scholarly journals Brane current algebras and generalised geometry from QP manifolds. Or, “when they go high, we go low”

2021 ◽  
Vol 2021 (11) ◽  
Author(s):  
Alex S. Arvanitakis
Keyword(s):  
Current Algebra ◽  
Poisson Algebra ◽  
Gauge Fields ◽  
Complex Structures ◽  
Poisson Brackets ◽  
Geometric Form ◽  
Free Current ◽  
Universal Expression ◽  
Current Algebras

Abstract We construct a Poisson algebra of brane currents from a QP-manifold, and show their Poisson brackets take a universal geometric form. This generalises a result of Alekseev and Strobl on string currents and generalised geometry to include branes with worldvolume gauge fields, such as the D3 and M5. Our result yields a universal expression for the ’t Hooft anomaly that afflicts isometries in the presence of fluxes. We determine the current algebra in terms of (exceptional) generalised geometry, and show that the tensor hierarchy gives rise to a brane current hierarchy. Exceptional complex structures produce pairs of anomaly-free current subalgebras on the M5-brane worldvolume.

scholarly journals Perturbative F-theory 10-brane and M-theory 5-brane

2021 ◽  
Vol 2021 (11) ◽  
Author(s):  
Machiko Hatsuda ◽  
Warren Siegel
Keyword(s):  
Current Algebra ◽  
Duality Theory ◽  
Virasoro Algebra ◽  
Space Time ◽  
Lagrangian Formulation ◽  
Gauge Fields ◽  
Duality Symmetry ◽  
M Theory ◽  
Current Algebras

Abstract The exceptional symmetry is realized perturbatively in F-theory which is the manifest U-duality theory. The SO(5) U-duality symmetry acts on both the 16 space-time coordinates and the 10 worldvolume coordinates. Closure of the Virasoro algebra requires the Gauss law constraints on the worldvolume. This set of current algebras describes a F-theory 10-brane. The SO(5) duality symmetry is enlarged to the SO(6) symmetry in the Lagrangian formulation. We propose actions of the F-theory 10-brane with SO(5) and SO(6) symmetries. The gauge fields of the latter action are coset elements of SO(6)/SO(6; ℂ) which include both the SO(5)/SO(5; ℂ) spacetime backgrounds and the worldvolume backgrounds. The SO(5) current algebra obtained from the Pasti-Sorokin-Tonin M5-brane Lagrangian leads to the theory behind M-theory, namely F-theory. We also propose an action of the perturbative M-theory 5-brane obtained by sectioning the worldvolume of the F-theory 10-brane.

scholarly journals TWO-POINT FUNCTIONS IN AFFINE CURRENT ALGEBRA AND CONJUGATE WEIGHTS

1998 ◽  
Vol 13 (16) ◽  
pp. 1281-1288 ◽  
Author(s):  
JØRGEN RASMUSSEN
Keyword(s):  
Lie Algebras ◽  
Current Algebra ◽  
Primary Field ◽  
Simple Lie Algebras ◽  
Arbitrary Weight ◽  
Current Algebras

The two-point functions in affine current algebras based on simple Lie algebras are constructed for all representations, integrable or non-integrable. The weight of the conjugate field to a primary field of arbitrary weight is immediately read off.

scholarly journals CURRENT ALGEBRA IN THE PATH INTEGRAL FRAMEWORK

1998 ◽  
Vol 13 (27) ◽  
pp. 2193-2198
Author(s):  
V. CÁRDENAS ◽  
S. LEPE ◽  
J. SAAVEDRA
Keyword(s):  
Path Integral ◽  
Current Algebra ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Integral Formalism ◽  
Path Integral Formalism ◽  
Current Algebras

In this letter we describe an approach to the current algebra based on the path integral formalism. We use this method for Abelian and non-Abelian quantum field theories in (1+1) and (2+1) dimensions and the correct expressions are obtained. Our results show the independence of the regularization of the current algebras.

scholarly journals THE EXTENSION STRUCTURE OF 2D MASSIVE CURRENT ALGEBRAS

1992 ◽  
Vol 07 (35) ◽  
pp. 3309-3318 ◽  
Author(s):  
J. LAARTZ
Keyword(s):  
Sigma Models ◽  
Current Algebra ◽  
Second Step ◽  
Two Dimensional ◽  
Split Extension ◽  
Nonlinear Sigma Models ◽  
Current Algebras

The extension structure of the two-dimensional current algebra of nonlinear sigma models is analyzed by introducing Kostant Sternberg (L, M) systems. It is found that the algebra obeys a two-step extension by Abelian ideals. The second step is a non-split extension of a representation of the quotient of the algebra by the first step of the extension. The cocycle which appears is analyzed.

scholarly journals CURRENT ALGEBRA FUNCTORS AND EXTENSIONS

2013 ◽  
Vol 25 (07) ◽  
pp. 1350012
Author(s):  
ANTON ALEKSEEV ◽  
PAVOL SEVERA ◽  
CORNELIA VIZMAN
Keyword(s):  
Lie Algebra ◽  
Lie Algebras ◽  
Current Algebra ◽  
Equivariant Cohomology ◽  
Sigma Model ◽  
Current Group ◽  
Group Extensions ◽  
Current Algebras

We show how the fundamental cocycles on current Lie algebras and the Lie algebra of symmetries for the sigma model are obtained via the current algebra functors introduced in [A. Alekseev and P. Severa, Equivariant cohomology and current algebras, Confluentes Math.4 (2012) 1250001, 40 pp.]. We present current group extensions integrating some of these current Lie algebra extensions.

scholarly journals COVARIANT PHASE SPACE FORMULATIONS OF SUPERPARTICLES AND SUPERSYMMETRIC WZW MODELS

1994 ◽  
Vol 09 (27) ◽  
pp. 2469-2480
Author(s):  
G. AU ◽  
B. SPENCE
Keyword(s):  
Phase Space ◽  
Poisson Brackets ◽  
Group Manifold ◽  
Current Algebras

We present new covariant phase space formulations of superparticles moving on a group manifold, deriving the fundamental Poisson brackets and current algebras. We show how these formulations naturally generalize to the supersymmetric Wess-Zumino-Witten models.

scholarly journals BGG reciprocity for current algebras

2015 ◽  
Vol 151 (7) ◽  
pp. 1265-1287 ◽  
Author(s):  
Vyjayanthi Chari ◽  
Bogdan Ion
Keyword(s):  
Lie Algebra ◽  
Current Algebra ◽  
Simple Lie Algebra ◽  
Finite Dimensional ◽  
Affine Lie Algebra ◽  
A Current ◽  
Current Algebras

In Bennett et al. [BGG reciprocity for current algebras, Adv. Math. 231 (2012), 276–305] it was conjectured that a BGG-type reciprocity holds for the category of graded representations with finite-dimensional graded components for the current algebra associated to a simple Lie algebra. We associate a current algebra to any indecomposable affine Lie algebra and show that, in this generality, the BGG reciprocity is true for the corresponding category of representations.

scholarly journals POISSON ALGEBRA OF WILSON LOOPS IN FOUR-DIMENSIONAL YANG-MILLS THEORY

1995 ◽  
Vol 10 (17) ◽  
pp. 2479-2505 ◽  
Author(s):  
S.G. RAJEEV ◽  
O.T. TURGUT
Keyword(s):  
Phase Space ◽  
Gauge Theories ◽  
Poisson Algebra ◽  
Coadjoint Orbit ◽  
Quadratic Algebra ◽  
Wilson Loops ◽  
Poisson Brackets ◽  
Canonical Structure ◽  
Gauge Invariant ◽  
Yang Mills

We formulate the canonical structure of Yang-Mills theory in terms of Poisson brackets of gauge-invariant observables analogous to Wilson loops. This algebra is nontrivial and tractable in a light cone formulation. For U (N) gauge theories the result is a Lie algebra while for SU (N) gauge theories it is a quadratic algebra. We also study the identities satisfied by the gauge-invariant observables. We suggest that the phase space of a Yang-Mills theory is a coadjoint orbit of our Poisson algebra; some partial results in this direction are obtained.

Size of the early universe and GUP

2019 ◽  
Vol 34 (22) ◽  
pp. 1950178
Author(s):  
Ljubisa Nesic ◽  
Darko Radovancevic
Keyword(s):  
Phase Space ◽  
Cosmological Model ◽  
Early Universe ◽  
Generalized Uncertainty Principle ◽  
Poisson Algebra ◽  
Poisson Brackets ◽  
Energy Term ◽  
Classical Version ◽  
One Dimensional ◽  
Potential Energy Term

This paper presents the effects of the Generalized Uncertainty Principle (GUP), i.e. its classical version expressed through the deformed Poisson brackets in the phase–space of a one-dimensional minisuperspace Friedmann cosmological model with a mixture of non-interacting dust and radiation. It is shown, in the case of this model, that starting from the specific representation of the deformed Poisson algebra, which corresponds to the change of the potential energy term of the oscillator, the size of the early universe can be related to its inflationary GUP expansion.

scholarly journals CURRENT ALGEBRAS AND QP-MANIFOLDS

2013 ◽  
Vol 10 (06) ◽  
pp. 1350024 ◽  
Author(s):  
NORIAKI IKEDA ◽  
KOZO KOIZUMI
Keyword(s):  
Higher Dimensions ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Poisson Brackets ◽  
Dirac Structure ◽  
Anomaly Cancellation ◽  
Graded Manifold ◽  
Graded Poisson Brackets ◽  
A Current ◽  
Current Algebras

Generalized current algebras introduced by Alekseev and Strobl in two dimensions are reconstructed by a graded manifold and a graded Poisson brackets. We generalize their current algebras to higher dimensions. QP-manifolds provide the unified structures of current algebras in any dimension. Current algebras give rise to structures of Leibniz/Loday algebroids, which are characterized by QP-structures. Especially, in three dimensions, a current algebra has a structure of a Lie algebroid up to homotopy introduced by Uchino and one of the authors, which has a bracket of a generalization of the Courant–Dorfman bracket. Anomaly cancellation conditions are reinterpreted as generalizations of the Dirac structure.

Sign in / Sign up

Export Citation Format

Share Document