Modular bootstrap revisited

doi:10.1007/jhep09(2018)061

Title: Modular bootstrap revisited

Full Record
Other Related Research

Abstract

We constrain the spectrum of two-dimensional unitary, compact conformal field theories with central charge c > 1 using modular bootstrap. Upper bounds on the gap in the dimension of primary operators of any spin, as well as in the dimension of scalar primaries, are computed numerically as functions of the central charge using semi-definite programming. Our bounds refine those of Hellerman and Friedan-Keller, and are in some cases saturated by known CFTs. In particular, we show that unitary CFTs with c < 8 must admit relevant deformations, and that a nontrivial bound on the gap of scalar primaries exists for c < 25. We also study bounds on the dimension gap in the presence of twist gaps, bounds on the degeneracy of operators, and demonstrate how “extremal spectra” which maximize the degeneracy at the gap can be determined numerically.

Authors:

^[1]; Lin, Ying -Hsuan ^[1]; Yin, Xi ^[1]

Harvard Univ., Cambridge, MA (United States). Jefferson Physical Lab.

Publication Date:: 2018-09-12

Research Org.:: Harvard Univ., Cambridge, MA (United States)

Sponsoring Org.:: USDOE

OSTI Identifier:: 1507580

Grant/Contract Number:: FG02-91ER40654

Resource Type:: Accepted Manuscript

Journal Name:: Journal of High Energy Physics (Online)

Additional Journal Information:: Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2018; Journal Issue: 9; Journal ID: ISSN 1029-8479

Publisher:: Springer Berlin

Country of Publication:: United States

Language:: English

Subject:: 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; AdS-CFT Correspondence; Black Holes; Conformal and W Symmetry; Conformal Field Theory

Citation Formats


                    Collier, Scott, Lin, Ying -Hsuan, and Yin, Xi. Modular bootstrap revisited.  United States: N. p., 2018. 
        Web.  doi:10.1007/jhep09(2018)061.

Copy to clipboard


                    Collier, Scott, Lin, Ying -Hsuan, & Yin, Xi. Modular bootstrap revisited.  United States.  doi:10.1007/jhep09(2018)061.

Copy to clipboard


                    Collier, Scott, Lin, Ying -Hsuan, and Yin, Xi. Wed .  
        "Modular bootstrap revisited".  United States.  doi:10.1007/jhep09(2018)061.  https://www.osti.gov/servlets/purl/1507580.

Copy to clipboard


                    
@article{osti_1507580,

  title        = {Modular bootstrap revisited},

  author       = {Collier, Scott and Lin, Ying -Hsuan and Yin, Xi},

  abstractNote = {We constrain the spectrum of two-dimensional unitary, compact conformal field theories with central charge c > 1 using modular bootstrap. Upper bounds on the gap in the dimension of primary operators of any spin, as well as in the dimension of scalar primaries, are computed numerically as functions of the central charge using semi-definite programming. Our bounds refine those of Hellerman and Friedan-Keller, and are in some cases saturated by known CFTs. In particular, we show that unitary CFTs with c < 8 must admit relevant deformations, and that a nontrivial bound on the gap of scalar primaries exists for c < 25. We also study bounds on the dimension gap in the presence of twist gaps, bounds on the degeneracy of operators, and demonstrate how “extremal spectra” which maximize the degeneracy at the gap can be determined numerically.},

  doi          = {10.1007/jhep09(2018)061},

  journal      = {Journal of High Energy Physics (Online)},

  number       = 9,

  volume       = 2018,

  place        = {United States},

  year         = {2018},

  month        = {9}

}

Copy to clipboard

Journal Article:

Free Publicly Available Full Text

Accepted Manuscript (DOE)

Publisher's Version of Record

DOI: 10.1007/jhep09(2018)061

Other availability

Search WorldCat to find libraries that may hold this journal

Save / Share:

Export Metadata

Save to My Library

Similar Records in DOE PAGES and OSTI.GOV collections:

Low-Temperature Methane Partial Oxidation to Syngas with Modular Nanocrystal Catalysts [Targeting Low-Temperature Methane Partial Oxidation to Syngas with Modular Nanocrystal Catalysts]

Journal Article Goodman, Emmett D. ; Latimer, Allegra A. ; Yang, An -Chih ; ... - ACS Applied Nano Materials

Here, the low-temperature conversion of methane into value-added products is an appealing goal due to the abundance of methane in the form of natural gas. Industrially, methane is used to produce synthesis gas (syngas), a precursor mixture used heavily in the production of ammonia, methanol, and synthetic fuels. In practice, this mixture is produced via the energy-intensive methane steam reforming reaction at temperatures between 750 and 1450 °C. The exothermic methane partial oxidation reaction stands as an alternative for syngas formation at lower temperatures, especially for gas to liquid fuels applications, yet awaits large-scale implementation due to dangerous operating conditionsmore »« less
DOI: 10.1021/acsanm.8b01256

Full Text Available
Impurities in a non-axisymmetric plasma. Transport and effect on bootstrap current

Journal Article Mollén, A. ; Landreman, M. ; Smith, H. M. ; ... - Physics of Plasmas

Impurities cause radiation losses and plasma dilution, and in stellarator plasmas the neoclassical ambipolar radial electric field is often unfavorable for avoiding strong impurity peaking. In this work we use a new continuum drift-kinetic solver, the SFINCS code (the Stellarator Fokker-Planck Iterative Neoclassical Conservative Solver) [M. Landreman et al., Phys. Plasmas 21 (2014) 042503] which employs the full linearized Fokker-Planck-Landau operator, to calculate neoclassical impurity transport coefficients for a Wendelstein 7-X (W7-X) magnetic configuration. We compare SFINCS calculations with theoretical asymptotes in the high collisionality limit. We observe and explain a 1/nu-scaling of the inter-species radial transport coefficient at lowmore »« less
Cited by 5
DOI: 10.1063/1.4935901

Full Text Available
Gyrokinetic neoclassical study of the bootstrap current in the tokamak edge pedestal with fully non-linear Coulomb collisions

Journal Article Hager, Robert ; Chang, C. S. - Physics of Plasmas

As a follow-up on the drift-kinetic study of the non-local bootstrap current in the steep edge pedestal of tokamak plasma by Koh et al. [Phys. Plasmas 19, 072505 (2012)], a gyrokinetic neoclassical study is performed with gyrokinetic ions and drift-kinetic electrons. Besides the gyrokinetic improvement of ion physics from the drift-kinetic treatment, a fully non-linear Fokker-Planck collision operator—that conserves mass, momentum, and energy—is used instead of Koh et al.'s linearized collision operator in consideration of the possibility that the ion distribution function is non-Maxwellian in the steep pedestal. An inaccuracy in Koh et al.'s result is found in the steepmore »« less
Cited by 7
DOI: 10.1063/1.4945615

Full Text Available
Compatibility of internal transport barrier with steady-state operation in the high bootstrap fraction regime on DIII-D

Journal Article Garofalo, Andrea M. ; Gong, Xianzu ; Grierson, Brian A. ; ... - Nuclear Fusion

Recent EAST/DIII-D joint experiments on the high poloidal beta tokamak regime in DIII-D have demonstrated fully noninductive operation with an internal transport barrier (ITB) at large minor radius, at normalized fusion performance increased by ≥30% relative to earlier work. The advancement was enabled by improved understanding of the “relaxation oscillations”, previously attributed to repetitive ITB collapses, and of the fast ion behavior in this regime. It was found that the “relaxation oscillations” are coupled core-edge modes 2 amenable to wall-stabilization, and that fast ion losses which previously dictated a large plasma-wall separation to avoid wall over-heating, can be reduced tomore »« less
Cited by 16
DOI: 10.1088/0029-5515/55/12/123025

Full Text Available
Limitations of bootstrap current models

Journal Article Belli, Emily A. ; Candy, Jefferey M. ; Meneghini, Orso ; ... - Plasma Physics and Controlled Fusion

We assess the accuracy and limitations of two analytic models of the tokamak bootstrap current: (1) the well-known Sauter model and (2) a recent modification of the Sauter model by Koh et al. For this study, we use simulations from the first-principles kinetic code NEO as the baseline to which the models are compared. Tests are performed using both theoretical parameter scans as well as core- to-edge scans of real DIII-D and NSTX plasma profiles. The effects of extreme aspect ratio, large impurity fraction, energetic particles, and high collisionality are studied. In particular, the error in neglecting cross-species collisional couplingmore »« less
Cited by 11
DOI: 10.1088/0741-3335/56/4/045006

Full Text Available

Similar Records