arXiv subjects

C. P. Burgess

Publications and source records attributed to C. P. Burgess.

At least 37 records · Page 2Linked to original sources

arXiv2023

Minimal decoherence from inflation

We compute the rate with which super-Hubble cosmological fluctuations are decohered during inflation, by their gravitational interactions with unobserved shorter-wavelength scalar and tensor modes. We do so using Open Effective Field Theory methods, that remain under control at the late times of observational interest, contrary to perturbative calculations. Our result is minimal in the sense that it only incorporates the self-interactions predicted by General Relativity in single-clock models (additional interaction channels should only speed up decoherence). We find that decoherence is both suppressed by the first slow-roll parameter and by the energy density during inflation in Planckian units, but that it is enhanced by the volume comprised within the scale of interest, in Hubble units. This implies that, for the scales probed in the Cosmic Microwave Background, decoherence is effective as soon as inflation proceeds above $\sim 5\times 10^{9}$ GeV. Alternatively, if inflation proceeds at GUT scale decoherence is incomplete only for the scales crossing out the Hubble radius in the last ~ 13 e-folds, of inflation. We also compute how short-wavelength scalar modes decohere primordial tensor perturbations, finding a faster rate unsuppressed by slow-roll parameters. Identifying the parametric dependence of decoherence, and the rate at which it proceeds, helps suggest ways to look for quantum effects.

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arXiv2023

Perils of Towers in the Swamp: Dark Dimensions and the Robustness of Effective Field Theories

Recently there has been an interesting revival of the idea to use large extra dimensions to address the dark energy problem, exploiting the (true) observation that towers of states with masses split, by $M^2_N = f(N) m^2,$ with $f$ an unbounded function of the integer $N$, sometimes contribute to the vacuum energy only an amount of order $m^D$ in $D$ dimensions. It has been argued that this fact is a consequence of swampland conjectures and may require a departure from Effective Field Theory (EFT) reasoning. We test this claim with calculations for Casimir energies in extra dimensions. We show why the domain of validity for EFTs ensures that the tower spacing scale $m$ is always an upper bound on the UV scale for the lower-energy effective theory; use of an EFT with a cutoff part way up a tower is not a controlled approximation. We highlight the role played by the sometimes-suppressed contributions from towers in extra-dimensional approaches to the cosmological constant problem, old and new, and point out difficulties encountered in exploiting it. We compare recent swampland realizations of these arguments with earlier approaches using standard EFT examples, discussing successes and limitations of both.

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arXiv2023

Gravity, Horizons and Open EFTs

Wilsonian effective theories exploit hierarchies of scale to simplify the description of low-energy behaviour and play as central a role for gravity as for the rest of physics. They are useful both when hierarchies of scale are explicit in a gravitating system and more generally for understanding precisely what controls the size of quantum corrections in gravitational systems. But effective descriptions are also relevant for open systems (e.g. fluid mechanics as a long-distance description of statistical systems) for which the `integrating out' of unobserved low-energy degrees of freedom complicate a straightforward application of Wilsonian methods. Observations performed only on one side of an apparent horizon provide examples where open system descriptions also arise in gravitational physics. This chapter describes some early adaptations of Open Effective Theories (i.e. techniques for exploiting hierarchies of scale in open systems) in gravitational settings. Besides allowing the description of new types of phenomena (such as decoherence) these techniques also have an additional benefit: they sometimes can be used to resum perturbative expansions at late times and thereby to obtain controlled predictions in a regime where perturbative predictions otherwise generically fail.

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arXiv2023

UV and IR Effects in Axion Quality Control

Motivated by recent discussions and the absence of exact global symmetries in UV completions of gravity we re-examine the axion quality problem (and naturalness issues more generally) using antisymmetric Kalb-Ramond (KR) fields rather than their pseudoscalar duals, as suggested by string and higher dimensional theories. Two types of axions can be identified: a model independent $S$-type axion dual to a two form $B_{μν}$ in 4D and a $T$-type axion coming directly as 4D scalar Kaluza-Klein (KK) components of higher-dimensional tensor fields. For $T$-type axions our conclusions largely agree with earlier workers for the axion quality problem, but we also reconcile why $T$-type axions can couple to matter localized on 3-branes with Planck suppressed strength even when the axion decay constants are of order the KK scale. For $S$-type axions, we review the duality between form fields and massive scalars and show how duality impacts naturalness arguments about the UV sensitivity of the scalar potential. In particular UV contributions on the KR side suppress contributions on the scalar side by powers of $m/M$ with $m$ the axion mass and $M$ the UV scale. We re-examine how the axion quality problem is formulated on the dual side and compare to recent treatments. We study how axion quality is affected by the ubiquity of $p$-form gauge potentials (for both $p=2$ and $p=3$) in string vacua and identify two criteria that can potentially lead to a problem. We also show why most fields do not satisfy these criteria, but when they do the existence of multiple fields also provides mechanisms for resolving it. We conclude that the quality problem is easily evaded.

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arXiv2022

Beyond SMEFT with $b \to c \,τ^- {\barν}$

Electroweak interactions assign a central role to the gauge group $SU(2)_L \times U(1)_Y$, which is either realized linearly (SMEFT) or nonlinearly (e.g., HEFT) in the effective theory obtained when new physics above the electroweak scale is integrated out. Although the discovery of the Higgs boson has made SMEFT the default assumption, nonlinear realization remains possible. The two can be distinguished through their predictions for the size of certain low-energy dimension-6 four-fermion operators: for these, HEFT predicts $O(1)$ couplings, while in SMEFT they are suppressed by a factor $v^2/Λ_{\rm NP}^2$, where $v$ is the Higgs vev. One such operator, $O_V^{LR} \equiv ({\bar τ} γ^μP_L ν)\, ( {\bar c} γ_μP_R b )$, contributes to $b \to c \,τ^- {\barν}$. We show that present constraints permit its non-SMEFT coefficient to have a HEFTy size. We also note that the angular distribution in ${\bar B} \to D^* (\to D π') \, τ^{-} (\to π^- ν_τ) {\barν}_τ$ contains enough information to extract the coefficients of all new-physics operators. Future measurements of this angular distribution can therefore tell us if non-SMEFT new physics is really necessary.

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arXiv2022

Yoga Dark Energy: Natural Relaxation and Other Dark Implications of a Supersymmetric Gravity Sector

We construct a class of 4D `yoga' (naturally relaxed) models for which the gravitational response of heavy-particle vacuum energies is strongly suppressed. The models contain three ingredients: (i) a relaxation mechanism, (ii) a very supersymmetric gravity sector coupled to matter for which supersymmetry is non-linearly realised, and (iii) an accidental approximate scale invariance expressed through the presence of a low-energy dilaton supermultiplet. All three are common in higher-dimensional and string constructions and although none suffices on its own, taken together they can dramatically suppress the net vacuum-energy density. The dilaton's {\it vev}~$τ$ determines the weak scale $M_W \sim M_p/\sqrtτ$. We compute the potential for $τ$ and find it can be stabilized in a local de Sitter minimum at sufficiently large field values to explain the electroweak hierarchy, doing so using input parameters no larger than $O(60)$ because the relevant potential arises as a rational function of $\lnτ$. The de Sitter vacuum energy at the minimum is order $c\, M_W^8 \propto 1/τ^4$, with $c \ll O(M_W^{-4})$. We discuss how to achieve $c \sim 1/M_p^4$ as required by observations. Scale invariance implies the dilaton couples to matter like a Brans-Dicke scalar with dangerously large coupling yet because it comes paired with an axion it can evade bounds through the novel screening mechanism described in {\tt ArXiV:2110.10352}. Cosmological axio-dilaton evolution predicts a natural quintessence model for Dark Energy, whose evolution can realize recent proposals to resolve the Hubble tension, and whose axion contributes to Dark Matter. We summarize inflationary implications and some remaining challenges, including the unusual supersymmetry breaking regime used and the potential for UV completions of our approach.

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arXiv2022

Axion Homeopathy: Screening Dilaton Interactions

Cosmologically active Brans-Dicke (or dilaton) scalar fields are generically ruled out by solar system tests of gravity unless their couplings to ordinary matter are much suppressed relative to gravitational strength, and this is a major hindrance when building realistic models of light dilatons coupled to matter. We propose a new mechanism for evading such bounds if matter also couples to a light axion, that exploits nonlinear target-space curvature interactions to qualitatively change how the fields respond to a gravitating source. We find that dilaton-matter couplings that would be excluded in the absence of an axion can become acceptable given an additional small axion-matter coupling, and this is possible because the axion-dilaton interactions end up converting the would-be dilaton profile into an axion profile. The trajectories of matter test bodies are then controlled by the much weaker axion-matter couplings and can easily be small enough to escape detection. We call this mechanism Axion Homeopathy because the evasion of the dilaton-coupling bounds persists for extremely small axion couplings provided only that they are nonzero. We explore the mechanism using axio-dilaton equations that are SL(2,R) invariant (as often appear in string compactifications), since for these the general solutions exterior to a spherically symmetric source can be found analytically. We use this solution to compute the relevant PPN parameters, $β$ and $γ$, and verify that their difference from unity can be much smaller than would have been true in the absence of axion-matter couplings and so can therefore evade the experimental bounds.

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arXiv2022

RG-Induced Modulus Stabilization: Perturbative de Sitter Vacua and Improved $\hbox{D3}$-$\overline{\hbox{D3}}$ Inflation

We propose a new mechanism that adapts to string theory a perturbative method for stabilizing moduli without leaving the domain of perturbative control, thereby evading the `Dine-Seiberg' problem. The only required nonperturbative information comes from the standard renormalization-group resummation of leading logarithms that allow us simultaneously to work to a fixed order in the perturbative parameter $α$ and to all orders in $α\lnτ$ where $τ$ is a large extra-dimensional modulus. The resulting potential is naturally minimized for moduli of order $τ\sim e^{1/α}$ and so can be exponentially large given ${\cal O}(10)$ input parameters. The mechanism relies on accidental low-energy scaling symmetries known to be generic and so is robust against UV details. The resulting compactifications generically break supersymmetry and 4D de Sitter solutions are relatively easy to achieve without additional uplifting. Variations on the theme lead to inflationary scenarios for which the size of the stabilized moduli differ significantly before and after inflation and so provide a dynamical mechanism whereby inflationary scales are much larger than late-time physical ($e.g.$~supersymmetry breaking) scales, with this hierarchy contingent on past cosmic evolution with the inflaton playing a secondary late-time role as a relaxation field. We apply this formalism to warped $\hbox{D3}$-$\overline{\hbox{D3}}$ inflation using non-linearly realized supersymmetry to describe the antibrane tension and the Coulomb interaction, and show how doing so our perturbative modulus stabilization mechanism evades the $η$-problem that usually plagues this scenario. We speculate about the relevance of our formalism to tachyon condensation at later stages of brane-antibrane annihilation.

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arXiv2021

Who's Afraid of the Supersymmetric Dark? The Standard Model vs Low-Energy Supergravity

Use of supergravity equations in astronomy and late-universe cosmology is often criticized on three grounds: (i) phenomenological success usually depends on the supergravity form for the scalar potential applying at the relevant energies; (ii) the low-energy scalar potential is extremely sensitive to quantum effects involving very massive particles and so is rarely well-approximated by classical calculations of its form; and (iii) almost all Standard Model particles count as massive for these purposes and none of these are supersymmetric. Why should Standard Model loops preserve the low-energy supergravity form even if supersymmetry is valid at energies well above the electroweak scale? We use recently developed tools for coupling supergravity to non-supersymmetric matter to estimate the loop effects of heavy non-supersymmetric particles on the low-energy effective action, and provide evidence that the supergravity form is stable against integrating out such particles (and so argues against the above objection). This suggests an intrinsically supersymmetric picture of Nature where supersymmetry survives to low energies within the gravity sector but not the visible sector (for which supersymmetry is instead non-linearly realized). We explore the couplings of both sectors in this picture and find that the presence of auxiliary fields in the gravity sector makes the visible sector share many features usually attributed to linearly realized supersymmetry although (unlike for the MSSM) a second Higgs doublet is not required for all Yukawa couplings to be non-vanishing and changes the dimension of the operator generating the Higgs mass. We discuss the naturalness of this picture and some of the implications it might have when searching for dark-sector physics.

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arXiv2021

Qubit Heating Near a Hotspot

Effective theories describing black hole exteriors contain many open-system features due to the large number of gapless degrees of freedom that lie beyond reach across the horizon. A simple solvable Caldeira-Leggett type model of a quantum field interacting within a small area with many unmeasured thermal degrees of freedom was recently proposed in arXiv:2106.09854 to provide a toy model of this kind of dynamics against which more complete black hole calculations might be compared. We here compute the response of a simple Unruh-DeWitt detector (or qubit) interacting with a massless quantum field $ϕ$ coupled to such a hotspot. Our treatment differs from traditional treatments of Unruh-DeWitt detectors by using Open-EFT tools to reliably calculate the qubit's late-time behaviour. We use these tools to determine the efficiency with which the qubit thermalizes as a function of its proximity to the hotspot. We identify a Markovian regime in which thermalization does occur, though only for qubits closer to the hotspot than a characteristic distance scale set by the $ϕ$-hotspot coupling. We compute the thermalization time, and find that it varies inversely with the $ϕ$-qubit coupling strength in the standard way.

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arXiv2021

Influence Through Mixing: Hotspots as Benchmarks for Basic Black-Hole Behaviour

Effective theories are being developed for fields outside black holes, often with an unusual open-system feel due to the influence of large number of degrees of freedom that lie out of reach beyond the horizon. What is often difficult when interpreting such theories is the absence of comparisons to simpler systems that share these features. We propose here such a simple model, involving a single external scalar field that mixes in a limited region of space with a `hotspot' containing a large number of hot internal degrees of freedom. Since the model is at heart gaussian it can be solved explicitly, and we do so for the mode functions and correlation functions for the external field once the hotspot fields are traced out. We compare with calculations that work perturbatively in the mixing parameter, and by doing so can precisely identify its domain of validity. We also show how renormalization-group EFT methods can allow some perturbative contributions to be resummed beyond leading order, verifying the result using the exact expression.

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arXiv2021

Fall-to-the-centre as a $\mathcal{PT}$ symmetry breaking transition

The attractive inverse square potential arises in a number of physical problems such as a dipole interacting with a charged wire, the Efimov effect, the Calgero-Sutherland model, near-horizon black hole physics and the optics of Maxwell fisheye lenses. Proper formulation of the inverse-square problem requires specification of a boundary condition (regulator) at the origin representing short-range physics not included in the inverse square potential and this generically breaks the Hamiltonian's continuous scale invariance in an elementary example of a quantum anomaly. The system's spectrum qualitatively changes at a critical value of the inverse-square coupling, and we here point out that the transition at this critical potential strength can be regarded as an example of a $\mathcal{PT}$ symmetry breaking transition. In particular, we use point particle effective field theory (PPEFT), as developed by Burgess et al [J. High Energy Phys., 2017(4):106, 2017], to characterize the renormalization group (RG) evolution of the boundary coupling under rescalings. While many studies choose boundary conditions to ensure the system is unitary, these RG methods allow us to systematically handle the richer case of nonunitary physics describing a source or sink at the origin (such as is appropriate for the charged wire or black hole applications). From this point of view the RG flow changes character at the critical inverse-square coupling, transitioning from a sub-critical regime with evolution between two real, unitary fixed points ($\mathcal{PT}$ symmetric phase) to a super-critical regime with imaginary, dissipative fixed points ($\mathcal{PT}$ symmetry broken phase) that represent perfect-sink and perfect-source boundary conditions, around which the flow executes limit-cycle evolution.

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arXiv2021

Quantum Hotspots: Mean Fields, Open EFTs, Nonlocality and Decoherence Near Black Holes

Effective theories describing black hole exteriors resemble open quantum systems inasmuch as many unmeasurable degrees of freedom beyond the horizon interact with those we can see. A solvable Caldeira-Leggett type model of a quantum field that mixes with many unmeasured thermal degrees of freedom on a shared surface was proposed in arXiv:2106.09854 to provide a benchmark against which more complete black hole calculations might be compared. We here use this model to test two types of field-theoretic approximation schemes that also lend themselves to describing black hole behaviour: Open EFT techniques (as applied to the fields themselves, rather than Unruh-DeWitt detectors) and mean-field methods. Mean-field methods are of interest because the effective Hamiltonians to which they lead can be nonlocal; a possible source for the nonlocality that is sometimes entertained as being possible for black holes in the near-horizon regime. Open EFTs compute the evolution of the field state, allowing discussion of thermalization and decoherence even when these occur at such late times that perturbative methods fail (as they often do). Applying both of these methods to a solvable system identifies their domains of validity and shows how their predictions relate to more garden-variety perturbative tools.

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arXiv2021

Qubits on the Horizon: Decoherence and Thermalization near Black Holes

We examine the late-time evolution of a qubit (or Unruh-De Witt detector) that hovers very near to the event horizon of a Schwarzschild black hole, while interacting with a free quantum scalar field. The calculation is carried out perturbatively in the dimensionless qubit/field coupling $g$, but rather than computing the qubit excitation rate due to field interactions (as is often done), we instead use Open EFT techniques to compute the late-time evolution to all orders in $g^2 t/r_s$ (while neglecting order $g^4 t/r_s$ effects) where $r_s = 2GM$ is the Schwarzschild radius. We show that for qubits sufficiently close to the horizon the late-time evolution takes a simple universal form that depends only on the near-horizon geometry, assuming only that the quantum field is prepared in a Hadamard-type state (such as the Hartle-Hawking or Unruh vacua). When the redshifted energy difference, $ω_\infty$, between the two qubit states (as measured by a distant observer looking at the detector) satisfies $ω_\infty r_s \ll 1$ this universal evolution becomes Markovian and describes an exponential approach to equilibrium with the Hawking radiation, with the off-diagonal and diagonal components of the qubit density matrix relaxing to equilibrium with different characteristic times, both of order $r_s/g^2$.

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arXiv2020

Cosmological Trans-Planckian Conjectures are not Effective

It is remarkable that the primordial fluctuations as revealed by the CMB coincide with what quantum fluctuations would look like if they were stretched across the sky by accelerated cosmic expansion. It has been observed that this same stretching also brings very small -- even trans-Planckian -- length scales up to observable sizes if extrapolated far enough into the past. This potentially jeopardizes later descriptions of late-time cosmology by introducing uncontrolled trans-Planckian theoretical errors into all calculations. Recent speculations, such as the Trans-Planckian Censorship Conjecture (TCC), have been developed to avoid this problem. We revisit old arguments why the consistency of (and control over) the Effective Field Theory (EFT) governing late-time cosmology is not necessarily threatened by the descent of modes due to universal expansion, even if EFT methods may break down at much earlier times. Failure of EFT methods only poses a problem if late-time predictions rely on non-adiabatic behaviour at these early times (such as is often true for bouncing cosmologies, for example). We illustrate our arguments using simple non-gravitational examples such as slowly rolling scalar fields and the spacing between Landau levels for charged particles in slowly varying magnetic fields, for which similar issues arise and are easier to understand. We comment on issues associated with UV completions. Our arguments need not invalidate speculative ideas like the TCC but suggest they are not required by the present evidence.

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arXiv2020

Precision Nuclear-Spin Effects in Atoms: EFT Methods for Reducing Theory Errors

We use effective field theory to compute the influence of nuclear structure on precision calculations of atomic energy levels. As usual, the EFT's effective couplings correspond to the various nuclear properties (such as the charge radius, nuclear polarizabilities, Friar and Zemach moments {\it etc.}) that dominate its low-energy electromagnetic influence on its surroundings. By extending to spinning nuclei the arguments developed for spinless ones in {\tt arXiv:1708.09768}, we use the EFT to show -- to any fixed order in $Zα$ (where $Z$ is the atomic number and $α$ the fine-structure constant) and the ratio of nuclear to atomic size -- that nuclear properties actually contribute to electronic energies through fewer parameters than the number of these effective nuclear couplings naively suggests. Our result is derived using a position-space method for matching effective parameters to nuclear properties in the EFT, that more efficiently exploits the simplicity of the small-nucleus limit in atomic systems. By showing that precision calculations of atomic spectra depend on fewer nuclear uncertainties than naively expected, this observation allows the construction of many nucleus-independent combinations of atomic energy differences whose measurement can be used to test fundamental physics (such as the predictions of QED) because their theoretical uncertainties are not limited by the accuracy of nuclear calculations. We provide several simple examples of such nucleus-free predictions for Hydrogen-like atoms.

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arXiv2020

UV Shadows in EFTs: Accidental Symmetries, Robustness and No-Scale Supergravity

We argue that accidental approximate scaling symmetries are robust predictions of weakly coupled string vacua, and show that their interplay with supersymmetry and other (generalised) internal symmetries underlies the ubiquitous appearance of no-scale supergravities in low-energy 4D EFTs. We identify 4 nested types of no-scale supergravities, and show how leading quantum corrections can break scale invariance while preserving some no-scale properties (including non-supersymmetric flat directions). We use these ideas to classify corrections to the low-energy 4D supergravity action in perturbative 10D string vacua, including both bulk and brane contributions. Our prediction for the Kähler potential at any fixed order in $α'$ and string loops agrees with all extant calculations. p-form fields play two important roles: they spawn many (generalised) shift symmetries; and space-filling 4-forms teach 4D physics about higher-dimensional phenomena like flux quantisation. We argue that these robust symmetry arguments suffice to understand obstructions to finding classical de Sitter vacua, and suggest how to get around them in UV complete models.

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arXiv2020

Nuclear Predictions for $H$ Spectroscopy without Nuclear Errors

Nuclear-structure effects often provide an irreducible theory error that prevents using precision atomic measurements to test fundamental theory. We apply newly developed effective field theory tools to Hydrogen atoms, and use them to show that (to the accuracy of present measurements) all nuclear finite-size effects (e.g. the charge radius, Friar moments, nuclear polarizabilities, recoil corrections, Zemach moments {\it etc.}) only enter into atomic energies through exactly two parameters, independent of any nuclear-modelling uncertainties. Since precise measurements are available for more than two atomic levels in Hydrogen, this observation allows the use of precision atomic measurements to eliminate the theory error associated with nuclear matrix elements. We apply this reasoning to the seven atomic measurements whose experimental accuracy is smaller than 10 kHz to provide predictions for nuclear-size effects whose theoretical accuracy is not subject to nuclear-modelling uncertainties and so are much smaller than 1 kHz. Furthermore, the accuracy of these predictions can improve as atomic measurements improve, allowing precision fundamental tests to become possible well below the 'irreducible' error floor of nuclear theory.

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