Search NASA⌕ Search

SEARCH · Search NASA

Results for “Sigma Models”

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 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Thermal partition function of $$ {J}_3{\overline{J}}_3 $$ deformed AdS3

Abstract We derive a compact formula for the one-loop, bosonic string partition function of Euclideanized$$ {J}_3{\overline{J}}_3 $$ J 3 J ¯ 3 deformedAdS 3 with periodic Euclidean time as an integral transform of the partition function of the undeformed EuclideanizedAdS 3 . Such a deformation is interpretable as an irrelevant “single-trace$$ T\overline{T} $$ T T ¯ deformation” of the boundary. We will do this by first establishing a formal procedure to compute a worldsheet torus zero point function for an exactly marginal$$ J\overline{J} $$ J J ¯ deformation of a sigma model with U(1) L × U(1) R global symmetry. We then describe how this procedure is implemented on SL(2,R) sigma model and its Euclidean continuation. Finally, we describe the embedding of the deformed SL(2,R) torus amplitude into critical string theory and interpret the result as the leading perturbative contribution to the thermal partition function of the deformed theory.

Physics↗
NASA NTRS1983

Three dimensional flow field inside compressor rotor, including blade boundary layers

The space marching code was modified in order to be able to predict the flow field inside a rotor passage, including the blade and hub wall boundary layers. The basic changes incorporated are modifications of the equations so that the code can handle three dimensional configurations with changes in the radial direction (for example changes in stagger angle, blade camber and thickness), extensions and modifications in order to implement a physically realistic turbulence model such as a k sigma model and an algebraic Reynolds stress model.

Pouagare, M.↗
DOE OSTI2026

Tensor renormalization group approach to critical phenomena via symmetry-twisted partition functions

The locality of field theories strongly constrains the possible behaviors of symmetry-twisted partition functions, and thus they serve as order parameters to detect low-energy realizations of global symmetries, such as spontaneous symmetry breaking (SSB). We demonstrate that the tensor renormalization group (TRG) offers an efficient framework to compute the symmetry-twisted partition functions, which enables us to detect the symmetry-breaking transition and also to study associated critical phenomena. As concrete examples of SSB, we investigate the two-dimensional (2D) classical Ising model and the three-dimensional (3D) classical 𝑂⁡(2) nonlinear sigma model, and we identify their critical points solely from the twisted partition function. By employing the finite-size scaling argument, we find the critical temperature 𝑇 𝑐 = 2.2017⁢(2) with the critical exponent 𝜈 = 0.663⁢(33) for the 3D 𝑂⁡(2) model. In addition, we also study the Berezinskii–Kosterlitz–Thouless (BKT) criticality of the 2D classical 𝑂⁡(2) model by extracting the helicity modulus from the twisted partition functions, and we obtain the BKT transition temperature, 𝑇 BKT = 0.8928⁢(2).

lattice field theory↗
NASA NTRS1998

A Monte Carlo Uncertainty Analysis of Ozone Trend Predictions in a Two Dimensional Model

We use Monte Carlo analysis to estimate the uncertainty in predictions of total O3 trends between 1979 and 1995 made by the Goddard Space Flight Center (GSFC) two-dimensional (2D) model of stratospheric photochemistry and dynamics. The uncertainty is caused by gas-phase chemical reaction rates, photolysis coefficients, and heterogeneous reaction parameters which are model inputs. The uncertainty represents a lower bound to the total model uncertainty assuming the input parameter uncertainties are characterized correctly. Each of the Monte Carlo runs was initialized in 1970 and integrated for 26 model years through the end of 1995. This was repeated 419 times using input parameter sets generated by Latin Hypercube Sampling. The standard deviation (a) of the Monte Carlo ensemble of total 03 trend predictions is used to quantify the model uncertainty. The 34% difference between the model trend in globally and annually averaged total O3 using nominal inputs and atmospheric trends calculated from Nimbus 7 and Meteor 3 total ozone mapping spectrometer (TOMS) version 7 data is less than the 46% calculated 1 (sigma), model uncertainty, so there is no significant difference between the modeled and observed trends. In the northern hemisphere midlatitude spring the modeled and observed total 03 trends differ by more than 1(sigma) but less than 2(sigma), which we refer to as marginal significance. We perform a multiple linear regression analysis of the runs which suggests that only a few of the model reactions contribute significantly to the variance in the model predictions. The lack of significance in these comparisons suggests that they are of questionable use as guides for continuing model development. Large model/measurement differences which are many multiples of the input parameter uncertainty are seen in the meridional gradients of the trend and the peak-to-peak variations in the trends over an annual cycle. These discrepancies unambiguously indicate model formulation problems and provide a measure of model performance which can be used in attempts to improve such models.

Considine, D. B.↗
NASA NTRS1997

Meta-Modeling: A Knowledge-Based Approach to Facilitating Model Construction and Reuse

In this paper, we introduce a new modeling approach called meta-modeling and illustrate its practical applicability to the construction of physically-based ecosystem process models. As a critical adjunct to modeling codes meta-modeling requires explicit specification of certain background information related to the construction and conceptual underpinnings of a model. This information formalizes the heretofore tacit relationship between the mathematical modeling code and the underlying real-world phenomena being investigated, and gives insight into the process by which the model was constructed. We show how the explicit availability of such information can make models more understandable and reusable and less subject to misinterpretation. In particular, background information enables potential users to better interpret an implemented ecosystem model without direct assistance from the model author. Additionally, we show how the discipline involved in specifying background information leads to improved management of model complexity and fewer implementation errors. We illustrate the meta-modeling approach in the context of the Scientists' Intelligent Graphical Modeling Assistant (SIGMA) a new model construction environment. As the user constructs a model using SIGMA the system adds appropriate background information that ties the executable model to the underlying physical phenomena under investigation. Not only does this information improve the understandability of the final model it also serves to reduce the overall time and programming expertise necessary to initially build and subsequently modify models. Furthermore, SIGMA's use of background knowledge helps eliminate coding errors resulting from scientific and dimensional inconsistencies that are otherwise difficult to avoid when building complex models. As a. demonstration of SIGMA's utility, the system was used to reimplement and extend a well-known forest ecosystem dynamics model: Forest-BGC.

Keller, Richard M.↗
DOE OSTI2024

Hidden zeros for particle/string amplitudes and the unity of colored scalars, pions and gluons

Recent years have seen the emergence of a new understanding of scattering amplitudes in the simplest theory of colored scalar particles — the Tr(Φ 3 ) theory — based on combinatorial and geometric ideas in the kinematic space of scattering data. In this paper we report a surprise: far from the toy model it appears to be, the “stringy” Tr(Φ 3 ) amplitudes secretly contains the scattering amplitudes for pions, as well as non-supersymmetric gluons, in any number of dimensions. The amplitudes for the different theories are given by one and the same function, related by a simple shift of the kinematics. This discovery was spurred by another fundamental observation: the tree-level Tr(Φ 3 ) field theory amplitudes have a hidden pattern of zeros when a special set of non-planar Mandelstam invariants is set to zero. These zeros are not manifest in Feynman diagrams but are made obvious by the connection of these amplitudes to the new understanding of associahedra arising from “causal diamonds” in kinematic space. Furthermore, near these zeros, the amplitudes simplify, by factoring into a non-trivial product of smaller amplitudes. Remarkably the amplitudes for pions and gluons are observed to also vanish in the same kinematical locus. These properties for Tr(Φ 3 ) amplitudes hold and further generalize to the “stringy” Tr(Φ 3 ) amplitudes. The “kinematic causal diamond” picture suggests a unique shift of the kinematic data that preserves the zeros, and this shift is precisely the one that unifies colored scalars, pions, and gluons into a single object. We will focus in this paper on explaining the hidden zeros and factorization properties and the connection between all the colored theories, working for simplicity at tree level. Subsequent works will describe this new formulation for the Non-linear Sigma Model and non-supersymmetric Yang-Mills theory, at all loop orders.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2026

Large deformations of Tr(Φ 3 ) and the world at infinity

The amplitudes of the non-linear sigma model can be obtained from those of Tr(Φ 3 ) theory by sending the kinematic (Mandelstam) variables to infinity in a certain direction. In this paper we characterize the behavior of Tr(Φ 3 ) amplitudes under a general class of large kinematic shifts called g-vector shifts. The objects that live in this world at infinity retain certain key amplitude-like properties, most notably factorization, and admit descriptions in terms of polytopes, but they are not generally amplitudes of any cognizable theory. We identify particular g-vector shifts that lead at infinity to mixed amplitudes involving two pions and any number of scalars, allowing us to provide polytopal descriptions of these amplitudes.

effective field theories↗
DOE OSTI2025

Failure of the large-N expansion in a bosonic tensor model

We study the tensor model generalization of the quantum p-spherical model in the large-N limit. While the tensor model has the same large-N expansion as the disordered quantum p-spherical model, its ground state is superextensive, in contradiction with large-N perturbation theory. Therefore, the large-N expansion of this model catastrophically fails at arbitrarily large-N, without any obvious signal in perturbation theory.

1/N Expansion↗
DOE OSTI2024

NS5-brane backgrounds and coset CFT partition functions

Worldsheet string theory is solvable for a variety of backgrounds involving Neveu-Schwarz fivebranes, in terms of gauged nonlinear sigma models on group manifolds. We compute the worldsheet torus partition function of these models, and propose gauging of null isometries as a unifying principle and conceptual framework for this large family of string backgrounds. In the process, we explain how partition functions of asymmetrically gauged Wess-Zumino-Witten models can be computed from the path integral, and organize and systematize various results scattered throughout the literature.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Celestial Quantum Error Correction. Part II. From qudits to celestial CFT

A holographic CFT description of asymptotically flat spacetimes inherits vacuum degeneracies and IR divergences from its gravitational dual. We devise a Quantum Error Correcting (QEC) framework to encode both effects as correctable fluctuations on the CFT dual. The framework is physically motivated by embedding a chain of qudits in the so-called Klein spacetime and then taking a continuum 𝑁 → ∞ limit. At finite 𝑁 the qudit chain 1) enjoys a discrete version of celestial symmetries and 2) supports a Gottesman-Kitaev-Preskill (GKP) code. The limit results in hard states with quantized BMS hair in the celestial torus forming the logical subspace, robust under errors induced by soft radiation. Technically, the construction leverages the recently studied 𝑤 1+∞ hierarchy of soft currents and its realization from a sigma model in twistor space.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Anomalies of 4d SpinG theories

Abstract We consider ’t Hooft anomalies of four-dimensional gauge theories whose fermion matter content admits Spin G (4) generalized spin structure, withGeither gauged or a global symmetry. We discuss methods to directly computew 2 ∪w 3 ’t Hooft anomalies involving Stiefel-Whitney classes of gauge and flavor symmetry bundles that such theories can have on non-spin manifolds, e.g.M 4 = ℂℙ 2 . Such anomalies have been discussed for SU(2) gauge theory with adjoint fermions, where they were shown to give an effect that was originally found in the Donaldson-Witten topological twist of$$ \mathcal{N} $$ N = 2 SYM theory. We directly compute these anomalies for a variety of theories, including generalGgauge theories with adjoint fermions, SU(2) gauge theory with fermions in general representations, and Spin(N) gauge theories with fundamental matter. We discuss aspects of matching these and other ’t Hooft anomalies in the IR phase where global symmetries are spontaneously broken, in particular for generalG gauge theory withN f adjoint Weyl fermions. For example, in the case ofN f = 2 we discuss anomaly matching in the IR phase consisting of$$ {h}_{G_{\textrm{gauge}}}^{\vee } $$ h G gauge ∨ copies of a ℂℙ 1 non-linear sigma model, including for thew 2 w 3 anomalies when formulated with$$ {\textrm{Spin}}_{\textrm{SU}{(2)}_{\textrm{global}}}(4) $$ Spin SU 2 global 4 structure.

Physics↗
DOE OSTI2025

Smooth splitting and zeros from on-shell recursion

We describe a new approach to understanding the origins of recently discovered “hidden zeros” and “smooth splitting” of tree-level amplitudes in Tr ϕ 3 , Non-Linear Sigma Model (NLSM), Yang-Mill-Scalar (YMS) and the special Galileon. Introducing a new type of linear shift in kinematic space we demonstrate that the mysterious splitting formulae follow from a simple contour integration argument in the style of on-shell recursion. The argument makes use of only standard notions of tree-level factorization on propagators, but assumes improved UV behavior in the form of the absence of a residue at infinity. In the case of Tr ϕ 3 and NLSM this is proven by identifying our shift as a special case of a more general construction called a g-vector shift; in the case of YMS it remains an unproven conjecture. This recursive perspective leads to numerous new results: we derive generalizations of the splitting formulae on more relaxed near-zero kinematics, including interesting new kinematic limits in which the amplitude splits into a triple-product; we also demonstrate that the uncolored special Galileon model has improved UV scaling and hence also splits. We also investigate the possible realization of hidden zeros in four dimensions. The conditions under which the dimensionality constraints are compatible with zero kinematics is investigated in detail for Tr ϕ 3 and YMS; for the latter we find they can be realized only with certain restrictions on external helicity states. The realizable 4d zeros are proven by a similar recursive argument based on BCFW and is found to generalize to a new class of intrinsically 4d “helicity zeros” present in all sectors of YM and also gravity.

effective field theories↗
DOE OSTI2024

A T-duality of non-supersymmetric heterotic strings and an implication for Topological Modular Forms

Abstract Motivated by recent developments connecting non-supersymmetric heterotic string theory to the theory of Topological Modular Forms (TMF), we show that the worldsheet theory with central charge (17,$$ \frac{3}{2} $$ 3 2 ) obtained by fibering the (E 8 ) 1 × (E 8 ) 1 current algebra over the two$$ \mathcal{N} $$ N = (0, 1) sigma model onS 1 with antiperiodic spin structure (such that theE 8 factors are exchanged as we go around the circle), is continuously connected to the (E 8 ) 2 theory in the Gaiotto Johnson-Freyd Witten sense of going “up and down the RG trajectories”. Combined with the work of Tachikawa and Yamashita, this furnishes a physical derivation of the fact that the (E 8 ) 2 theory corresponds to the unique nontrivial torsion element [(E 8 ) 2 ] of TMF 31 with zero mod-2 elliptic genus.

Physics↗
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 OSTI2024

Quantum Fluctuations and Multifractally enhanced Superconductivity in Disordered Thin Films

The interplay between electron–electron interactions and weak localization (or anti-localization) phenomena in two-dimensional systems can significantly enhance the superconducting transition temperature. For this work, we develop the theory of quantum fluctuations within such multifractally enhanced superconducting states in thin films. In conditions of weak disorder, we employ the Finkel’stein nonlinear sigma model to derive an effective action for the superconducting order parameter and the quasiclassical Green’s function, meticulously accounting for the influence of quantum fluctuations. This effective action, applicable for interactions of any strength, reveals the critical role of well-known collective modes in a dirty superconductor, and its saddle-point analysis leads to modified Usadel and gap equations. These equations comprehensively incorporate the renormalizations stemming from the interplay between interactions and disorder, resulting in the non-trivial energy dependence of the gap function. Notably, our analysis establishes a direct relation between the self-consistent gap equation at the superconducting transition temperature and the known renormalization group equations for interaction parameters in the normal state.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2026

Chiral anomaly: From vacuum to Columbia plot

Here, we use a low-energy effective approach, the extended linear sigma model, to study realizations of the U(1) A anomaly with different operators, linear and quadratic in the ’t Hooft determinant. After discussing the parameterization in agreement with vacuum’s phenomenology, we investigate the influence of these different anomaly terms on the Columbia plot: the square of the ’t Hooft determinant favors a cross-over for small quark masses. Finally, we also discuss the extension of the ’t Hooft determinant to cases in which different mesonic multiplets interact with each other. Novel chiral anomalous interaction terms involving excited (pseudo)scalar states, pseudovector, and pseudotensor mesons are expressed via a mathematical extension of the determinant, denoted as a polydeterminant.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

Cascading from $\mathscr{N}$ = 2 supersymmetric Yang–Mills theory to confinement and chiral symmetry breaking in adjoint QCD

We argue that adjoint QCD in 3 + 1 dimensions, with any SU(N) gauge group and two Weyl fermion flavors (i.e. one adjoint Dirac fermion), confines and spontaneously breaks its chiral symmetries via the condensation of a fermion bilinear. We flow to this theory from pure $\mathscr{N}$ = 2 SUSY Yang–Mills theory with the same gauge group, by giving a SUSY-breaking mass M to the scalars in the $\mathscr{N}$ = 2 vector multiplet. This flow can be analyzed rigorously at small M, where it leads to a deconfined vacuum at the origin of the $\mathscr{N}$ = 2 Coulomb branch. The analysis can be extended to all M using an Abelian dual description that arises from the N multi-monopole points of the $\mathscr{N}$ = 2 theory. At each such point, there are N −1 hypermultiplet Higgs fields h$^{i=1,2}_m$, which are SU(2) R doublets. We provide a detailed study of the phase diagram as a function of M, by analyzing the semi-classical phases of the dual using a combination of analytic and numerical techniques. The result is a cascade of first-order phase transitions, along which the Higgs fields h i m successively turn on, and which interpolates between the Coulomb branch at small M, where all h$^{i}_m$ = 0, and a maximal Higgs branch, where all h$^{i}_m$ ≠ 0, at sufficiently large M. We show that this maximal Higgs branch precisely matches the confining and chiral symmetry breaking phase of two-flavor adjoint QCD, including its broken and unbroken symmetries, its massless spectrum, and the expected large-N scaling of various observables. The spontaneous breaking pattern SU(2) R → U(1) R , consistent with the Vafa–Witten theorem, is ensured by an intricate alignment mechanism for the h$^{i}_m$ in the dual, and leads to a CP 1 sigma model of increasing radius along the cascade.

D’Hoker, Eric [Univ. of California, Los Angeles, C↗
DOE OSTI2025

Disoriented isospin condensates in heavy-ion collisions

Anomalous neutral to charged kaon correlations measured by the ALICE collaboration have defied usual explanations. We propose that the large fluctuations could arise because of a disoriented isospin condensate where there is an imbalance between up and down condensates at the time kaons hadronize. This could happen in heavy-ion collisions when the quark condensate re-forms as the system cools and the approximate chiral symmetry of QCD is broken. Within the linear sigma model, we show that the energy cost of forming a disoriented isospin condensate is small making it very plausible.

Kapusta, Joseph [University of Minnesota, Minneapo↗