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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2011

Nonrelativistic scale anomaly, and composite operators with complex scaling dimensions

Research Highlights: > Nonrelativistic scale anomaly leads to operators with complex scaling dimensions. > We study an operator O={psi}{psi} in quantum mechanics with 1/r{sup 2} potenial. > The propagator of the composite operator is analytically computed. - Abstract: It is demonstrated that a nonrelativistic quantum scale anomaly manifests itself in the appearance of composite operators with complex scaling dimensions. In particular, we study nonrelativistic quantum mechanics with an inverse square potential and consider a composite s-wave operator O={psi}{psi}. We analytically compute the scaling dimension of this operator and determine the propagator <0|TOO{sup +}|0>. The operator O represents an infinite tower of bound states with a geometric energy spectrum. Operators with higher angular momenta are briefly discussed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2012

Critical scaling dimension of D-module representations of N=4,7,8 superconformal algebras and constraints on superconformal mechanics

At critical values of the scaling dimension {lambda}, supermultiplets of the global N-extended one-dimensional supersymmetry algebra induce D-module representations of finite superconformal algebras (the latters being identified in terms of the global supermultiplet and its critical scaling dimension). For N=4,8 and global supermultiplets (k,N,N-k), the exceptional superalgebras D(2, 1;{alpha}) are recovered for N=4, with a relation between {alpha} and the scaling dimension given by {alpha}= (2 -k){lambda}. For N=8 and k{ne} 4 all four N=8 finite superconformal algebras are recovered, at the critical values {lambda}{sub k}=(1/k-4), with the following identifications: D(4, 1) for k= 0, 8, F(4) for k= 1, 7, A(3, 1) for k= 2, 6 and D(2, 2) for k= 3, 5. The N=7 global supermultiplet (1, 7, 7, 1) induces, at {lambda}=-(1/4), a D-module representation of the exceptional superalgebra G(3). D-module representations are applicable to the construction of superconformal mechanics in a Lagrangian setting. The isomorphism of the D(2, 1;{alpha}) algebras under an S{sub 3} group action on {alpha}, coupled with the relation between {alpha} and the scaling dimension {lambda}, induces non-trivial constraints on the admissible models of N=4 superconformal mechanics. The existence of new superconformal models is pointed out. For example, coupled (1, 4, 3) and (3, 4, 1) supermultiplets generate an N=4 superconformal mechanics if {lambda} is related to the golden ratio. The relation between classical versus quantum D-module representations is presented.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Monopole scaling dimension using Monte-Carlo simulation

In this paper, we present a practical Monte Carlo determination of the scaling dimensions Δ Q of flux Q Abelian monopoles through finite-size scaling analysis of the free energy to introduce the background field of classical Dirac monopole-antimonopole pair at critical points of three-dimensional lattice theories. We validate the method in free fermion theory, and by verifying the particle-vortex duality between the monopole scaling dimension at the inverse-XY fixed point and the charge scaling dimension at the XY fixed point. Finally, at the O(2) Wilson-Fisher fixed point of the XY model, we determine the critical exponents Δ 1 = 0.13(2), Δ 2 = 0.29(1) and Δ 3 = 0.47(2), which we find to be proportional to the finite-size critical spectrum of monopoles on square torus.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2015

Mechanical properties of materials with nanometer scale dimensions and microstructures

The three-year grant for which this final report is required extends from 2011 to 2015, including a one-year, no-cost extension. But this is just the latest in a long series of grants from the Division of Materials Sciences of DOE and its predecessor offices and agencies. These include contracts or grants from: the Metallurgy Branch of the U.S. Atomic Energy Commission (from the late 1960s to the mid-1970s), the Materials Science Program of the U.S. Energy Research and Development Administration (from the mid- to late- 1970s), and the Division of Materials Science of the Office of Basic Energy Sciences of the U.S. Department of Energy (from the early 1980s to the present time). Taken all together, these offices have provided nearly continuous support for our research for nearly 50 years. As we have said on many occasions, this research support has been the best we have ever had, by far. As we look back on the nearly five decades of support from the Division of Materials Sciences and the predecessor offices, we find that the continuity of support that we have enjoyed has allowed us to be most productive and terms of papers published, doctoral students graduated and influence on the field of materials science. This report will, of course, cover the three-year period of the present grant, in summary form, but will also make reference to the output that resulted from support of previous grants from the Division of Materials Sciences and its predecessor offices.

36 MATERIALS SCIENCE↗
DOE OSTI2016

Precision islands in the Ising and O(N ) models

We make precise determinations of the leading scaling dimensions and operator product expansion (OPE) coefficients in the 3d Ising, O(2), and O(3) models from the conformal bootstrap with mixed correlators. We improve on previous studies by scanning over possible relative values of the leading OPE coefficients, which incorporates the physical information that there is only a single operator at a given scaling dimension. The scaling dimensions and OPE coefficients obtained for the 3d Ising model, (Δ σ , Δ ϵ , λ σσϵ , λ ϵϵϵ ) = (0.5181489(10), 1.412625(10), 1.0518537(41), 1.532435(19) , give the most precise determinations of these quantities to date.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Computing the Central Charge of the 3D Ising CFT Using Quantum Finite Elements

The 3D Ising conformal field theory (CFT) describes different physical systems, such as uniaxial magnets or fluids, at their critical points. In absence of an analytical solution for the 3D Ising model, the scaling dimensions and operator product expansion (OPE) coefficients characterizing this CFT must be determined numerically. The currently most-cited values for these quantities have been obtained from the conformal bootstrap, while lattice calculations have so far only produced reliable results for the scaling dimensions involved in calculating the critical exponents. Using Quantum Finite Elements to investigate critical \(\phi^4\)-theory on \(\mathbb{R}\times\mathbb{S}^2\), we show in this work that it is possible to extract scaling dimensions and OPE coefficients of the 3D Ising CFT by fitting the lattice four-point function with expectations from the operator product expansion for the radially quantized CFT and extrapolating to the continuum limit. This way, we have for the first time been able to use Monte Carlo simulations to compute the central charge of the theory.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2018

Low-energy effective field theory below the electroweak scale: anomalous dimensions

We compute the one-loop anomalous dimensions of the low-energy effective Lagrangian below the electroweak scale, up to terms of dimension six. The theory has 70 dimension-five and 3631 dimension-six Hermitian operators that preserve baryon and lepton number, as well as additional operators that violate baryon number and lepton number. The renormalization group equations for the quark and lepton masses and the QCD and QED gauge couplings are modified by dimension-five and dimension-six operator contributions. We compute the renormalization group equations from one insertion of dimension-five and dimension-six operators, as well as two insertions of dimension-five operators, to all terms of dimension less than or equal to six. As a result, the use of the equations of motion to eliminate operators can be ambiguous, and we show how to resolve this ambiguity by a careful use of field redefinitions.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

Carving out OPE space and precise O(2) model critical exponents

We develop new tools for isolating CFTs using the numerical bootstrap. A “cutting surface” algorithm for scanning OPE coefficients makes it possible to find islands in high-dimensional spaces. Together with recent progress in large-scale semidefinite programming, this enables bootstrap studies of much larger systems of correlation functions than was previously practical. We apply these methods to correlation functions of charge-0, 1, and 2 scalars in the 3d O(2) model, computing new precise values for scaling dimensions and OPE coefficients in this theory. Our new determinations of scaling dimensions are consistent with and improve upon existing Monte Carlo simulations, sharpening the existing decades-old 8σ discrepancy between theory and experiment.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2018

Universal bounds on operator dimensions from the average null energy condition

We show that the average null energy condition implies novel lower bounds on the scaling dimensions of highly-chiral primary operators in four-dimensional conformal field theories. Denoting the spin of an operator by a pair of integers ($k\overline{k}\ $) specifying the transformations under chiral su (2) rotations, we explicitly demonstrate these new bounds for operators transforming in (k, 0) and (k, 1) representations for sufficiently large k. Based on these calculations, along with intuition from free field theory, we conjecture that in any unitary conformal field theory, primary local operators of spin ($k\overline{k}\ $) and scaling dimension Δ satisfy Δ ≥ max{$k\overline{k}\ $}. If |$k-\overline{k}\ $| > 4 , this is stronger than the unitarity bound.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Operator origin of anomalous dimensions in de Sitter space

The late-time limit of the power spectrum for heavy (principal series) fields in de Sitter (dS) space yields a series of polynomial terms with complex scaling dimensions. Such scaling behavior is expected to result from an associated operator with a complex dimension. In a free theory, these complex dimensions are known to match the constraints imposed by unitarity on the space of states. Yet, perturbative corrections to the scaling behavior of operators are naively inconsistent with unitary evolution of the quantum fields in dS space. This paper demonstrates how to compute one-loop corrections to the scaling dimensions that appear in the two-point function from the field theory description in terms of local operators. We first show how to evaluate these anomalous dimensions using Mellin space, which has the feature that it naturally accommodates a scaleless regulator. We then explore the consequences for the soft de Sitter effective theory (SdSET) description that emerges in the long wavelength limit. Carefully matching between the UV and SdSET descriptions requires the introduction of novel nondynamical “operators” in the effective theory. This is not only necessary to reproduce results extracted from the Källén-Lehmann representation (that use the space of unitary states directly), but it is also required by general arguments that invoke positivity. Published by the American Physical Society 2025

Cohen, Timothy↗
DOE OSTI2016

Φ 3 theory with F 4 flavor symmetry in 6 – 2ϵ dimensions: 3-loop renormalization and conformal bootstrap

Here, we consider Φ 3 theory in 6 – 2ϵ with F 4 global symmetry. The beta function is calculated up to 3 loops, and a stable unitary IR fixed point is observed. The anomalous dimensions of operators quadratic or cubic in Φ are also computed. We then employ conformal bootstrap technique to study the fixed point predicted from the perturbative approach. For each putative scaling dimension of Φ(Δ Φ ), we obtain the corresponding upper bound on the scaling dimension of the second lowest scalar primary in the 26 representation (Δ 26 2nd ) which appears in the OPE of Φ × Φ. In D = 5.95, we observe a sharp peak on the upper bound curve located at Δ Φ equal to the value predicted by the 3-loop computation. In D = 5, we observe a weak kink on the upper bound curve at (Δ Φ , Δ 26 2nd ) = (1.6, 4).

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2018

The singularity structure of scale-invariant rank-2 Coulomb branches

We compute the spectrum of scaling dimensions of Coulomb branch operators in 4d rank-2 N=2 superconformal field theories. Only a finite rational set of scaling dimensions is allowed. It is determined by using information about the global topology of the locus of metric singularities on the Coulomb branch, the special Kähler geometry near those singularities, and electric-magnetic duality monodromies along orbits of the U(1) R symmetry. With this beind said, a set of novel topological and geometric results are developed which promise to be useful for the study and classification of Coulomb branch geometries at all ranks.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2018

Monopole operators in U(1) Chern-Simons-matter theories

We report on monopole operators at the infrared fixed points of U(1) Chern-Simons-matter theories (QED 3 , scalar QED 3 , $\mathcal{N}$=1 SQED 3 , and $\mathcal{N}$=2 SQED 3 ) with N matter flavors and Chern-Simons level k. We work in the limit where both N and k are taken to be large with κ = k/ N fixed. In this limit, we extract information about the low-lying spectrum of monopole operators from evaluating the S 2 × S 1 partition function in the sector where the S 2 is threaded by magnetic flux 4πq. At leading order in N , we find a large number of monopole operators with equal scaling dimensions and a wide range of spins and flavor symmetry irreducible representations. In two simple cases, we deduce how the degeneracy in the scaling dimensions is broken by the 1/ N corrections. For QED 3 at κ = 0, we provide conformal bootstrap evidence that this near-degeneracy is in fact maintained to small values of N . For $\mathcal{N}$=2 SQED 3 , we discover that the lowest dimension monopole operator is generically non-BPS.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

Low-rank Sachdev-Ye-Kitaev models

Motivated by recent proposals of experimental realization of fast scramblers, we study a family of solvable variants of the ($\textit{q}$ = 4) Sachdev-Ye-Kitaev model in which the rank and eigenvalue distribution of the coupling matrix $J_{ ij,kl}$ are tuneable. When the rank is proportional to the number of fermions, the low temperature behavior is sensitive to the eigenvalue distribution. We obtain a complete classification of the possible non-Fermi liquid quantum phases. These include two previously studied phases whose fermion scaling dimension depends continuously on the rank; we show that they are maximally chaotic, but necessitate an extensively degenerate or negative semidefinite coupling matrix. In this work, more generic distributions give rise to “almost Fermi liquids” with a scaling dimension Δ = 1/2, but which differ from a genuine Fermi liquid in quasiparticle decay rate, quantum Lyapunov exponent, and/or specific heat.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Phases of $ \mathcal{N} $ = 2 Sachdev-Ye-Kitaev models

We study N = 2 supersymmetric Sachdev-Ye-Kitaev (SYK) models with com- plex fermions at non-zero background charge. Motivated by multi-charge supersymmetric black holes, we propose a new N = 2 SYK model with multiple U(1) symmetries, integer charges, and a non-vanishing supersymmetric index, realizing features not present in known SYK models. In both models, a conformal solution with a super-Schwarzian mode emerges at low temperatures, signaling the appearance of nearly AdS2/BPS physics. However, in contrast to complex SYK, the fermion scaling dimension depends on the background charge in the conformal limit. For a critical charge, we find a high to low entropy phase transition in which the conformal solution ceases to be valid. This transition has a simple interpretation– the fermion scaling dimension violates the unitarity bound. We offer some comments on a holographic interpretation for supersymmetric black holes.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2015

Higgs production and decay in models of a warped extra dimension with a bulk Higgs

Warped extra-dimension models in which the Higgs boson is allowed to propagate in the bulk of a compact AdS 5 space are conjectured to be dual to models featuring a partially composite Higgs boson. They offer a framework with which to investigate the implications of changing the scaling dimension of the Higgs operator, which can be used to reduce the constraints from electroweak precision data. In the context of such models, we calculate the cross section for Higgs production in gluon fusion and the H → γγ decay rate and show that they are finite (at one-loop order) as a consequence of gauge invariance. The extended scalar sector comprising the Kaluza-Klein excitations of the Standard Model scalars is constructed in detail. The largest effects are due to virtual KK fermions, whose contributions to the cross section and decay rate introduce a quadratic sensitivity to the maximum allowed value y * of the random complex entries of the 5D anarchic Yukawa matrices. We find an enhancement of the gluon-fusion cross section and a reduction of the H → γγ rate as well as of the tree-level Higgs couplings to fermions and electroweak gauge bosons. As a result, we perform a detailed study of the correlated signal strengths for different production mechanisms and decay channels as functions of y * , the mass scale of Kaluza-Klein resonances and the scaling dimension of the composite Higgs operator.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗