Search NASA⌕ Search

SEARCH · Search NASA

Results for “large N 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 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Classification of all $\mathcal{N}\geq 3$ moduli space orbifold geometries at rank 2

We classify orbifold geometries which can be interpreted as moduli spaces of four-dimensional \mathcal{N}\geq 3 𝒩 ≥ 3 superconformal field theories up to rank 2 (complex dimension 6). The large majority of the geometries we find correspond to moduli spaces of known theories or discretely gauged version of them. Remarkably, we find 6 geometries which are not realized by any known theory, of which 3 have an \mathcal{N}=2 𝒩 = 2 Coulomb branch slice with a non-freely generated coordinate ring, suggesting the existence of new, exotic \mathcal{N}=3 𝒩 = 3 theories.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Quantum Aspects of Natural Top Quark Condensation

In top quark condensation the Brout-Englert-Higgs (BEH) boson is a $\bar{t}t$ bound state. With a UV completion of a single coloron exchange interaction, a recent semiclassical treatment gave a novel theory of the BEH boson as an extended object with composite scale $M_0\sim 6$ TeV. Presently we obtain the semiclassical theory as an effective action, using the source/Legendre transformation techniques of Jackiw, \etal, and fermion loop effects in the large-$N_c$ limit by deploying an auxiliary field to implement the sum of leading fermion loop diagrams. The theory remains natural at the loop level, with fine tuning at the level of a few %, and the effective coupling of the 4-fermion interaction, $\bar{g}_0^2$, is significantly enhanced by quantum loops over the fundamental coloron coupling, $g_0^2$. Hence a relatively weaker ``topcolor'' theory can produce critical coupling in the effective BEH bound state theory.

Hill, Christopher T. [Fermilab; Wisconsin U., Madi↗
NASA NTRS1990

Ballooning stability of anisotropic, rotating plasmas

The linearized equation of motion is given in a Lagrangian representation for a rotating plasma with anisotropic pressure. A WKB theory is developed for large-n ballooning modes in an axisymmetric configuration with field-aligned and rigid toroidal flows. In the presence of field-aligned flows, it is shown that a resonance occurs which is strongly suggestive of a generalized mirror instability. In the presence of toroidal rotation, a possible stabilizing effect is identified for P(normal) greater than P(parallel). Finally, as a special case of the theory, the necessary and sufficient conditions for stability in a static, anisotropic plasma are obtained.

Wang, X.-H.↗
DOE OSTI2021

Searching for gauge theories with the conformal bootstrap

Infrared fixed points of gauge theories provide intriguing targets for the modern conformal bootstrap program. In this work we provide some preliminary evidence that a family of gauged fermionic CFTs saturate bootstrap bounds and can potentially be solved with the conformal bootstrap. We start by considering the bootstrap for SO( N ) vector 4-point functions in general dimension D . In the large N limit, upper bounds on the scaling dimensions of the lowest SO( N ) singlet and traceless symmetric scalars interpolate between two solutions at Δ = D/ 2 – 1 and Δ = D – 1 via generalized free field theory. In 3D the critical O ( N ) vector models are known to saturate the bootstrap bounds and correspond to the kinks approaching Δ = 1 / 2 at large N . We show that the bootstrap bounds also admit another infinite family of kinks \( {\mathcal{T}}_D \) , which at large N approach solutions containing free fermion bilinears at Δ = D – 1 from below. The kinks \( {\mathcal{T}}_D \) appear in general dimensions with a D -dependent critical N * below which the kink disappears. We also study relations between the bounds obtained from the bootstrap with SO( N ) vectors, SU( N ) fundamentals, and SU( N ) × SU( N ) bi-fundamentals. We provide a proof for the coincidence between bootstrap bounds with different global symmetries. We show evidence that the proper symmetries of the underlying theories of \( {\mathcal{T}}_D \) are subgroups of SO( N ), and we speculate that the kinks \( {\mathcal{T}}_D \) relate to the fixed points of gauge theories coupled to fermions.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Probing supersymmetric black holes with surface defects

It has long been conjectured that the large N deconfinement phase transition of $\mathcal{N}$ = 4 SU(N) super-Yang-Mills corresponds via AdS/CFT to the Hawking-Page transition in which black holes dominate the thermal ensemble, and quantitative evidence of this has come through the recent matching of the superconformal index of $\frac{1}{16}$-BPS states to the supersymmetric black hole entropy. Here we introduce the half-BPS Gukov-Witten surface defect as a probe of the superconformal index, which also serves as an order parameter for the deconfinement transition. This can be studied directly in field theory as a modification of the usual unitary matrix model or in the dual description as a D3-brane probe in the background of a (complex) supersymmetric black hole. Using a saddle point approximation, we determine our defect index in the large N limit as a simple function of the chemical potentials and show independently that it is reproduced by the renormalized action of the brane in the black hole background. Along the way, we also comment on the Cardy limit and the thermodynamics of the D3-brane in the generalized ensemble. The defect index sharply distinguishes between the confining and the deconfining phases of the gauge theory and thus is a supersymmetric non-perturbative order parameter for these large N phase transitions which deserves further investigation. Finally, our work provides an example where the properties of a black hole coupled to an external system can be analyzed precisely.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Interacting CFTs for all couplings: thermal versus entanglement entropy at large N

In this paper, I calculate the large N limit of marginal O(N) models with non-polynomial potentials in arbitrary odd dimensions d. This results in a new class of interacting pure conformal field theories (CFTs) in d = 3 + 4n for any n ϵ $\mathbb{Z}$ + . Similarly, in d = 3 + 4n I calculate the thermal entropy for all couplings on R 2+4n × S 1 for n = 0, 1, 2, 3. In 2+1 dimensions I find the strong-to-weak coupling ratio of the thermal entropy to be 4/5, matching recent results, and further extend this analysis to higher odd dimensions. Next, I calculated the vacuum entanglement entropy ${s}_{\textrm{EE}}^d$ on S d–2 for all couplings in arbitrary odd d in the large N limit. I find the vacuum entanglement entropy on S d–2 to be not only solvable but also constant for all couplings λ. Thus, in the large N limit, the vacuum entanglement entropy on S d–2 for odd d is constant for all λ, in contrast to the thermal entropy which is shown to also be monotonically decreasing with λ in d = 3 + 4n.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Celestial Dual for Maximal Helicity Violating Amplitudes

It is shown that a 2D conformal field theory consisting of a central charge c Liouville theory, a chiral level one, rank N Kac-Moody algebra, and a weight − 3 / 2 free fermion holographically generate 4D maximal helicity violating tree-level scattering amplitudes. The correlators of this 2D conformal field theory give directly the 4D leaf amplitudes associated to a single hyperbolic slice of flat space. The 4D celestial amplitudes arise in a large- N and semiclassical large- c limit, according to the holographic dictionary, as a translationally invariant combination of leaf amplitudes. A step in the demonstration is showing that the semiclassical limit of Liouville correlators are given by contact 3D anti–de Sitter Witten diagrams. Published by the American Physical Society 2024

Physics↗
DOE OSTI2020

Microscopic entropy of rotating electrically charged AdS 4 black holes from field theory localization

We employ supersymmetric localization to determine the exact partition function of 3d N = 2 gauge theories on a background given by a round S 2 fibered over a circle and certain complexified background fields. The Coulomb branch localization locus includes monopole configurations, and the partition function reduces to a matrix model. We consider the partition function of the ABJM theory on this background as an explicit case. We verify that the large-N limit of the ABJM theory partition function produces, in the Cardy limit, the entropy function of the dual rotating, electrically charged asymptotically AdS 4 supersymmetric black holes and thus provides a microscopic explanation for the Bekenstein-Hawking entropy.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

Rotating black hole entropy from M5-branes

We compute the superconformal index of 3d N = 2 superconformal field theories obtained from N M5-branes wrapped on a hyperbolic 3-manifold. Exploiting the 3d-3d correspondence, we use perturbative invariants of SL(N, C) Chern-Simons theory to determine the superconformal index in the large N limit, including corrections logarithmic in N. The leading order partition function provides a microscopic foundation for the entropy function of the dual rotating asymptotically AdS 4 black holes. We also verify that the supergravity one-loop contribution to the log N term coincides with the field theoretic result. We propose a 3d-3d formulation for the refined topologically twisted index, and provide strong evidence in support of its vanishing — which agrees with the fact that the expected dual rotating magnetically-charged black hole does not exist. This provides an interesting link between gravity and a tantalizing mathematical result.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Hydrodynamic theory of scrambling in chaotic long-range interacting systems

The Fisher-Kolmogorov-Petrovsky-Piskunov (FKPP) equation provides a mean-field theory of out-of-time-ordered commutators in locally interacting quantum chaotic systems at high energy density. In systems with power-law interactions, the corresponding fractional-derivative FKPP equation provides an analogous mean-field theory. However, the fractional FKPP description is potentially subject to strong quantum fluctuation effects, so it is not clear a priori if it provides a suitable effective description for generic chaotic systems with power-law interactions. Here, in this work, we study this problem using a model of coupled quantum dots with interactions decaying as 1/r α , where each dot hosts N degrees of freedom. The large-N limit corresponds to the mean-field description, while quantum fluctuations contributing to the OTOC can be modeled by 1/N corrections consisting of a cutoff function and noise. Within this framework, we show that the parameters of the effective theory can be chosen to reproduce the butterfly light cone scalings previously found for N=1 and generic finite N. In order to reproduce these scalings, the fractional index μ in the FKPP equation needs to be shifted from the naïve value of μ=2⁢α–1 to a renormalized value μ=2⁢α–2. We provide supporting analytic evidence for the cutoff model and numerical confirmation for the full fractional FKPP equation with cutoff and noise.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Subleading corrections to the free energy in a theory with N 5/3 scaling

We numerically investigate the sphere partition function of a Chern-Simons-matter theory with SU(N) gauge group at level k coupled to three adjoint chiral multiplets that is dual to massive IIA theory. Beyond the leading order N 5/3 behavior of the free energy, we find numerical evidence for a term of the form (2/9) log N. We conjecture that this term may be universal in theories with N 5/3 scaling in the large-N limit with the Chern-Simons level k held fixed.

1/N Expansion↗
DOE OSTI2021

Strong Rashba-Dresselhaus Effect in Nonchiral 2D Ruddlesden-Popper Perovskites

Chirality transfer from organic chiral molecules to lead halides is theorized as the origin of the strong Rashba-Dresselhaus effect causing large circular dichroism (CD) and circularly polarized luminescence (CPL) in metal halide perovskites (MHPs). In this report a concrete empirical evidence is provided that such strong CD and CPL can occur even in nonchiral 2D Ruddlesden-Popper perovskites (RPPs) (BA) 2 (MA) n-1 Pb n I 3n+1 (where MA = CH 3 NH 3 and BA = CH 3 (CH 2 ) 3 NH 3 ). The CD and CPL responses occurring at the excitonic transition of the MHPs are strongest (≈100 mdeg and 4.8%, respectively) when a single lead halide octahedral [PbI 6 ] 4- layer is repeatedly stacked between two nonchiral molecules BA + (n = 1). However, they are rapidly quenched as n increases. It is hypothesized that strong Rashba-Dresselhaus splitting in the 2D RPPs originates the strong CD and CPL signatures. Density functional theory calculations reveal that the large interlayer distortions in the inorganic layers at the organic/inorganic interface give rise to the strong Rashba-Dresselhaus splitting. A Rashba-Dresselhaus field of ≈600 and ≈50 mT for n = 1 and 2, respectively, is estimated by magnetic circular dichroism spectroscopy. The studies may have significant impact on designing 2D RPPs with large Rashba-Dresselhaus effects at room temperature for spintronic applications.

circular dichroism↗
DOE OSTI2020

Minimally entangled state preparation of localized wave functions on quantum computers

Initializing a single site of a lattice scalar field theory into an arbitrary state with support throughout the quantum register requires $O(2^{nQ})$ entangling gates on a quantum computer with $n_Q$ qubits per site. It is conceivable that instead initializing to functions that are good approximations to states may have utility in reducing the number of required entangling gates. In the case of a single site of a noninteracting scalar field theory, initializing to a symmetric exponential wave function requires $n_Q – 1$ entangling gates, the minimal number necessary to create an entangled state of all $n_Q$ qubits. This is compared with the $2^{nQ – 1} + n_Q – 3 + δ_{nQ, 1}$ required for a symmetric Gaussian wave function. In this work, we explore the initialization of one-site $(n_Q = 4)$, two-site $(n_Q = 3)$, and three-site ( n Q = 3 ) noninteracting scalar field theories with symmetric exponential wave functions using IBM's quantum simulators and quantum devices (Poughkeepsie and Tokyo). With the digitizations attainable with $n_Q = 3,4$, these tensor-product wave functions are found to have large overlap with a Gaussian wave function and provide a suitable low-noise initialization for improvement and Somma inflation. Further, in performing these simulations, we have employed a workflow that interleaves calibrations to mitigate systematic errors in production. The calibrations allow tolerance cuts on gate performance including the fidelity of the symmetrizing Hadamard gate, both in vacuum $(|\textbf{0}\gg^{\bigotimes nQ})$ and in medium ($n_Q –1$ qubits initialized to an exponential function). The results obtained in this work are relevant to systems beyond scalar field theories, such as the deuteron radial wave function, two- and three-dimensional Cartesian-space wave functions, and nonrelativistic multinucleon systems built on a localized eigenbasis.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

Universal Location of the Yang-Lee Edge Singularity in O( N ) Theories

We determine a previously unknown universal quantity, the location of the Yang-Lee edge singularity for the O(N) theories in a wide range of N and various dimensions. At large N, we reproduce the N→∞ analytical result on the location of the singularity and, additionally, we obtain the mean-field result for the location in d=4 dimensions. In order to capture the nonperturbative physics for arbitrary N, d and complex-valued external fields, we use the functional renormalization group approach.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Cardy expansion of 3d superconformal indices and corrections to the dual black hole entropy

We consider the superconformal index of three-dimensional $\mathcal{N}$ = 2 supersymmetric field theories computed via localization on S 1 × S 2 . We systematically develop an expansion where the ratio of the radius of S 1 to the radius of S 2 is taken very small — a Cardy-like expansion. We emphasize the sub-leading structures in this Cardy-like expansion as well as their interplay with the large-N limit for theories with gauge group of the form product of U(N) factors. We demonstrate that taking the large-N limit first leads to an expression for the effective action yielding the index that only includes terms proportional to 1/β and powers of β i=0,1,2 where β is the ratio of radii. As we depart from the β → 0 limit for finite N, we find indications of non-perturbative contributions of the form e –1/β . We present an explicit evaluation of the superconformal index for the ABJM theory in the large-N limit that is exact in β up to non-perturbative corrections. For the ABJM theory we explore the implications of the Cardy-like expansion for corrections to the entropy of the rotating, electricallly charged, asymptotically AdS 4 dual black hole. Interestingly, we find a closed form for the entropy that includes all perturbative corrections in β and takes the form of the leading order expression but with shifted charges.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS1993

Second-order solution for determining density and velocity fields of galaxies

In this Letter, I use second-order Lagrangian perturbation theory to calculate an analytical expression relating density to velocity in a gravitating system. This solution can be used to compare peculiar velocity field measurements with observations of large-scale structure. The predictions of both linear theory and second-order theory are compared with the results of N-body simulations. While linear theory systematically overestimates the velocity flows in high-density regions, the second-order corrections calculated herein remove this systematic error.

Gramann, Mirt↗