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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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DOE OSTI2024

Conformal BK equation at QCD Wilson-Fisher point

High-energy scattering in pQCD in the Regge limit is described by the evolution of Wilson lines governed by the BK equation. In the leading order, the BK equation is conformally invariant and the eigenfunctions of the linearized BFKL equation are powers. It is a common belief that at d ≠ 4 the BFKL equation is useless since unlike d = 4 case it cannot be solved by usual methods. However, we demonstrate that at critical Wilson-Fisher point of QCD the relevant part of NLO BK restores the conformal invariance so the solutions are again powers. As a check of our approach to high-energy amplitudes at the Wilson-Fisher point, we calculate the anomalous dimensions of twist-2 light-ray operators in the Regge limit j → 1.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Holographic solar systems and hydrogen atoms: non-relativistic physics in AdS and its CFT dual

We study a non-relativistic limit of physics in AdS which retains the curvature through a harmonic Newtonian potential. This limit appears in a CFT dual through the spectrum of operators of large dimension and correlation functions of those operators with appropriate kinematics. In an additional flat spacetime limit, the spectrum is determined by scattering phase shifts (proportional to anomalous dimensions), and a CFT correlation function is proportional to the S-matrix. In particular, we describe the effect of resonances on the spectrum and correlation functions. As an example, we discuss the Coulomb potential (describing solar systems and hydrogen atoms in AdS) in detail.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Scaling similarities and quasinormal modes of D0 black hole solutions

We study the gravity solution dual to the D0 brane quantum mechanics, or BFSS matrix model, in the ’t Hooft limit. The classical physics described by this gravity solution is invariant under a scaling transformation, which changes the action with a specific critical exponent, sometimes called the hyperscaling violating exponent. We present an argument for this critical exponent from the matrix model side, which leads to an explanation for the peculiar temperature dependence of the entropy in this theory, S ∝ T 9/5 . We also present a similar argument for all other Dp-brane geometries. We then compute the black hole quasinormal modes. This involves perturbing the finite temperature geometry. These perturbations can be easily obtained by a mathematical trick where we view the solution as the dimensional reduction of an Ad S2+9/5 × S 8 geometry.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Goldstone bosons on celestial sphere and conformal soft theorems

In this paper, we study celestial amplitudes of Goldstone bosons and conformal soft theorems. Motivated by the success of soft bootstrap in momentum space and the important role of the soft limit behavior of tree-level amplitudes, our goal is to extend some of the methods to the celestial sphere. The crucial ingredient of the calculation is the Mellin transformation, which transforms four-dimensional scattering amplitudes to correlation functions of primary operators in the celestial CFT. The soft behavior of the amplitude is then translated to the singularities of the correlator. Only for amplitudes in “UV completed theories” (with sufficiently good high energy behavior) the Mellin integration can be properly performed. In all other cases, the celestial amplitude is only defined in a distributional sense with delta functions. We provide many examples of celestial amplitudes in UV-completed models, including linear sigma models and Z-theory, which is a certain completion of the SU(N) non-linear sigma model. We also comment on the BCFW-like and soft recursion relations for celestial amplitudes and the extension of soft bootstrap ideas.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Universal bounds on CFT Distance Conjecture

For any unitary conformal field theory in two dimensions with the central charge c, we prove that, if there is a nontrivial primary operator whose conformal dimension ∆ vanishes in some limit on the conformal manifold, the Zamolodchikov distance t to the limit is infinite, the approach to this limit is exponential ∆ = exp(−αt + O(1)), and the decay rate obeys the universal bounds c−1/2 ≤ α ≤ 1. In the limit, we also find that an infinite tower of primary operators emerges without a gap above the vacuum and that the conformal field theory becomes locally a tensor product of a sigma-model in the large radius limit and a compact theory. As a corollary, we establish a part of the Distance Conjecture about gravitational theories in three-dimensional anti-de Sitter space. In particular, our bounds on α indicate that the emergence of exponentially light states is inevitable as the moduli field corresponding to t rolls beyond the Planck scale along the steepest path and that this phenomenon can begin already at the curvature scale of the bulk geometry. We also comment on implications of our bounds for gravity in asymptotically flat spacetime by taking the flat space limit and compare with the Sharpened Distance Conjecture.

AdS-CFT Correspondence↗
DOE OSTI2023

Standard Model in conformal geometry: Local vs gauged scale invariance

Here, we discuss comparatively local versus gauged Weyl symmetry beyond Standard Model (SM) and Einstein gravity and their geometric interpretation. The SM and Einstein gravity admit a natural embedding in Weyl integrable geometry which is a special limit of Weyl conformal (non-metric) geometry. The theory has a local Weyl scale symmetry but no associated gauge boson. Unlike previous models with such symmetry, this embedding is truly minimal i.e. with no additional fields beyond SM and underlying geometry. This theory is compared to a similar minimal embedding of SM and Einstein gravity in Weyl conformal geometry (SMW) which has a full gauged scale invariance, with an associated Weyl gauge boson. At large field values, both theories give realistic, Starobinsky–Higgs like inflation. The broken phase of the current model is the decoupling limit of the massive Weyl gauge boson of the broken phase of SMW, while the local scale symmetry of the current model is part of the larger gauged scale symmetry of SMW. Hence, the current theory has a gauge embedding in SMW. Unlike in the SMW, we note that in models with local scale symmetry the associated current is trivial, which is a concern for the physical meaning of this symmetry. Therefore, the SMW is a more fundamental UV completion of SM in a full gauge theory of scale invariance that generates Einstein gravity in the (spontaneously) broken phase, as an effective theory.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

The Gross-Neveu-Yukawa archipelago

We perform a bootstrap analysis of a mixed system of four-point functions of bosonic and fermionic operators in parity-preserving 3d CFTs with O(N) global symmetry. Our results provide rigorous bounds on the scaling dimensions of the O(N)-symmetric Gross-Neveu-Yukawa (GNY) fixed points, constraining these theories to live in isolated islands in the space of CFT data. We focus on the cases N = 1, 2, 4, 8, which have applications to phase transitions in condensed matter systems, and compare our bounds to previous analytical and numerical results.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Bounding irrelevant operators in the 3d Gross-Neveu-Yukawa CFTs

We perform a numerical bootstrap study of scalar operators in the critical 3d Gross-Neveu-Yukawa models, a family of conformal field theories containing N Majorana fermions in the fundamental representation of an O(N) global symmetry. We compute rigorous bounds on the scaling dimensions of the next-to-lowest parity-even and parity-odd singlet scalars at N = 2, 4, and 8. All of these dimensions have lower bounds greater than 3, implying that there are only two relevant singlet scalars and placing constraints on the RG flow structure of these theories.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Topological symplectic Kondo effect

Multiple conduction channels interacting with a quantum impurity—a spin in the conventional “multichannel Kondo effect” or a topological mesoscopic device (“topological Kondo effect”)—has been proposed as a platform to realize anyonic quasiparticles. However, the above implementations require either perfect channel symmetry or the use of Majorana fermions. Here, in this work, we propose a Majorana-free mesoscopic setup which implements the Kondo effect of the symplectic Lie group and can harbor emergent anyons (including Majorana fermions, Fibonacci anyons, and parafermions) even in the absence of perfect channel symmetry. In addition to the detailed prescription of the implementation, we present the strong coupling solution by mapping the model to the multichannel Kondo effect associated to an internal symmetry and exploit conformal field theory to predict the nontrivial scaling of a variety of observables, including conductance, as a function of temperature. This work does not only open the door for robust Kondo-based anyon platforms, but also sheds light on the physics of strongly correlated materials with competing order parameters.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Improving modular bootstrap bounds with integrality

We propose methods that efficiently impose integrality — i.e., the condition that the coefficients of characters in the partition function must be integers — into numerical modular bootstrap. We demonstrate the method with a number of examples where it can be used to strengthen modular bootstrap results. First, we show that, with a mild extra assumption, imposing integrality improves the bound on the maximal allowed gap in dimensions of operators in theories with a U(1) c symmetry at c = 3, and reduces it to the value saturated by the SU(4) 1 WZW model point of c = 3 Narain lattices moduli space. Second, we show that our method can be used to eliminate all but a discrete set of points saturating the bound from previous Virasoro modular bootstrap results. Finally, when central charge is close to 1, we can slightly improve the upper bound on the scaling dimension gap.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Mass-induced confinement near the sill of the conformal window

We revisit standard arguments for hyperscaling of the spectrum when a nonzero fermion mass is introduced to a gauge-fermion theory which is conformal in the infrared limit. With some general assumptions, we argue that the induced confinement scale will be significantly enhanced near the edge of the conformal to confining transition. This enhancement can allow for the fermion mass to be arbitrarily small compared to the confinement scale. This scale separation may allow for apparent spontaneous breaking of chiral symmetry within the conformal window, which may be of interest for construction of dilaton effective field theories in this regime.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

A model of persistent breaking of continuous symmetry

We consider a UV-complete field-theoretic model in general dimensions, including d=2+1, which consists of two copies of the long-range vector models, with O(m) and O(N-m) global symmetry groups, perturbed by double-trace operators. Using conformal perturbation theory we find weakly-coupled IR fixed points for N\geq 6 N ≥ 6 that reveal a spontaneous breaking of global symmetry. Namely, at finite temperature the lower rank group is broken, with the pattern persisting at all temperatures due to scale-invariance. We provide evidence that the models in question are unitary and invariant under full conformal symmetry. Furthermore, we show that this model exhibits a continuous family of weakly interacting field theories at finite N.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

Near conformal perturbation theory in SYK type models

We present a systematic procedure to extract the dynamics of the low energy soft mode in SYK type models with a single energy scale J and emergent reparametrization symmetry in the IR. This is given in the framework of the perturbative scheme of arXiv:1608.07567 based on a specific (off-shell) breaking of conformal invariance in the UV, adjusted to yield the exact large-N saddle point. While this breaking term formally vanishes on-shell, it has a non-trivial effect on correlation functions and the effective action. In particular, it leads to the Schwarzian action with a specific coupling to bi-local matter. The method is applied to the evaluation of O(1) corrections to the correlation function of bi-locals. As a byproduct we confirm precise agreement with the explicit, symmetry breaking procedure. We provide a verification in the large q limit (Liouville theory), where the correlators can be calculated exactly at all length scales. In this case, our scheme illuminates how the enhanced O(J) and the subleading O(1) contributions originate from the Schwarzian dynamics of the soft mode and its interaction with h = 2 (bi-local) matter.

1/N expansion↗
DOE OSTI2025

Unraveling trace anomaly of supradense matter via neutron star compactness scaling

The trace anomaly Δ ≡ 1/3 −𝑃/𝜖 =1/3 −𝜙 quantifies the possibly broken conformal symmetry in supradense matter under pressure 𝑃 at energy density 𝜖. Perturbative QCD (pQCD) predicts a vanishing Δ at extremely high energy or baryon densities when the conformal symmetry is realized but its behavior at intermediate densities reachable in neutron stars (NSs) is still very uncertain. The extraction of Δ from NS observations strongly depends on the employed model for nuclear equation of state (EOS). Using the IPAD-TOV method based on an intrinsic and perturbative analysis of the dimensionless (IPAD) Tolman-Oppenheimer-Volkoff (TOV) equations that are further verified numerically by using 10 5 EOSs generated randomly with a metamodel in a very broad EOS parameter space constrained by terrestrial nuclear experiments and astrophysical observations, here we first show that the compactness 𝜉 ≡ 𝐺⁡𝑀 NS /𝑅⁢𝑐 2 ≡ 𝑀 NS /𝑅 of a NS with mass 𝑀 NS and radius 𝑅 scales very accurately with $\bar{Π}$ c ≡ $Π$ c · (1 +18⁢X/25) ≡ X/(1 +3⁢X 2 +4⁢X) · (1 +18⁢X/25) where X ≡ 𝜙 c = 𝑃 c /𝜖 c is the ratio of pressure over energy density at NS centers. The scaling of NS compactness thus enables one to readily read off the central trace anomaly Δ c = 1/3 −X directly from the observational data of either the mass-radius or red-shift measurements. Finally, we then demonstrate indeed that the available NS data themselves from recent X-ray and gravitational wave observations can determine model insensitively the trace anomaly as a function of energy density in NS cores, providing a stringent test of existing NS models and a clear guidance in a new direction for further understanding the nature and EOS of supradense matter.

nuclear astrophysics↗
DOE OSTI2021

Reduced conformal symmetry

We construct field theories in 2 + 1 dimensions with multiple conformal symmetries acting on only one of the spatial directions. These can be considered a conformal extension to “subsystem scale invariances”, borrowing the language often used for fractons.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Spontaneous breaking of U(1) symmetry in coupled complex SYK models

As shown in [1], two copies of the large N Majorana SYK model can produce spontaneous breaking of a Z 2 symmetry when they are coupled by appropriate quartic terms. In this paper we similarly study two copies of the complex SYK model coupled by a quartic term preserving the U(1) x U(1) symmetry. We also present a tensor counterpart of this coupled model. When the coefficient α of the quartic term lies in a certain range, the coupled large N theory is nearly conformal. We calculate the scaling dimensions of fermion bilinear operators as functions of α. We show that the operator c$^†_{1i}$c 2i , which is charged under the axial U(1) symmetry, acquires a complex dimension outside of the line of fixed points. We derive the large N Dyson-Schwinger equations and show that, outside the fixed line, this U(1) symmetry is spontaneously broken at low temperatures because this operator acquires an expectation value. We support these findings by exact diagonalizations extrapolated to large N.

1/N expansion↗
DOE OSTI2021

Unnuclear physics: Conformal symmetry in nuclear reactions

Significance Symmetry plays a key role in modern physics as a guiding principle for fundamental theories of nature. We use the nonrelativistic conformal symmetry to predict universal energy spectra of final states in reactions of quantum particles at vastly different length scales. Our work extends Georgi’s “unparticle” proposal to nonrelativistic spin-1/2 fermions in the unitary regime of strong interactions. These systems form so-called unparticles, which behave characteristically different from normal particles. They can be engineered with ultracold atoms and occur naturally in nuclear reactions with multiple neutrons—a situation we dub “unnuclear physics.” We present the general scenario of unnuclear physics, apply it to identify unnuclei in nuclear reactions, and highlight the opportunity to measure unnuclei at radioactive beam facilities.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Generalized multifractality at spin quantum Hall transition

Generalized multifractality characterizes scaling of eigenstate observables at Anderson-localization critical points. We explore generalized multifractality in 2D systems, with the main focus on the spin quantum Hall (SQH) transition in superconductors of symmetry class C. Relations and differences with the conventional integer quantum Hall (IQH) transition are also studied. Using the field-theoretical formalism of non-linear sigma-model, we derive the pure-scaling operators representing generalizing multifractality and then “translate” them to the language of eigenstate observables. Performing numerical simulations on network models for SQH and IQH transitions, we confirm the analytical predictions for scaling observables and determine the corresponding exponents. Remarkably, the generalized-multifractality exponents at the SQH critical point strongly violate the generalized parabolicity of the spectrum, which implies violation of the local conformal invariance at this critical point.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗