scholarly journals Null reductions of the M5-brane

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Neil Lambert ◽  
Tristan Orchard
Keyword(s):  
Normal Bundle ◽  
Gauge Theories ◽  
Killing Vector ◽  
Abelian Extension ◽  
Dimensional Spacetime ◽  
General Reduction

Abstract We perform a general reduction of an M5-brane on a spacetime that admits a null Killing vector, including couplings to background 4-form fluxes and possible twisting of the normal bundle. We give the non-abelian extension of this action and present its supersymmetry transformations. The result is a class of supersymmetric non-Lorentzian gauge theories in 4+1 dimensions, which depend on the geometry of the six-dimensional spacetime. These can be used for DLCQ constructions of M5-branes reduced on various manifolds.

scholarly journals Cohomological localization of $$ \mathcal{N} $$ = 2 gauge theories with matter

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Guido Festuccia ◽  
Anastasios Gorantis ◽  
Antonio Pittelli ◽  
Konstantina Polydorou ◽  
Lorenzo Ruggeri
Keyword(s):  
Vector Field ◽  
Extended Supersymmetry ◽  
General Framework ◽  
Gauge Theories ◽  
Killing Vector ◽  
Killing Vector Field ◽  
Explicit Result ◽  
Yang Mills ◽  
Self Duality ◽  
Witten Theory

Abstract We construct a large class of gauge theories with extended supersymmetry on four-dimensional manifolds with a Killing vector field and isolated fixed points. We extend previous results limited to super Yang-Mills theory to general $$ \mathcal{N} $$ N = 2 gauge theories including hypermultiplets. We present a general framework encompassing equivariant Donaldson-Witten theory and Pestun’s theory on S4 as two particular cases. This is achieved by expressing fields in cohomological variables, whose features are dictated by supersymmetry and require a generalized notion of self-duality for two-forms and of chirality for spinors. Finally, we implement localization techniques to compute the exact partition function of the cohomological theories we built up and write the explicit result for manifolds with diverse topologies.

CURRENT COMMUTATOR ANOMALIES AND CHIRAL ANOMALIES IN THE CANONICAL FORMALISM

1988 ◽  
Vol 03 (07) ◽  
pp. 691-701 ◽  
Author(s):  
SHINOBU HOSONO ◽  
KOICHI SEO
Keyword(s):  
Electric Field ◽  
Regularization Method ◽  
Gauge Theories ◽  
Canonical Formalism ◽  
Current Commutator ◽  
Current Divergence ◽  
Dimensional Spacetime ◽  
Current Electric Field

Without recourse to the Bjorken-Johnson-Low (BJL) method, current-current and current-electric-field commutator anomalies are evaluated in chiral gauge theories in two-and four-dimensional spacetime with the help of a gauge covariant regularization method. The results are consistent with previous analyses through the BJL method, and partially confirmed Faddeev’s conjecture on the commutator anomalies of the Gauss law constraint operators within the canonical formalism. The chiral anomalies of the current divergence are derived from these commutator anomalies in the Weyl gauge where current-electric-field commutator anomalies play important roles.

ABSENCE OF APPARENT HORIZONS IN TRANSLATIONALLY-INVARIANT EINSTEIN–MAXWELL SPACETIMES

2004 ◽  
Vol 13 (03) ◽  
pp. 517-526
Author(s):  
SÉRGIO M. C. V. GONÇALVES
Keyword(s):  
Vector Field ◽  
Lie Group ◽  
Killing Vector ◽  
Cosmic Censorship ◽  
Killing Vector Field ◽  
Dimensional Spacetime ◽  
Apparent Horizons ◽  
Spacetime Metric ◽  
Group Of Isometries

We show that (3+1) Einstein–Maxwell spacetimes admitting a global, spacelike, one-parameter Lie group of isometries of translational type cannot contain apparent horizons. The only assumption made is that of the existence of a global spacelike Killing vector field with infinite open orbits; the four-dimensional spacetime metric is otherwise completely arbitrary. We discuss the implications of this result for the hoop and cosmic censorship conjectures.

scholarly journals Proper semiconformal symmetries of spacetimes with divergence-free semiconformal curvature tensor

Filomat ◽  
2019 ◽  
Vol 33 (16) ◽  
pp. 5191-5198
Author(s):  
Musavvir Ali ◽  
Naeem Pundeer ◽  
Young Suh
Keyword(s):  
Vector Field ◽  
Scalar Curvature ◽  
Curvature Tensor ◽  
Killing Vector ◽  
Petrov Type ◽  
Killing Vector Field ◽  
Dimensional Spacetime ◽  
Divergence Free ◽  
Symmetric Spacetime

In the present paper, the symmetries admitted by semiconformal curvature tensor in semiconformally symmetric spacetime have been studied and we show that a four-dimensional spacetime admitting a proper semiconformal symmetry is semiconformally flat or of the Petrov type N. It is also shown that a four-dimensional spacetime with divergence-free semiconformal curvature tensor admitting a proper semiconformal symmetry is locally of the Petrov type O or has four distinct principal null directions. In both the cases, we found that if the spacetime admits an infinitesimal semiconformal Killing vector field then the scalar curvature of the spacetime vanishes.

scholarly journals Constructing the CKVs of Bianchi III and V spacetimes

2019 ◽  
Vol 34 (39) ◽  
pp. 1950326
Author(s):  
Antonios Mitsopoulos ◽  
Michael Tsamparlis ◽  
Andronikos Paliathanasis
Keyword(s):  
Killing Vector ◽  
Conformal Factor ◽  
Conformal Killing ◽  
Two Dimensional ◽  
Homothetic Vector ◽  
Dimensional Spacetime ◽  
Space Of Constant Curvature ◽  
Bianchi Iii ◽  
Bianchi V ◽  
Reduced Space

We determine the conformal algebra of Bianchi III and Bianchi V spacetimes or, equivalently, we determine all Bianchi III and Bianchi V spacetimes which admit a proper conformal Killing vector (CKV). The algorithm that we use has been developed in [M. Tsamparlis et al.Class. Quantum. Grav. 15, 2909 (1998)] and concerns the computation of the CKVs of decomposable spacetimes. The main point of this method is that a decomposable space admits a CKV if the reduced space admits a gradient homothetic vector, the latter being possible only if the reduced space is flat or a space of constant curvature. We apply this method in a stepwise manner starting from the two-dimensional spacetime which admits an infinite number of CKVs and we construct step by step the Bianchi III and V spacetimes by assuming that CKVs survive as we increase the dimension of the space. We find that there is only one Bianchi III and one Bianchi V spacetime which admit at maximum one proper CKV. In each case, we determine the CKV and the corresponding conformal factor. As a first application in these two spacetimes, we study the kinematics of the comoving observers and the dynamics of the corresponding cosmological fluid. As a second application, we determine in these spacetimes generators of the Lie symmetries of the wave equation.

On the geometry of Killing vector field

2019 ◽  
Vol 2019 (2) ◽  
pp. 62-67
Author(s):  
R.A. Ilyasova
Keyword(s):  
Vector Field ◽  
Killing Vector ◽  
Killing Vector Field

Some Properties of Para-Sasakian Manifolds

2017 ◽  
Vol 5 (2) ◽  
pp. 73-78
Author(s):  
Jay Prakash Singh ◽  
Keyword(s):  
Vector Field ◽  
Killing Vector ◽  
Sasakian Manifold ◽  
Subject Classification ◽  
Killing Vector Field ◽  
Sasakian Manifolds ◽  
Geometric Properties ◽  
Paper Author

In this paper author present an investigation of some differential geometric properties of Para-Sasakian manifolds. Condition for a vector field to be Killing vector field in Para-Sasakian manifold is obtained. Mathematics Subject Classification (2010). 53B20, 53C15.

Geometry and Quantum Dynamics

2017 ◽  
Author(s):  
Laurent Baulieu ◽  
John Iliopoulos ◽  
Roland Sénéor
Keyword(s):  
General Relativity ◽  
Quantum Dynamics ◽  
Gauge Theories ◽  
Brst Symmetry ◽  
Abelian Gauge ◽  
Yang Mills ◽  
History Of ◽  
Brst Invariance

A geometrical derivation of Abelian and non- Abelian gauge theories. The Faddeev–Popov quantisation. BRST invariance and ghost fields. General discussion of BRST symmetry. Application to Yang–Mills theories and general relativity. A brief history of gauge theories.

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