Orbifold groupoids Gaiotto, Davide; Kulp, Justin
The journal of high energy physics,
02/2021, Volume:
2021, Issue:
2
Journal Article
Peer reviewed
Open access
A
bstract
We review the properties of orbifold operations on two-dimensional quantum field theories, either bosonic or fermionic, and describe the “Orbifold groupoids” which control the composition ...of orbifold operations. Three-dimensional TQFT’s of Dijkgraaf-Witten type will play an important role in the analysis. We briefly discuss the extension to generalized symmetries and applications to constrain RG flows.
We explore constraints on (1+1)d unitary conformal field theory with an internal ZN global symmetry, by bounding the lightest symmetry-preserving scalar primary operator using the modular bootstrap. ...Among the other constraints we have found, we prove the existence of a ZN-symmetric relevant/marginal operator if N−1≤c≤9−N for N≤4, with the end points saturated by various Wess-Zumino-Witten models that can be embedded into (e8)1. Its existence implies that robust gapless fixed points are not possible in this range of c if only a ZN symmetry is imposed microscopically. We also obtain stronger, more refined bounds that depend on the 't Hooft anomaly of the ZN symmetry.
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We investigate possible renormalization-group fixed points at nonzero coupling in ϕ3 theories in six spacetime dimensions, using beta functions calculated to the four-loop level. We analyze three ...theories of this type, with (a) a one-component scalar, (b) a scalar transforming as the fundamental representation of a global SU(N) symmetry group, and (c) a scalar transforming as a bi-adjoint representation of a global SU(N) ⊗ SU(N) symmetry. We do not find robust evidence for such fixed points in theories (a) or (b). Theory (c) has the special feature that the one-loop term in the beta function is zero; implications of this are discussed.
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A reanalysis of ππ amplitudes for all important partial waves below about 2 GeV is presented. A set of once subtracted dispersion relations with imposed crossing symmetry condition is used to modify ...unitary multichannel amplitudes in the S, P, D, and F waves. So far, these specific amplitudes constructed in our works and many other analyses have been fitted only to experimental data and therefore do not fulfill the crossing symmetry condition. In the present analysis, the self-consistent, i.e., unitary and fulfilling the crossing symmetry, amplitudes for the S, P, D, and F waves are formed. The proposed very effective and simple method of modification of the ππ amplitudes does not change their previous original mathematical structure, and the method can be easily applied in various other analyses.
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•Normative data for physiological gait asymmetry is currently missing.•Useful recommendations for particular acquisition devices should be given.•A substantial portion of measured data is not ...employed in symmetry analysis.•A new subgroup of symmetry measures has emerged — complete gait cycle measures.•The definition of gait symmetry should be reconsidered.
Gait symmetry is important in measuring gait pattern alterations for establishing the level of functional limitation due to pathology, observing its changes over time and evaluating rehabilitative intervention effects. The aim of this topical review is twofold: 1) to present used symmetry measures and summarize their application to a diverse range of gait data and to demonstrate their capabilities in their utilization in research and practice, 2) to expose newly developed symmetry measures and highlight their perspectives. We divided symmetry measures into four subgroups: symmetry indices, complete gait cycle symmetry measures, statistically-based measures and approaches, and nonlinear measures. For each, we will discuss their advantages and limitations and raise new questions and recommendations about their development and clinical use.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UL, UM, UPCLJ, UPUK, ZRSKP
We have considered a model E. Ma and D. Wegman, Phys. Rev. Lett. 107, 061803 (2011), where masses and a mixing pattern for neutrinos are governed by six Higgs triplets and A4 symmetry. In this model ...we have applied a certain diagonalization procedure through which we have shown that neutrino masses can have both normal or inverted hierarchy. We have also shown that current neutrino oscillation data can be explained in this model.
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Since the end of the 19th century when the prominent Norwegian mathematician Sophus Lie created the theory of Lie algebras and Lie groups and developed the method of their applications for solving ...differential equations, his theory and method have continuously been the research focus of many well-known mathematicians and physicists. This book is devoted to recent development in Lie theory and its applications for solving physically and biologically motivated equations and models. The book contains the articles published in two Special Issue of the journal Symmetry, which are devoted to analysis and classification of Lie algebras, which are invariance algebras of real-word models; Lie and conditional symmetry classification problems of nonlinear PDEs; the application of symmetry-based methods for finding new exact solutions of nonlinear PDEs (especially reaction-diffusion equations) arising in applications; the application of the Lie method for solving nonlinear initial and boundary-value problems (especially those for modelling processes with diffusion, heat transfer, and chemotaxis).
We present a recently developed Maple-based “GeM” software package for automated symmetry and conservation law analysis of systems of partial and ordinary differential equations (DE). The package ...contains a collection of powerful easy-to-use routines for mathematicians and applied researchers. A standard program that employs “GeM” routines for symmetry, adjoint symmetry or conservation law analysis of any given DE system occupies several lines of Maple code, and produces output in the canonical form. Classification of symmetries and conservation laws with respect to constitutive functions and parameters present in the given DE system is implemented. The “GeM” package is being successfully used in ongoing research. Run examples include classical and new results.
Title of program: GeM
Catalogue identifier: ADYK_v1_0
Program summary URL:
http://cpc.cs.qub.ac.uk/summaries/ADYK_v1_0
Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland
Licensing provisions: none
Computers: PC-compatible running Maple on MS Windows or Linux; SUN systems running Maple for Unix on OS Solaris
Operating systems under which the program has been tested: Windows 2000, Windows XP, Linux, Solaris
Programming language used: Maple 9.5
Memory required to execute with typical data: below 100 Megabytes
No. of lines in distributed program, including test data, etc.: 4939
No. of bytes in distributed program, including test data, etc.: 166 906
Distribution format: tar.gz
Nature of physical problem: Any physical model containing linear or nonlinear partial or ordinary differential equations.
Method of solution: Symbolic computation of Lie, higher and approximate symmetries by Lie's algorithm. Symbolic computation of conservation laws and adjoint symmetries by using multipliers and Euler operator properties. High performance is achieved by using an efficient representation of the system under consideration and resulting symmetry/conservation law determining equations: all dependent variables and derivatives are represented as symbols rather than functions or expressions.
Restrictions on the complexity of the problem: The
GeM module routines are normally able to handle ODE/PDE systems of high orders (up to order seven and possibly higher), depending on the nature of the problem. Classification of symmetries/conservation laws with respect to one or more arbitrary constitutive functions of one or two arguments is normally accomplished successfully.
Typical running time: 1–20 seconds for problems that do not involve classification; 5–1000 seconds for problems that involve classification, depending on complexity.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UL, UM, UPCLJ, UPUK
One of the challenges of the modern photonics is to develop all‐optical devices enabling increased speed and energy efficiency for transmitting and processing information on an optical chip. It is ...believed that the recently suggested Parity‐Time (PT) symmetric photonic systems with alternating regions of gain and loss can bring novel functionalities. In such systems, losses are as important as gain and, depending on the structural parameters, gain compensates losses. Generally, PT systems demonstrate nontrivial non‐conservative wave interactions and phase transitions, which can be employed for signal filtering and switching, opening new prospects for active control of light. In this review, we discuss a broad range of problems involving nonlinear PT‐symmetric photonic systems with an intensity‐dependent refractive index. Nonlinearity in such PT symmetric systems provides a basis for many effects such as the formation of localized modes, nonlinearly‐induced PT‐symmetry breaking, and all‐optical switching. Nonlinear PT‐symmetric systems can serve as powerful building blocks for the development of novel photonic devices targeting an active light control.
The paper provides an overview of the topic of parity‐time (PT) symmetric optical structures incorporating spatially distributed regions of gain and loss, and it covers both theoretical and experimental studies of nonlinear optical phenomena in such structures. The concepts of nonlinearity enhancement and symmetry‐breaking transitions are also discussed. Various effects and applications of PT‐symmetric photonics are considered in detail, including all‐optical switching, tuneable signal amplification, scattering and unidirectional propagation, as well as self‐trapping and soliton effects.
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FZAB, GIS, IJS, KILJ, NLZOH, NUK, OILJ, SAZU, SBCE, SBMB, UL, UM, UPUK
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