scholarly journals The Generalized Hypergeometric Structure of the Ward Identities of CFT’s in Momentum Space in d > 2

Axioms ◽  
2020 ◽  
Vol 9 (2) ◽  
pp. 54
Author(s):  
Claudio Corianò ◽  
Matteo Maria Maglio
Keyword(s):  
Hypergeometric Functions ◽  
Conformal Symmetry ◽  
Coordinate Space ◽  
Conformal Field Theories ◽  
Conformal Invariant ◽  
Ward Identities ◽  
Conformal Field ◽  
The Past ◽  
Dual Variables ◽  
Appell Functions

We review the emergence of hypergeometric structures (of F4 Appell functions) from the conformal Ward identities (CWIs) in conformal field theories (CFTs) in dimensions d > 2. We illustrate the case of scalar 3- and 4-point functions. 3-point functions are associated to hypergeometric systems with four independent solutions. For symmetric correlators, they can be expressed in terms of a single 3K integral—functions of quadratic ratios of momenta—which is a parametric integral of three modified Bessel K functions. In the case of scalar 4-point functions, by requiring the correlator to be conformal invariant in coordinate space as well as in some dual variables (i.e., dual conformal invariant), its explicit expression is also given by a 3K integral, or as a linear combination of Appell functions which are now quartic ratios of momenta. Similar expressions have been obtained in the past in the computation of an infinite class of planar ladder (Feynman) diagrams in perturbation theory, which, however, do not share the same (dual conformal/conformal) symmetry of our solutions. We then discuss some hypergeometric functions of 3 variables, which define 8 particular solutions of the CWIs and correspond to Lauricella functions. They can also be combined in terms of 4K integral and appear in an asymptotic description of the scalar 4-point function, in special kinematical limits.

scholarly journals Defect conformal blocks from Appell functions

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Ilija Burić ◽  
Volker Schomerus
Keyword(s):  
Field Theory ◽  
Correlation Function ◽  
Conformal Field Theory ◽  
Hypergeometric Functions ◽  
Conformal Symmetry ◽  
Scalar Fields ◽  
Conformal Blocks ◽  
Conformal Field ◽  
Additional Defect ◽  
Appell Functions

Abstract We develop a group theoretical formalism to study correlation functions in defect conformal field theory, with multiple insertions of bulk and defect fields. This formalism is applied to construct the defect conformal blocks for three-point functions of scalar fields. Starting from a configuration with one bulk and one defect field, for which the correlation function is determined by conformal symmetry, we explore two possibilities, adding either one additional defect or bulk field. In both cases it is possible to express the blocks in terms of classical hypergeometric functions, though the case of two bulk and one defect field requires Appell’s function F4.

scholarly journals GRAVITY DUAL FOR REGGEON FIELD THEORY AND NONLINEAR QUANTUM FINANCE

2009 ◽  
Vol 24 (32) ◽  
pp. 6197-6222 ◽  
Author(s):  
YU NAKAYAMA
Keyword(s):  
Field Theory ◽  
Conformal Invariance ◽  
Field Theories ◽  
Conformal Field Theories ◽  
Conformal Invariant ◽  
Galilean Invariance ◽  
Scale Invariant ◽  
Conformal Field ◽  
Nonlinear Quantum ◽  
Reggeon Field Theory

We study scale invariant but not necessarily conformal invariant deformations of nonrelativistic conformal field theories from the dual gravity viewpoint. We present the corresponding metric that solves the Einstein equation coupled with a massive vector field. We find that, within the class of metric we study, when we assume the Galilean invariance, the scale invariant deformation always preserves the nonrelativistic conformal invariance. We discuss applications to scaling regime of Reggeon field theory and nonlinear quantum finance. These theories possess scale invariance but may or may not break the conformal invariance, depending on the underlying symmetry assumptions.

scholarly journals Momentum space parity-odd CFT 3-point functions

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Sachin Jain ◽  
Renjan Rajan John ◽  
Abhishek Mehta ◽  
Amin A. Nizami ◽  
Adithya Suresh
Keyword(s):  
Momentum Space ◽  
Field Theories ◽  
Conformal Field Theories ◽  
Ward Identities ◽  
Conformal Field ◽  
Weight Shifting ◽  
Conserved Currents

Abstract We study the parity-odd sector of 3-point functions comprising scalar operators and conserved currents in conformal field theories in momentum space. We use momentum space conformal Ward identities as well as spin-raising and weight-shifting operators to fix the form of some of these correlators. Wherever divergences appear we discuss their regularisation and renormalisation using appropriate counter-terms.

Ward Identities for W ∞ , Conformal Field Theories on a Torus

1991 ◽  
Vol 16 (4) ◽  
pp. 493-496
Author(s):  
Chao-Shang Huang ◽  
Liang-Xin Li ◽  
De-Hai Zhang
Keyword(s):  
Field Theories ◽  
Conformal Field Theories ◽  
Ward Identities ◽  
Conformal Field

NONARCHIMEDEAN CONFORMAL FIELD THEORIES

1989 ◽  
Vol 04 (18) ◽  
pp. 4877-4908 ◽  
Author(s):  
EZER MELZER
Keyword(s):  
Correlation Functions ◽  
Central Charge ◽  
Conformal Symmetry ◽  
Conformal Group ◽  
Field Theories ◽  
Dimensional Euclidean Space ◽  
Conformal Field Theories ◽  
Linear Transformations ◽  
Associative Algebras ◽  
Conformal Field

We present a general formalism for conformal field theories defined on a non-Archimedean field. Such theories are defined by complex-valued correlation functions of fields of a [Formula: see text]-adic variable. Conformal invariance is imposed by requiring the correlation functions to be unchanged under fractional linear transformations, the latter forming the full analogue of the conformal group in two-dimensional, euclidean space-time. All fields in the theory can be taken to be "primary", under the "non-Archimedean conformal group". The conformal symmetry fixes completely the form of all correlation functions, once we are given the weight-spectrum of the theory and the OPE coefficients (which must be the structure constants of certain commutative, associative algebras). We explicitly construct non-Archimedean CFT's having the same weight spectrum as that of Archimedean models of central charge c < 1. The OPE coefficients of these "local" Archimedean and non-Archimedean models are related by adelic formulae.

scholarly journals Five-dimensional non-Lorentzian conformal field theories and their relation to six-dimensions

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
N. Lambert ◽  
A. Lipstein ◽  
R. Mouland ◽  
P. Richmond
Keyword(s):  
Correlation Functions ◽  
Conformal Symmetry ◽  
Field Theories ◽  
Conformal Field Theories ◽  
Dimensional Theory ◽  
Superconformal Field Theories ◽  
Yang Mills ◽  
Conformal Field ◽  
Instanton Number ◽  
Do So

Abstract We study correlation functions in five-dimensional non-Lorentzian theories with an SU(1, 3) conformal symmetry. Examples of such theories have recently been obtained as Ω-deformed Yang-Mills Lagrangians arising from a null reduction of six-dimensional superconformal field theories on a conformally compactified Minkowski space. The correlators exhibit a rich structure with many novel properties compared to conventional correlators in Lorentzian conformal field theories. Moreover, identifying the instanton number with the Fourier mode number of the dimensional reduction offers a hope to formulate six-dimensional conformal field theories in terms of five-dimensional Lagrangian theories. To this end we show that the Fourier decompositions of six-dimensional correlation functions solve the Ward identities of the SU(1, 3) symmetry, although more general solutions are possible. Conversely we illustrate how one can reconstruct six-dimensional correlation functions from those of a five-dimensional theory, and do so explicitly at 2- and 3-points. We also show that, in a suitable decompactification limit Ω → 0, the correlation functions become those of the DLCQ description.

scholarly journals Non-Lorentzian avatars of (1,0) theories

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
N. Lambert ◽  
T. Orchard
Keyword(s):  
Field Theory ◽  
Gauge Field ◽  
Conformal Symmetry ◽  
Minkowski Spacetime ◽  
Gauge Field Theories ◽  
Field Theories ◽  
Conformal Field Theories ◽  
Superconformal Field Theories ◽  
Conformal Field

Abstract We construct five-dimensional non-Lorentzian Lagrangian gauge field theories with an SU(1, 3) conformal symmetry and 12 (conformal) supersymmetries. Such theories are interesting in their own right but can arise from six-dimensional (1, 0) superconformal field theories on a conformally compactified Minkowski spacetime. In the limit that the conformal compactification is removed the Lagrangians we find give field theory formulations of DLCQ constructions of six-dimensional (1, 0) conformal field theories.

scholarly journals Thermal conformal blocks

2019 ◽  
Vol 7 (2) ◽  
Author(s):  
Yan Gobeil ◽  
Alexander Maloney ◽  
Gim Seng Ng ◽  
Jie-qiang Wu
Keyword(s):  
Hypergeometric Functions ◽  
Analytic Formula ◽  
Conformal Block ◽  
Integral Representations ◽  
Field Theories ◽  
Conformal Field Theories ◽  
Conformal Blocks ◽  
Generalized Hypergeometric Functions ◽  
Conformal Field ◽  
General Dimension

We study conformal blocks for thermal one-point-functions on the sphere in conformal field theories of general dimension. These thermal conformal blocks satisfy second-order Casimir differential equations and have integral representations related to AdS Witten diagrams. We give an analytic formula for the scalar conformal block in terms of generalized hypergeometric functions. As an application, we deduce an asymptotic formula for the three-point coefficients of primary operators in the limit where two of the operators are heavy.

Integrability: From Statistical Systems to Gauge Theory

2019 ◽  
Keyword(s):  
Field Theory ◽  
Gauge Theory ◽  
Summer School ◽  
Condensed Matter ◽  
Theoretical Physics ◽  
Conformal Field ◽  
The Past ◽  
Background Material ◽  
Supersymmetric Gauge ◽  
Statistical Systems

This volume contains lectures delivered at the Les Houches Summer School ‘Integrability: from statistical systems to gauge theory’ held in June 2016. The School was focussed on applications of integrability to supersymmetric gauge and string theory, a subject of high and increasing interest in the mathematical and theoretical physics communities over the past decade. Relevant background material was also covered, with lecture series introducing the main concepts and techniques relevant to modern approaches to integrability, conformal field theory, scattering amplitudes, and gauge/string duality. The book will be useful not only to those working directly on integrablility in string and guage theories, but also to researchers in related areas of condensed matter physics and statistical mechanics.

scholarly journals Standardizing human brain parcellations

2021 ◽  
Vol 8 (1) ◽  
Author(s):  
Ross M. Lawrence ◽  
Eric W. Bridgeford ◽  
Patrick E. Myers ◽  
Ganesh C. Arvapalli ◽  
Sandhya C. Ramachandran ◽  
...  
Keyword(s):  
Human Brain ◽  
Coordinate Space ◽  
The Past ◽  
File Storage ◽  
Statistical Inferences ◽  
Standardized Protocol ◽  
Storage Format ◽  
Labeling Scheme ◽  
Selection Of ◽  
Brain Atlases

AbstractUsing brain atlases to localize regions of interest is a requirement for making neuroscientifically valid statistical inferences. These atlases, represented in volumetric or surface coordinate spaces, can describe brain topology from a variety of perspectives. Although many human brain atlases have circulated the field over the past fifty years, limited effort has been devoted to their standardization. Standardization can facilitate consistency and transparency with respect to orientation, resolution, labeling scheme, file storage format, and coordinate space designation. Our group has worked to consolidate an extensive selection of popular human brain atlases into a single, curated, open-source library, where they are stored following a standardized protocol with accompanying metadata, which can serve as the basis for future atlases. The repository containing the atlases, the specification, as well as relevant transformation functions is available in the neuroparc OSF registered repository or https://github.com/neurodata/neuroparc.

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