Infinite Dimensional Algebras and (2+1)-Dimensional Field Theories: Yet Another View of gl(∞); Some New Algebras

1991 ◽  
pp. 171-177
Author(s):  
Jens Hoppe
Keyword(s):  
Field Theories ◽  
Infinite Dimensional

scholarly journals p-BRANES AS COMPOSITE ANTISYMMETRIC TENSOR FIELD THEORIES

1998 ◽  
Vol 13 (08) ◽  
pp. 1263-1292 ◽  
Author(s):  
CARLOS CASTRO
Keyword(s):  
Tensor Field ◽  
Target Space ◽  
Field Theories ◽  
Antisymmetric Tensor ◽  
Field Equations ◽  
Light Cone Gauge ◽  
Infinite Dimensional ◽  
Dimensional Group ◽  
Antisymmetric Tensor Field ◽  
Covariant Action

p′-brane solutions to rank p+1 composite antisymmetric tensor field theories of the kind developed by Guendelman, Nissimov and Pacheva are found when the dimensionality of space–time is D=(p+1)+(p′+1). These field theories possess an infinite-dimensional group of global Noether symmetries, that of volume-preserving diffeomorphisms of the target space of the scalar primitive field constituents. Crucial in the construction of p′ brane solutions are the duality transformations of the fields and the local gauge field theory formulation of extended objects given by Aurilia, Spallucci and Smailagic. Field equations are rotated into Bianchi identities after the duality transformation is performed and the Clebsch potentials associated with the Hamilton–Jacobi formulation of the p′ brane can be identified with the duals of the original scalar primitive constituents. Explicit examples are worked out the analog of S and T duality symmetry are discussed. Different types of Kalb–Ramond actions are given and a particular covariant action is presented which bears a direct relation to the light cone gauge p-brane action.

scholarly journals BRST QUANTIZATION AND THE PRODUCT FORMULA FOR THE RAY-SINGER TORSION

1995 ◽  
Vol 10 (12) ◽  
pp. 1779-1805 ◽  
Author(s):  
CHARLES NASH ◽  
DENJOE O’CONNOR
Keyword(s):  
Finite Elements ◽  
Topological Field Theories ◽  
Brst Quantization ◽  
Product Formula ◽  
Field Theories ◽  
Analytic Torsion ◽  
Quantum Field ◽  
Infinite Dimensional ◽  
New Class ◽  
Topological Field

We give a quantum field theoretic derivation of the formula obeyed by the Ray-Singer torsion on product manifolds. Such a derivation has proved elusive up to now. We use a BRST formalism which introduces the idea of an infinite dimensional Universal Gauge Fermion, and is of independent interest, being applicable to situations other than the ones considered here. We are led to a new class of Fermionic topological field theories. Our methods are also applicable to combinatorially defined manifolds and methods of discrete approximation, such as the use of a simplicial lattice or finite elements. The topological field theories discussed provide a natural link between the combinatorial and analytic torsion.

scholarly journals INTEGRABLE FIELD THEORIES DERIVED FROM 4-D SELF-DUAL GRAVITY

1996 ◽  
Vol 11 (07) ◽  
pp. 545-552 ◽  
Author(s):  
TATSUYA UENO
Keyword(s):  
Integrable Field Theories ◽  
Sigma Models ◽  
Einstein Equation ◽  
Differential Form ◽  
The Self ◽  
Higgs Bundle ◽  
Field Theories ◽  
Infinite Dimensional ◽  
Dimensional Group ◽  
Integrable Field

We reformulate the self-dual Einstein equation as a trio of differential form equations for simple two-forms. Using them, we can quickly show the equivalence of the theory and 2-D sigma models valued in infinite-dimensional group, which was shown by Park and Husain earlier. We also derive other field theories including the 2-D Higgs bundle equation. This formulation elucidates the relation among these field theories.

scholarly journals Infinite dimensional groups and Riemann surface field theories

1996 ◽  
Vol 176 (2) ◽  
pp. 321-351 ◽  
Author(s):  
A. L. Carey ◽  
K. C. Hannabuss
Keyword(s):  
Riemann Surface ◽  
Field Theories ◽  
Infinite Dimensional ◽  
Surface Field

THE HIDDEN KAC-MOODY SYMMETRY OF THE GEOMETRIC ACTIONS

1990 ◽  
Vol 05 (30) ◽  
pp. 2503-2513 ◽  
Author(s):  
H. ARATYN ◽  
E. NISSIMOV ◽  
S. PACHEVA
Keyword(s):  
Group Composition ◽  
General Scheme ◽  
Field Theories ◽  
Coadjoint Orbits ◽  
Arbitrary Field ◽  
Noether Symmetries ◽  
Infinite Dimensional ◽  
Main Application ◽  
Composition Laws ◽  
Geometric Action

A general formalism is proposed to study infinite-dimensional Noether symmetries in arbitrary field theories on group coadjoint orbits as well as in their gauged versions (coset geometric models). The basic tools are generalized group composition laws valid for any geometric action. As a main application, we present a general scheme for constructing the "hidden" Kac-Moody currents.

scholarly journals Swing surfaces and holographic entanglement beyond AdS/CFT

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Luis Apolo ◽  
Hongliang Jiang ◽  
Wei Song ◽  
Yuan Zhong
Keyword(s):  
Black Holes ◽  
Lorentz Invariance ◽  
Entanglement Entropy ◽  
Three Dimensional ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Asymptotically Flat ◽  
Infinite Dimensional ◽  
Holographic Entanglement Entropy

Abstract We propose a holographic entanglement entropy prescription for general states and regions in two models of holography beyond AdS/CFT known as flat3/BMSFT and (W)AdS3/WCFT. Flat3/BMSFT is a candidate of holography for asymptotically flat three- dimensional spacetimes, while (W)AdS3/WCFT is relevant in the study of black holes in the real world. In particular, the boundary theories are examples of quantum field theories that feature an infinite dimensional symmetry group but break Lorentz invariance. Our holographic entanglement entropy proposal is given by the area of a swing surface that consists of ropes, which are null geodesics emanating from the entangling surface at the boundary, and a bench, which is a spacelike geodesic connecting the ropes. The proposal is supported by an extension of the Lewkowycz-Maldacena argument, reproduces previous results based on the Rindler method, and satisfies the first law of entanglement entropy.

Symmetries, conservation laws and variational principles for vector field theories†

1996 ◽  
Vol 120 (2) ◽  
pp. 369-384 ◽  
Author(s):  
Ian M. Anderson ◽  
Juha Pohjanpelto
Keyword(s):  
Conservation Laws ◽  
Variational Principles ◽  
Field Theories ◽  
Conserved Quantities ◽  
Lagrange Equations ◽  
Differential Identities ◽  
Infinite Dimensional ◽  
Independent Variables ◽  
Generalized Symmetries ◽  
And Variational Principles

The interplay between symmetries, conservation laws, and variational principles is a rich and varied one and extends well beyond the classical Noether's theorem. Recall that Noether's first theorem asserts that to every r dimensional Lie algebra of (generalized) symmetries of a variational problem there are r conserved quantities for the corresponding Euler-Lagrange equations. Noether's second theorem asserts that infinite dimensional symmetry algebras (depending upon arbitrary functions of all the independent variables) lead to differential identities for the Euler-Lagrange equations.

4-D SELF-DUAL INSTANTONS FROM 2-D SIGMA MODEL

1992 ◽  
Vol 07 (supp01b) ◽  
pp. 781-789 ◽  
Author(s):  
Q-HAN PARK
Keyword(s):  
Sigma Model ◽  
Field Theories ◽  
Maxwell System ◽  
Conformal Field Theories ◽  
Yang Mills ◽  
Infinite Dimensional ◽  
Conformal Field ◽  
Integrable Deformation ◽  
Large N ◽  
Higher Dimensional

4-d self-dual gravity and Yang-Mills theories are identified with 2-d sigma models taking values in infinite dimensional groups. This allows us to view 4-d self-dual theories as "large N limits" of 2-d conformal field theories. We also find a possible "integrable deformation" of 4-d self-dual gravity leading to the Einstein-Maxwell system and discuss its implication in the context of higher dimensional integrability.

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