arXiv2026

Moduli Bounds from Spin-2 Sum Rules

Mirbabayi and Villadoro have provided strong numerical evidence for a universal upper bound on the mass of the lightest scalar field in gravitational Kaluza--Klein (KK) theories. This bound states that the lightest KK graviton, with mass $m_{1}$, must couple to at least one scalar with mass $m_{\rm sc}$ such that $(m_{\rm sc} /m_{1})^2 \leq 4/3$. We give a proof of this bound using the approach of the conformal bootstrap applied to sum rules for massive spin-2 scattering amplitudes. We additionally show that each heavier KK graviton, with mass $m_n$, must couple to at least one scalar with mass $m_{\rm sc}$ such that $(m_{\rm sc} /m_{n})^2 < 36/25$.

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arXiv2026

Radial Solutions of Multi-Field de Sitter Galileons

We study static, spherically symmetric screening solutions in the $\mathfrak{so}(N)$-invariant multi-field de Sitter Galileon theory, with matter couplings preserving the internal symmetry. Unlike in flat space, the de Sitter radial problem is affected both by the cosmological horizon and by the possible appearance of a finite strong-coupling radius, where the radial equation becomes singular and the effective description breaks down. Near the source, the quartic interaction governs the nonlinear screened branch, while farther away the quadratic terms dominate, defining a de Sitter analog of the Vainshtein radius at their crossover. A screened solution is viable only if this crossover occurs before the strong-coupling radius is reached. We study perturbations around the radial background and identify branches for which perturbations are stable and subluminal, within a restricted radial domain set by the strong-coupling point. Finally, we compare the de Sitter and Anti-de Sitter cases, isolating effects due to curvature from those specific to the cosmological horizon. Our results indicate that curvature can alleviate the superluminality issues that arise in Galileon theories for appropriate choices of matter couplings, though this comes at the price of a finite region of validity for the effective theory.

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arXiv2026

De Sitter Representations

We review the representations of so(1,D), the algebra of isometries of D dimensional de Sitter space. We cover the representations in all D, including mixed symmetry representations and fermionic representations, and connect them to the various types of fields that can propagate on de Sitter space. The presentation is from a physics point of view, favoring concrete constructions over abstract considerations.

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arXiv2026

Quantum Signatures of Cosmic Topology: How Casimir Backreaction Transmits Isotropy Violation

A finite, scheme-independent Casimir contribution to the stress-energy tensor arises naturally for quantum fields in universes with non-trivial spatial topology. We compute this Casimir stress-energy tensor contribution for a conformally coupled scalar field and for a minimally coupled scalar field. We show that, for the conformally coupled case, the backreaction of this contribution to the Einstein equations during an expanding de Sitter phase drives anisotropic expansion even when the Universe begins in a locally homogeneous and isotropic state. We conclude that quantum imprints of the underlying non-trivial topology inevitably give rise to local departures from homogeneity and isotropy.

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arXiv2026

Conformal Killing Tensors, Noether Currents and Higher-Spin Shift Symmetries in (A)dS Space

For certain mass values, shift symmetries appear among massive higher spin fields propagating on (anti-) de Sitter spacetime. On the one hand, Noether's theorem assigns a set of conserved currents for each shift symmetric field, one current for each of the independent shift symmetries. On the other hand, each shift symmetric field comes with a higher-rank conserved field strength that can be contracted with a conformal Killing tensor (CKT) to form another set of conserved currents, one for each independent CKT. This second set is naively much larger than the first. We conjecture, and prove in the first few cases, that these two sets are the same once we account for the redundancy due to trivial currents that is implicit in Noether's theorem. For each field, only one branch of the CKTs is non-trivial. As we range over all the mass values and spins of the shift symmetric fields, each kind of CKT gets used exactly once in a non-trivial current.

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arXiv2025

Constraints on Long-Range Forces in De Sitter Space

The representation theory of de Sitter space admits partially massless (PM) particles, but whether such particles can participate in consistent interacting theories remains unclear. We investigate the consistency of theories containing PM fields, particularly when these fields are coupled to gravity. Our strategy exploits the fact that PM fields correspond to partially conserved currents on the spacetime boundary, which generate symmetries. These symmetries place stringent constraints on correlation functions of charged operators, allowing us to test the consistency of a proposed bulk spectrum. When the assumed operator content violates these constraints, the corresponding bulk theory is ruled out. Applying this framework, we show that, in four-dimensional de Sitter space, PM fields of spin 2 or 3 (at depth 0) cannot couple consistently to gravity: such couplings necessitate additional massive fields, which are inevitably non-unitary. In higher dimensions, however, the constraints can be satisfied without violating unitarity if further PM fields are included. The resulting structure leads to additional charge conservation laws, which suggests that consistency may ultimately require an infinite tower of higher-spin PM fields, akin to the situation for ordinary higher-spin symmetries. The methods developed here provide powerful constraints on possible long-range interactions in de Sitter space and delineate the landscape of consistent quantum field theories in cosmological spacetimes.

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arXiv2025

A Note on the AdS/CFT Equivalence Transformation for Galileons in General Dimensions

The AdS/CFT equivalence transformation is a field redefinition that relates the Weyl dilaton and AdS brane realizations of broken conformal symmetry. Acting on theories with second order equations of motion, it maps the conformal galileons to the DBI galileons for a flat brane probing an AdS bulk. Here we extend this map to arbitrary dimensions and resolve an apparent puzzle regarding the Wess-Zumino terms in odd dimensions.

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arXiv2025

A Partially Massless Superconductor

We describe a Higgs mechanism for the partially massless graviton. In order to do so, we first construct a covariant fracton-like effective field theory on de Sitter space that linearly realizes a dipolar shift symmetry. The global symmetry of this theory can be gauged by coupling it to a partially massless spin-2 gauge field. When the fractonic matter condenses, the dipole symmetry is spontaneously broken, the resulting Goldstone mode is a galileon and the partially massless graviton combines with this mode and becomes fully massive. At long distances, the phenomenology of this theory is captured by a quasi-topological field theory and displays many features analogous to those of the superconducting phase in electromagnetism, including gapless edge modes and persistent currents. We also describe the generalization to higher spins.

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arXiv2025

Multi-Galileons in Curved Space

Using the probe brane construction of higher derivative effective field theories, extended to higher co-dimensions and curved spaces, we construct galileon and DBI theories on de Sitter space with N fields and an so(N) internal symmetry, non-linearly realizing the symmetries of a higher dimensional de Sitter space. In some cases, the theory admits a non-trivial vacuum that spontaneously breaks the so(N) symmetry, and around this vacuum the Goldstone modes have vanishing kinetic terms and become infinitely strongly coupled. This gives an example of a scalar effective field theory with two de Sitter vacua, one of which appears to have Boulware-Deser-like ghosts, and one of which does not.

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arXiv2024

Hidden Conformal Symmetry of the Discrete Series Scalars in dS$_2$

In $D$ dimensional de Sitter space, a scalar field has an infinite tower of special tachyonic mass values at which enhanced shift symmetries appear. After modding out by these shift symmetries, these fields correspond to the unitary irreducible representations of the de Sitter group known as the discrete series. We show that in $D=2$ these theories have global conformal symmetry. In all but the massless case, these theories have no stress tensor and the conformal symmetry does not act in the usual way on the scalar field. We find the conformal symmetry by explicitly computing the correlators of the shift invariant local operators and showing that they take conformally invariant forms. We also demonstrate how these fields are self dual in $D=2$, and dual to the shift invariant massive vector fields, which are therefore also conformally invariant.

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arXiv2024

Scale and Conformal Invariance on (A)dS

We examine the question of scale versus conformal invariance on maximally symmetric curved backgrounds and study general 2-derivative conformally invariant free theories of vectors and tensors. For spacetime dimension $D>4$, these conformal theories can be diagonalized into standard massive fields in which unbroken conformal symmetry non-trivially mixes components of different spins. In $D=4$, the tensor case becomes a conformal theory mixing a partially massless spin-2 field with a massless spin-1 field. For massless linearized gravity in $D = 4$, we confirm through direct calculation that correlation functions of gauge-invariant operators take the conformally invariant form, despite the absence of standard conformal symmetry at the level of the action.

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arXiv2024

Dualities Among Massive, Partially Massless and Shift Symmetric Fields on (A)dS

We catalog all the electromagnetic-like dualities that exist between free dynamical bosonic fields of arbitrary symmetry type and mass on (anti-) de Sitter space in all dimensions, including dualities among the partially massless and shift symmetric fields. This generalizes to all these field types the well known fact that a massless $p$-form is dual to a massless $(D-p-2)$-form in $D$ spacetime dimensions. In the process, we describe the structure of the Weyl modules (the spaces of local operators linear in the fields and their derivative relations) for all the massive, partially massless and shift symmetric fields.

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arXiv2024

Impossible Symmetries and Conformal Gravity

We explore the physics of relativistic gapless phases defined by a mixed anomaly between two generalized conserved currents. The gapless modes can be understood as Goldstone modes arising from the nonlinear realization of (generically higher-form) symmetries arising from these currents. In some cases, the anomaly cannot be reproduced by any local and unitary theory, indicating that the corresponding symmetries are impossible, in the sense that they cannot appear in a Lorentzian physical system. We consider many examples of the general construction. Most notably, we study conformal gravity from this perspective, describing the higher-form symmetries of the linear theory and showing how it can be understood in terms of anomalies. Along the way we clarify some aspects of electric-magnetic duality in linear conformal gravity.

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arXiv2023

Fermionic Shift Symmetries in (Anti) de Sitter Space

We study extended shift symmetries that arise for fermionic fields on anti-de Sitter (AdS) space and de Sitter (dS) space for particular values of the mass relative to the curvature scale. We classify these symmetries for general mixed-symmetry fermionic fields in arbitrary dimension and describe how fields with these symmetries arise as the decoupled longitudinal modes of massive fermions as they approach partially massless points. For the particular case of AdS$_4$, we look for non-trivial Lie superalgebras that can underly interacting theories that involve these fields. We study from this perspective the minimal such theory, the Akulov--Volkov theory on AdS$_4$, which is a non-linear theory of a spin-$1/2$ Goldstino field that describes the spontaneous breaking of ${\cal N}=1$ supersymmetry on AdS$_4$ down to the isometries of AdS$_4$. We show how to write the nonlinear supersymmetry transformation for this theory using the fermionic ambient space formalism. We also study the Lie superalgebras of candidate multi-field examples and rule out the existence of a supersymmetric special galileon on AdS$_4$.

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arXiv2023

Equivalence of EFTs and Time-Like Extra Dimensions

A flat 3-brane probing a five dimensional anti-de Sitter space has the same symmetries and symmetry breaking pattern as one probing a five dimensional de Sitter space with two time directions. Despite the seemingly different physical set ups, we show that the effective field theory of the brane bending mode is identical in both cases. In particular, despite "wrong" signs in the DBI action for the two-time de Sitter case, the theories have the same S-matrix. This is consistent with the expectation that effective field theories are determined solely by their degrees of freedom and pattern of symmetry breaking, even in the case of spacetime symmetries. We comment further on the equivalence between the Weyl/dilaton and DBI representations of the EFT of broken conformal symmetry.

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arXiv2023

Shift Symmetries and AdS/CFT

Massive fields on anti-de Sitter (AdS) space enjoy galileon-like shift symmetries at particular values of their masses. We explore how these shift symmetries are realized through the boundary conformal field theory (CFT), at the level of the 2-point functions. In the alternate quantization scheme in which the dual conformal field gets the smaller $Δ_-$ conformal dimension, the shift symmetry is realized as a gauge symmetry in the dual CFT, so that only shift invariant operators are true conformal primary fields. In the standard quantization scheme the shift symmetry acts on the source, leading to Ward identities that take the form of integral constraints.

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arXiv2022

Shift Symmetries for p-Forms and Mixed Symmetry Fields on (A)dS

Massive fields on (anti) de Sitter space realize extended shift symmetries at particular values of their masses. We find these symmetries for all bosonic p-forms and mixed symmetry fields, in arbitrary spacetime dimension. These shift symmetric fields correspond to the missing longitudinal modes of mixed symmetry partially massless fields where the top row of the Young tableau is activated.

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arXiv2022

Gravity as a gapless phase and biform symmetries

We study effective field theories (EFTs) enjoying (maximal) biform symmetries. These are defined by the presence of a conserved (electric) current that has the symmetries of a Young tableau with two columns of equal length. When these theories also have a topological (magnetic) biform current, its conservation law is anomalous. We go on to show that this mixed anomaly uniquely fixes the two-point function between the electric and magnetic currents. We then perform a Källén-Lehmann spectral decomposition of the current-current correlator, proving that there is a massless mode in the spectrum, whose masslessness is protected by the anomaly. Furthermore, the anomaly gives rise to a universal form of the EFT whose most relevant term, which resembles the linear Einstein action, dominates the infrared physics. As applications of this general formalism, we study the theories of a Galileon superfluid and linearized gravity. Thus, one can view the masslessness of the graviton as being protected by the anomalous biform symmetries. The associated EFT provides an organizing principle for gravity at low energies in terms of physical symmetries, and allows interactions consistent with linearized diffeomorphism invariance. These theories are not ultraviolet-complete, the relevant symmetries can be viewed as emergent, nor do they include the nonlinearities necessary to make them fully diffeomorphism invariant, so there is no contradiction with the expectation that quantum gravity cannot have any global symmetries.

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