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DOE OSTI2014

Infrared consistency and the weak gravity conjecture

The weak gravity conjecture (WGC) asserts that an Abelian gauge theory coupled to gravity is inconsistent unless it contains a particle of charge q and mass m such that q ≥ m/m Pl . This criterion is obeyed by all known ultraviolet completions and is needed to evade pathologies from stable black hole remnants. In this paper, we explore the WGC from the perspective of low-energy effective field theory. Below the charged particle threshold, the effective action describes a photon and graviton interacting via higher-dimension operators. We derive infrared consistency conditions on the parameters of the effective action using i ) analyticity of light-by-light scattering, ii ) unitarity of the dynamics of an arbitrary ultraviolet completion, and iii ) absence of superluminality and causality violation in certain non-trivial backgrounds. For convenience, we begin our analysis in three spacetime dimensions, where gravity is non-dynamical but has a physical effect on photon-photon interactions. We then consider four dimensions, where propagating gravity substantially complicates all of our arguments, but bounds can still be derived. Operators in the effective action arise from two types of diagrams: those that involve electromagnetic interactions (parameterized by a charge-to-mass ratio q/m) and those that do not (parameterized by a coefficient γ). In conclusion, infrared consistency implies that q/m is bounded from below for small γ.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2014

Constraints on chiral operators in N = 2 SCFTs

We study certain higher-spin chiral operators in N = 2 superconformal field theories (SCFTs). In Lagrangian theories, or in theories related to Lagrangian theories by generalized Argyres-Seiberg-Gaiotto duality (“type A” theories in our classification), we give a simple superconformal representation theory proof that such operators do not exist. This argument is independent of the details of the superconformal index. We then use the index to show that if a theory is not of type A but has an N = 2-preserving deformation by a relevant operator that takes it to a theory of this type in the infrared, the ultraviolet theory cannot have these higher-spin operators either. As an application of this discussion, we give a simple prescription to extract the 2a - c conformal anomaly directly from the superconformal index. We also comment on how this procedure works in the holographic limit.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2015

Strong CP and SUZ 2

Solutions to the strong CP problem typically introduce new scales associated with the spontaneous breaking of symmetries. Absent any anthropic argument for small θ ¯ , these scales require stabilization against ultraviolet corrections. Supersymmetry offers a tempting stabilization mechanism, since it can solve the “big” electroweak hierarchy problem at the same time. One family of solutions to strong CP, including generalized parity models, heavy axion models, and heavy η' models, introduces Z 2 copies of (part of) the Standard Model and an associated scale of Z 2 -breaking. We review why, without additional structure such as supersymmetry, the Z 2 -breaking scale is unacceptably tuned. We then study “SUZ 2 ” models, supersymmetric theories with Z 2 copies of the MSSM. We find that the addition of SUSY typically destroys the Z 2 protection of θ ¯ = 0 , even at tree level, once SUSY and Z 2 are broken. In theories like supersymmetric completions of the twin Higgs, where Z 2 addresses the little hierarchy problem but not strong CP, two axions can be used to relax θ ¯ .

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2015

6d $ \mathcal{N}=\left(1,\;0\right) $ theories on S 1 /T 2 and class S theories: part II

Here, we study the T 2 compactification of a class of 6d $ \mathcal{N}=\left(1,\;0\right) $ theories that is Higgsable to $ \mathcal{N}=\left(2,\;0\right) $ theories. We show that the resulting 4d N=2 theory at the origin of the Coulomb branch and the parameter space is generically given by two superconformal matter sectors coupled by an infrared-free gauge multiplet and another conformal gauge multiplet. Our analysis utilizes the 5d theories obtained by putting the same class of 6d theories on S 1 . Our class includes, among others, the 6d theories describing multiple M 5 branes on an ALE singularity, and we analyze them in detail. The resulting 4d theory has manifestly both the SL(2,Z) and the full flavor symmetry. We also discuss in detail the special cases of 6d theories where the infrared-free gauge multiplet is absent. In an appendix, we give a field-theoretical argument for an F-theoretic constraint that forbids a particular 6d anomaly-free matter content, as an application of our analysis.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2016

First sound in holographic superuids at zero temperature

Within the context of AdS/CFT, the gravity dual of an s-wave superfluid is given by scalar QED on an asymptotically AdS spacetime. While this conclusion is vastly supported by numerical arguments, here we provide an analytical proof that this is indeed the case. In conclusion, working at zero temperature, we explicitly find the quadratic action for the superfluid phonon at the boundary in an arbitrary number of dimensions and for an arbitrary scalar field potential, recovering the known dispersion relation for conformal first sound.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2017

Einstein gravity 3-point functions from conformal field theory

We report on stress tensor correlation functions in four-dimensional conformal field theories with large N and a sparse spectrum. Theories in this class are expected to have local holographic duals, so effective field theory in anti-de Sitter implies that the stress tensor sector should exhibit universal, gravity-like behavior. At the linearized level, the hallmark of locality in the emergent geometry is that stress tensor three-point functions $\langle$T T T $\rangle$, normally specified by three constants, should approach a universal structure controlled by a single parameter as the gap to higher spin operators is increased. We demonstrate this phenomenon by a direct CFT calculation. Stress tensor exchange, by itself, violates causality and unitarity unless the three-point functions are carefully tuned, and the unique consistent choice exactly matches the prediction of Einstein gravity. Under some assumptions about the other potential contributions, we conclude that this structure is universal, and in particular, that the anomaly coefficients satisfy a ≈ c as conjectured by Camanho et al. The argument is based on causality of a four-point function, with kinematics designed to probe bulk locality, and invokes the chaos bound of Maldacena, Shenker, and Stanford.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2017

Conformal solids and holography

We argue that a SO( d ) magnetic monopole in an asymptotically AdS space-time is dual to a d -dimensional strongly coupled system in a solid state. In light of this, it would be remiss of us not to dub such a field configuration solidon . In the presence of mixed boundary conditions, a solidon spontaneously breaks translations (among many other symmetries) and gives rise to Goldstone excitations on the boundary — the phonons of the solid. We derive the quadratic action for the boundary phonons in the probe limit and show that, when the mixed boundary conditions preserve conformal symmetry, the longitudinal and transverse sound speeds are related to each other as expected from effective field theory arguments. We then include backreaction and calculate the free energy of the solidon for a particular choice of mixed boundary conditions, corresponding to a relevant multi-trace deformation of the boundary theory. We find such free energy to be lower than that of thermal AdS. This suggests that our solidon undergoes a solid-to-liquid first order phase transition by melting into a Schwarzschild-AdS black hole as the temperature is raised.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2018

A neutrinoless double beta decay master formula from effective field theory

We present a master formula describing the neutrinoless-double-beta decay (0νββ) rate induced by lepton-number-violating (LNV) operators up to dimension nine in the Standard Model Effective Field Theory. We provide an end-to-end framework connecting the possibly very high LNV scale to the nuclear scale, through a chain of effective field theories. Starting at the electroweak scale, we integrate out the heavy Standard Model degrees of freedom and we match to an SU(3) c Ⓧ U(1) em effective theory. After evolving the resulting effective Lagrangian to the QCD scale, we use chiral perturbation theory to derive the lepton-number-violating chiral Lagrangian. The chiral Lagrangian is used to derive the two-nucleon 0νββ transition operators to leading order in the chiral power counting. Based on renormalization arguments we show that in various cases short-range two-nucleon operators need to be enhanced to leading order. We show that all required nuclear matrix elements can be taken from existing calculations. Our final result is a master formula that describes the 0νββ rate in terms of phase-space factors, nuclear matrix elements, hadronic low-energy constants, QCD evolution factors, and high-energy LNV Wilson coefficients, including all the interference terms. Our master formula can be easily matched to any model where LNV originates at energy scales above the electroweak scale. As an explicit example, we match our formula to the minimal left-right-symmetric model in which contributions of operators of different dimension compete, and we discuss the resulting phenomenology.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2020

Towards a classification of rank r $\mathscr{N}$ = 2 SCFTs. Part II. Special Kahler stratification of the Coulomb branch

We study the stratification of the singular locus of four dimensional $\mathscr{N}$ = 2 Coulomb branches. We present a set of self-consistency conditions on this stratification which can be used to extend the classification of scale-invariant rank 1 Coulomb branch geometries to two complex dimensions, and beyond. The calculational simplicity of the arguments presented here stems from the fact that the main ingredients needed - the rank 1 deformation patterns and the pattern of inclusions of rank 2 strata - are discrete topological data which satisfy strong self-consistency conditions through their relationship to the central charges of the SCFT. This relationship of the stratification data to the central charges is used here, but is derived and explained in a companion paper by one of the authors. We illustrate the use of these conditions by re-analyzing many previously-known examples of rank 2 SCFTs, and also by finding examples of new theories. The power of these conditions stems from the fact that for Coulomb branch stratifications a conjecturally complete list of physically allowed “elementary slices” is known. By contrast, constraining the possible elementary slices of symplectic singularities relevant for Higgs branch stratifications remains an open problem.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2021

Proof of the universal density of charged states in QFT

We prove a recent conjecture by Harlow and Ooguri concerning a universal formula for the charged density of states in QFT at high energies for global symmetries associated with finite groups. An equivalent statement, based on the entropic order parameter associated with charged operators in the thermofield double state, was proven in a previous article by Casini, Huerta, Pontello, and the present author. Here we describe how the statement about the entropic order parameter arises, and how it gets transformed into the universal density of states. The use of the certainty principle, relating the entropic order and disorder parameters, is crucial for the proof. We remark that although the immediate application of this result concerns charged states, the origin and physics of such density can be understood by looking at the vacuum sector only. We also describe how these arguments lie at the origin of the so-called entropy equipartition in these type of systems, and how they generalize to QFT’s on non-compact manifolds.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2024

Mixed gauge-global symmetries, elliptic modes, and black hole thermodynamics in Hořava-Lifshitz gravity

In Hořava-Lifshitz gravity, a putative consistent theory of quantum gravity for which there is evidence for both black hole thermodynamics and a holographic construction, spacetime is endowed with a preferred dynamical spacelike foliation. The theory has a leaf reparameterization symmetry that is neither global nor local gauge, hyperbolic and elliptic equations of motion, a lack of splittability, and universal horizon black hole solutions. The reparameterization symmetry is “mixed”: it is a local symmetry in one coordinate yet global on each leaf. More broadly it is an example of both unfree and projectable gauge symmetries. The mixed symmetry and associated charge has not yet been accounted for in calculations of universal horizon thermodynamics in Hořava-Lifshitz gravity. This has led to problems, in particular the failure of the first law in a class of asymptotically AdS solutions where the normal to the leaves of the foliation is not aligned with the time translation Killing vector at infinity. We show how the dynamics of the charge corresponding to this symmetry coupled with the other features above resolves this issue. We then briefly comment how this mixed symmetry, the corresponding charge, and the elliptic equations of motion also conspire to evade recent holographic arguments for only local gauge fields in consistent theories of quantum gravity due to the lack of splittability of the elliptic equation and associated mode.

Global Symmetries↗

DOE OSTI2025

Entanglement Cost for Infinite-Dimensional Physical Systems

We prove that the entanglement cost equals the regularized entanglement of formation for any infinite-dimensional quantum state ρ ΑΒ with finite quantum entropy on at least one of the subsystems A or B. This generalizes a foundational result in quantum information theory that was previously formulated only for operations and states on finite-dimensional systems. The extension to infinite-dimensional systems is nontrivial because the conventional tools for establishing both the direct and converse bounds, i.e., strong typicality, monotonicity, and asymptotic continuity, are no longer directly applicable. To address this problem, we construct a new entanglement dilution protocol for infinite-dimensional states implementable by local operations and a finite amount of one-way classical communication (one-way LOCC), using weak and strong typicality multiple times. We also prove the optimality of this protocol among all protocols, even under infinite-dimensional separable operations, by developing an argument based on alternative forms of monotonicity and asymptotic continuity of the entanglement of formation for infinite-dimensional states. Along the way, we derive a new integral representation for the quantum entropy of infinite-dimensional states, which we believe to be of independent interest. Our results allow us to fully characterize an important operational entanglement measure—the entanglement cost—for all infinite-dimensional physical systems.

Complexity↗

DOE OSTI2011

Singular Perturbation for the Discounted Continuous Control of Piecewise Deterministic Markov Processes

This paper deals with the expected discounted continuous control of piecewise deterministic Markov processes (PDMP's) using a singular perturbation approach for dealing with rapidly oscillating parameters. The state space of the PDMP is written as the product of a finite set and a subset of the Euclidean space Double-Struck-Capital-R {sup n}. The discrete part of the state, called the regime, characterizes the mode of operation of the physical system under consideration, and is supposed to have a fast (associated to a small parameter {epsilon}>0) and a slow behavior. By using a similar approach as developed in Yin and Zhang (Continuous-Time Markov Chains and Applications: A Singular Perturbation Approach, Applications of Mathematics, vol. 37, Springer, New York, 1998, Chaps. 1 and 3) the idea in this paper is to reduce the number of regimes by considering an averaged model in which the regimes within the same class are aggregated through the quasi-stationary distribution so that the different states in this class are replaced by a single one. The main goal is to show that the value function of the control problem for the system driven by the perturbed Markov chain converges to the value function of this limit control problem as {epsilon} goes to zero. This convergence is obtained by, roughly speaking, showing that the infimum and supremum limits of the value functions satisfy two optimality inequalities as {epsilon} goes to zero. This enables us to show the result by invoking a uniqueness argument, without needing any kind of Lipschitz continuity condition.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2011

Pathwise Solutions of the 2-D Stochastic Primitive Equations

In this work we consider a stochastic version of the Primitive Equations (PEs) of the ocean and the atmosphere and establish the existence and uniqueness of pathwise, strong solutions. The analysis employs novel techniques in contrast to previous works (Ewald et al. in Anal. Appl. (Singap.) 5(2):183-198, 2007; Glatt-Holtz and Ziane in Discrete Contin. Dyn. Syst. Ser. B 10(4):801-822, 2008) in order to handle a general class of nonlinear noise structures and to allow for physically relevant boundary conditions. The proof relies on Cauchy estimates, stopping time arguments and anisotropic estimates.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2012

Sharp Observability Estimates for a System of Two Coupled Nonconservative Hyperbolic Equations

We consider a system of two coupled nonconservative wave equations. For this system, we prove several observability estimates. Those observability estimates are sharp in the sense that they lead by duality to the controllability (exact or approximate) of the coupled system with a single control acting through one of the equations only while keeping the same controllability time as for a single equation. Existing results in the literature either require two controls, or in the case of a single control, they have a controllability time that blows up as the coupling parameter goes to zero. Our proofs rely on: (i) Carleman estimates, (ii) energy estimates and (iii) localizing arguments. The results obtained complement and improve, in some sense, earlier results while at the same time providing new uniqueness results.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2013

Large Deviations and Importance Sampling for Systems of Slow-Fast Motion

In this paper we develop the large deviations principle and a rigorous mathematical framework for asymptotically efficient importance sampling schemes for general, fully dependent systems of stochastic differential equations of slow and fast motion with small noise in the slow component. We assume periodicity with respect to the fast component. Depending on the interaction of the fast scale with the smallness of the noise, we get different behavior. We examine how one range of interaction differs from the other one both for the large deviations and for the importance sampling. We use the large deviations results to identify asymptotically optimal importance sampling schemes in each case. Standard Monte Carlo schemes perform poorly in the small noise limit. In the presence of multiscale aspects one faces additional difficulties and straightforward adaptation of importance sampling schemes for standard small noise diffusions will not produce efficient schemes. It turns out that one has to consider the so called cell problem from the homogenization theory for Hamilton-Jacobi-Bellman equations in order to guarantee asymptotic optimality. We use stochastic control arguments.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2013

Nonlinear Diffusions and Stable-Like Processes with Coefficients Depending on the Median or VaR

The paper is devoted to the well-posedness for nonlinear McKean-Vlasov type diffusions with coefficients depending on the median or, more generally, on the {alpha}-quantile of the underlying distribution. The median is not a continuous function on the space of probability measures equipped with the weak convergence. This is one reason why well-posedness of the SDE considered in the paper does not follow by standard arguments.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2015

A Deep Quench Approach to the Optimal Control of an Allen–Cahn Equation with Dynamic Boundary Conditions and Double Obstacles

In this paper, we investigate optimal control problems for Allen-Cahn variational inequalities with a dynamic boundary condition involving double obstacle potentials and the Laplace-Beltrami operator. The approach covers both the cases of distributed controls and of boundary controls. The cost functional is of standard tracking type, and box constraints for the controls are prescribed. We prove existence of optimal controls and derive first-order necessary conditions of optimality. The general strategy is the following: we use the results that were recently established by two of the authors for the case of (differentiable) logarithmic potentials and perform a so-called “deep quench limit”. Using compactness and monotonicity arguments, it is shown that this strategy leads to the desired first-order necessary optimality conditions for the case of (non-differentiable) double obstacle potentials.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗