Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Conformal Field Theory”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 361 records · Page 20

Multiscale Modeling of Vinyl-Addition Polynorbornenes: The Effect of Stereochemistry

Vinyl-addition polynorbornenes are candidates for designing high-performance polymers due to unique characteristics, which include a high glass transition temperature associated with a rigid backbone. Recent studies have established that the processability and properties of these polymers can be fine-tuned by using targeted substitutions. However, synthesis with different catalysts results in materials with distinct properties, potentially due to the presence of various stereoisomers that are difficult to quantify experimentally. Herein, we develop all-atom models of polynorbornene oligomers based on classical force fields and density functional theory. To establish the relationship between chemical architecture, chain conformations, and melt structure, we perform detailed molecular dynamics simulations with the fine-tuned atomistic force field and propose simpler coarse-grained descriptions to address the high molecular weight limit. All-atom simulations of oligomers suggest high glass transition temperatures in the range of 550–600 K. In the melt state (800 K), meso chains form highly rigid extended coils (C∞≈11) with amorphous structural characteristics similar to the X-ray diffraction data observed in the literature. In contrast, simulations with racemo chains predict highly helical tubular chain conformations that could promote assembly into crystalline structures.

Polymer Science↗

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. Published by the American Physical Society 2025

Farnsworth, Kara (ORCID:000000020200078X)↗

Celestial gluon amplitudes from the outside in

We show that, given a two-dimensional realization of the celestial OPE in self-dual Yang-Mills, we can find a scalar source around which scattering amplitudes replicate correlation functions computed from the 2D ‘gluon’ operators in a limit where a dynamic massless scalar decouples. We derive conditions on the two-dimensional three-point correlation function so that such a source exists and give two particular examples of this construction, one in which gluons are constructed from vertex operators in the semiclassical limit of Liouville theory and another in which the soft gluons arise from generalized free fields. Finally, we identify a bulk dual to the level of the boundary Kac-Moody algebra and discuss moving beyond the decoupling limit.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

On effective field theories with celestial duals

We show that associativity of the tree-level OPE in a celestial CFT imposes constraints on the coupling constants of the corresponding bulk theory. These constraints are the same as those derived in [9] from the Jacobi identity of the algebra of soft modes. The constrained theories are interesting as apparently well-defined celestial CFTs with a deformed w 1+∞ symmetry algebra. We explicitly work out the ramifications of these constraints on scattering amplitudes involving gluons, gravitons and scalars in these theories. We find that all four-point amplitudes constructible solely from holomorphic or anti-holomorphic three-point amplitudes vanish on the support of these constraints, which implies that all purely holomorphic or purely anti-holomorphic higher-point amplitudes vanish.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

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↗

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↗

Superadditivity at large charge

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.

effective field theories↗

Generalized models for inflationary preheating: Oscillations and symmetries

The paradigm of the inflationary universe provides a possible explanation for several observed cosmological properties. In order for such solutions to be successful, the universe must convert the energy stored in the inflaton potential into standard model particles through a process known as reheating. In this paper, we reconsider the reheating process for the case where the inflaton potential respects an approximate (but spontaneously broken) conformal symmetry during the reheating epoch. After reviewing the Effective Field Theory of Reheating, we present solutions for the nonlinear oscillations of the inflaton field, derive the corresponding Hill’s equation for the coupled reheating field, and determine the stability diagram for parametric resonance. For this class of models —the simplest realization being a scalar field with a quartic term—the expansion of the universe drives the coupled field toward a more unstable part of parameter space, in contrast to the standard case. We also generalize this class of models to include quadratic breaking terms in the potential during the reheating epoch and address the process of stability in that universality class of models.

Barrowes, Leia [University of Michigan, Ann Arbor]↗

3d N=4 Bootstrap and Mirror Symmetry

We investigate the non-BPS realm of 3d {N} = 4 N = 4 superconformal field theory by uniting the non-perturbative methods of the conformal bootstrap and supersymmetric localization, and utilizing special features of 3d {N} = 4 N = 4 theories such as mirror symmetry and a protected sector described by topological quantum mechanics (TQM). Supersymmetric localization allows for the exact determination of the conformal and flavor central charges, and the latter can be fed into the mini-bootstrap of the TQM to solve for a subset of the OPE data. We examine the implications of the Z_2 Z 2 mirror action for the SCFT single- and mixed-branch crossing equations for the moment map operators, and apply numerical bootstrap to obtain universal constraints on OPE data for given flavor symmetry groups. A key ingredient in applying the bootstrap analysis is the determination of the mixed-branch superconformal blocks. Among other results, we show that the simplest known self-mirror theory with SU(2) \times SU(2) S U ( 2 ) × S U ( 2 ) flavor symmetry saturates our bootstrap bounds, which allows us to extract the non-BPS data and examine the self-mirror Z_2 Z 2 symmetry thereof.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

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↗

Chiral algebra, localization, modularity, surface defects, and all that

We study the 2D vertex operator algebra (VOA) construction in 4D N = 2 superconformal field theories on S 3 × S 1 , focusing on both old puzzles and new observations. The VOA lives on a two-torus T 2 ⊂ S 3 × S 1 , it is 1 2 Z -graded, and this torus is equipped with the natural choice of spin structure (1,0) for the Z + 1 2 -graded operators, corresponding to the NS sector vacuum character. By analyzing the possible refinements of the Schur index that preserves the VOA, we find that it admits discrete deformations, which allows access to the remaining spin structures (1,1), (0,1), and (0,0), of which the latter two involve the inclusion of a particular surface defect. For Lagrangian theories, we perform the detailed analysis: we describe the natural supersymmetric background, perform localization, and derive the gauged symplectic boson action on a torus in any spin structure. In the absence of flavor fugacities, the 2D and 4D path integrals precisely match, including the Casimir factors. We further analyze the 2D theory: we identify its integration cycle and the two-point functions and interpret flavor holonomies as screening charges in the VOA. Next, we make some observations about modularity; the T-transformation acts on our four partition functions and lifts to a large diffeomorphism on S 3 × S 1 . More interestingly, we generalize the four partition functions on the torus to an infinite family labeled by both the spin structure and the integration cycle inside the complexified maximal torus of the gauge group. Members of this family transform into one another under the full modular group, and we confirm the recent observation that the S-transform of the Schur index in Lagrangian theories exhibits logarithmic behavior. Finally, we comment on how locally our background reproduces the Ω-background.

97 MATHEMATICS AND COMPUTING↗

On triality defects in 2d CFT

We consider the triality fusion category discovered in the c = 1 Kosterlitz-Thouless theory. We analyze this fusion category using the tools from the group theoretical fusion category and compute the simple lines, fusion rules and F-symbols. We then studied the physical implication of this fusion category including deriving the spin selection rule, computing the asymptotic density of states of irreducible representations of the fusion category symmetries, and analyzing its anomaly and constraints under the renormalization group flow. There is another set of F-symbols for the fusion categories with the same fusion rule known in the literature. We find these two solutions are different as they lead to different spin selection rules. This gives a complete list of the fusion categories with the same fusion rule by the classification result in.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

The reflected entanglement spectrum for free fermions

We consider the reflected entropy and the associated entanglement spectrum for free fermions reduced to two intervals in 1 + 1 dimensions. Working directly in the continuum theory the reflected entropy can be extracted from the spectrum of a singular integral equation whose kernel is determined by the known free fermion modular evolved correlation function. We find the spectrum numerically and analytically in certain limits. For intervals that almost touch the reflected entanglement spectrum approaches the spectrum of the thermal density matrix. This suggests that the reflected entanglement spectrum is well suited to the task of extracting physical data of the theory directly from the ground state wave function.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Dispersive sum rules in AdS 2

Dispersion relations for S-matrices and CFT correlators translate UV consistency into bounds on IR observables. In this note, we construct dispersive sum rules for 1D CFTs. We use them to prove bounds on higher-derivative couplings in weakly-coupled non-gravitational EFTs in AdS2. At the leading order in the bulk-point limit, the bounds agree with the flat-space result. We compute the leading universal effect of finite AdS radius on the bounds. Along the way, we give an explicit formula for anomalous dimensions in general higher-derivative contact Witten diagrams in AdS 2 .

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

The dual of non-extremal area: differential entropy in higher dimensions

The Ryu-Takayanagi formula relates entanglement entropy in a field theory to the area of extremal surfaces anchored to the boundary of a dual AdS space. It is interesting to ask if there is also an information theoretic interpretation of the areas of non-extremal surfaces that are not necessarily boundary-anchored. In general, the physics outside such surfaces is associated to observers restricted to a time-strip in the dual boundary field theory. When the latter is two-dimensional, it is known that the differential entropy associated to the strip computes the length of the dual bulk curve, and has an interpretation in terms of the information cost in Bell pairs of restoring correlations inaccessible to observers in the strip. A general realization of this formalism in higher dimensions is unknown. We first prove a no-go theorem eliminating candidate expressions for higher dimensional differential entropy based on entropic c-theorems. Then we propose a new formula in terms of an integral of shape derivatives of the entanglement entropy of ball shaped regions. Our proposal stems from the physical requirement that differential entropy must be locally finite and conformally invariant. Demanding cancelation of the well-known UV divergences of entanglement entropy in field theory guides us to our conjecture, which we test for surfaces in AdS 4 . Our results suggest a candidate c-function for field theories in arbitrary dimensions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Analysis of accelerated motion in the theory of relativity

Conventional treatments of accelerated motion in the theory of relativity have led to certain difficulties of interpretation. Certain reversals in the apparent gravitational field of an accelerated body may be avoided by simpler analysis based on the use of restricted conformal transformations. In the conformal theory the velocity of light remains constant even for experimenters in accelerated motion. The problem considered is that of rectilinear motion with a variable velocity. The motion takes place along the x or x' axis of two coordinate systems.

Jones, R. T.↗

Solution Structure and Scaling Laws of Cylindrical and Tapered Bottlebrush Polymers

Bottlebrush polymers are a unique class of macromolecular architectures with a plethora of potential industrial and pharmaceutical applications that critically depend on the bottlebrush shape and dimensions. Here, a systematic series of 12 cylindrical and 12 cone-shaped (tapered) bottlebrush polymers with poly(tert-butyl acrylate) (PtBA) or polystyrene (PS) side chains were synthesized using the sequential addition of macromonomers ring-opening metathesis polymerization (SAM-ROMP) grafting-through method. Small-angle neutron scattering (SANS) studies on dilute solutions of the two types of bottlebrush polymers provided noninvasive characterization of their structural dimensions and chain conformations. Simulated SANS traces, generated using coarse-grained molecular dynamics simulations, reproduced the distinctive features observed in the experimental SANS signals and provided necessary validation for data modeling. The combined analysis of experimental and simulated SANS signals yielded key structural and conformational parameters, including the bottlebrush radius, length, and Kuhn length as well as the excluded volume parameter and the correlation length of the polymer side chains. Importantly, the obtained structural parameters followed well-defined scaling laws as a function of the backbone and side chain degrees of polymerization, as predicted by mean field theories. In conclusion, these findings provide clear experimental and computational evidence of the interdependence of structural and conformational properties in an important class of polymer architectures.

36 MATERIALS SCIENCE↗