scholarly journals An E11 invariant gauge fixing

2018 ◽  
Vol 33 (01) ◽  
pp. 1850009 ◽  
Author(s):  
Michaella Pettit ◽  
Peter West
Keyword(s):  
Direct Product ◽  
Tangent Space ◽  
Space Time ◽  
Vector Representation ◽  
Alternative Derivation ◽  
Four Dimensions ◽  
Gauge Fixing ◽  
Cartan Involution ◽  
Low Levels ◽  
Invariant Gauge

We consider the nonlinear realisation of the semi-direct product of [Formula: see text] and its vector representation which leads to a space-time with tangent group that is the Cartan involution invariant subalgebra of [Formula: see text]. We give an alternative derivation of the invariant tangent space metric that this space–time possesses and compute this metric at low levels in eleven, five and four dimensions. We show that one can gauge fix the nonlinear realisation in an [Formula: see text] invariant manner.

scholarly journals Irreducible representations of E theory

2019 ◽  
Vol 34 (24) ◽  
pp. 1950133 ◽  
Author(s):  
Peter West
Keyword(s):  
Irreducible Representation ◽  
Direct Product ◽  
Simple Form ◽  
Light Cone ◽  
Degrees Of Freedom ◽  
Irreducible Representations ◽  
Vector Representation ◽  
Maximal Supergravity ◽  
Duality Relations ◽  
Cartan Involution

We construct the [Formula: see text] theory analogue of the particles that transform under the Poincaré group, that is, the irreducible representations of the semi-direct product of the Cartan involution subalgebra of [Formula: see text] with its vector representation. We show that one such irreducible representation has only the degrees of freedom of 11-dimensional supergravity. This representation is most easily discussed in the light cone formalism and we show that the duality relations found in [Formula: see text] theory take a particularly simple form in this formalism. We explain that the mysterious symmetries found recently in the light cone formulation of maximal supergravity theories are part of [Formula: see text]. We also argue that our familiar space–times have to be extended by additional coordinates when considering extended objects such as branes.

HAMILTONIAN THEORY OF THE RELATIVISTIC STRING

1990 ◽  
Vol 02 (03) ◽  
pp. 355-398 ◽  
Author(s):  
G.P. Pron’ko
Keyword(s):  
String Theory ◽  
Spectral Problem ◽  
Dimensional Space ◽  
Space Time ◽  
Point Of View ◽  
Relativistic String ◽  
Hamiltonian Theory ◽  
Gauge Fixing ◽  
Dimensional Space Time ◽  
Invariant Gauge

The relativistic string theory is considered from the Hamiltonian point of view. It is proposed to formulate the dynamics of string in d-dimensional space-time with the help of the auxiliary spectral problem. This approach gives the possibility to construct a completely new set of variables of string relevant for Lorentz-invariant gauge fixing. The notion of smooth string is introduced for which the successive relativistic invariant quantization could be done explicitly for the d=4 case.

scholarly journals E theory in seven dimensions

2019 ◽  
Vol 34 (25) ◽  
pp. 1950135 ◽  
Author(s):  
Michaella Pettit ◽  
Peter West
Keyword(s):  
Direct Product ◽  
Dynkin Diagram ◽  
Equations Of Motion ◽  
Space Time ◽  
Vector Representation ◽  
Dimensional Theory

We construct the nonlinear realisation of the semi-direct product of [Formula: see text] and its vector representation in its decomposition into the subalgebra [Formula: see text] to find a seven-dimensional theory. The resulting equations of motion essentially follow from the Dynkin diagram of [Formula: see text] and if one restricts them to contain only the usual fields of supergravity and the derivatives with respect to the usual coordinates of space–time then these are the equations of motion of seven-dimensional supergravity.

One-loop effects in N = 4 supersymmetry

1996 ◽  
Vol 74 (3-4) ◽  
pp. 176-181
Author(s):  
D. G. C. McKeon
Keyword(s):  
Radiative Corrections ◽  
Loop Order ◽  
Four Dimensions ◽  
Yang Mills ◽  
Yukawa Couplings ◽  
Gauge Fixing ◽  
Component Field ◽  
Β Function ◽  
Supersymmetric Theories ◽  
Invariant Gauge

It has been demonstrated that in massless supersymmetric theories, finite radiative corrections to the superpotential can occur (viz. the nonrenormalization theorems can be circumvented). In this paper, we examine the consequences of this in N = 4 supersymmetric Yang–Mills theory, a model in which the β function is known to be zero. It is shown that radiative corrections to the superpotential arise at one loop order in this theory contrary to the expectations of the nonrenormalization theorem, but that their form depends on which formulation of the model is used. When one uses a superfield formulation involving an N = 1 vector superfield and three N = 1 chiral superfields in conjunction with a supersymmetric (but not SU(4)) invariant gauge fixing, then at one-loop order, the radiative generation of terms in the superpotential means that the equality of the gauge and Yukawa couplings and indeed of different Yukawa couplings is lost. If one uses the component field formulation of the N = 4 model in the Wess–Zumino gauge with a covariant, SU(4) invariant (but not supersymmetric invariant) gauge fixing, then the SU(4) invariance is maintained, but the gauge and Yukawa couplings are no longer equal. We also consider computations in the component field formulation in the Wess–Zumino gauge using an N = 1 super Yang–Mills theory in ten dimensions, dimensionally reduced to four dimensions, with a ten-dimensional covariant gauge fixing condition. This formulation ensures that there is no distinction between gauge and Yukawa couplings and that SU(4) invariance is automatically preserved; however, supersymmetry is broken by the gauge fixing procedure.

scholarly journals E11, brane dynamics and duality symmetries

2018 ◽  
Vol 33 (13) ◽  
pp. 1850080 ◽  
Author(s):  
Peter West
Keyword(s):  
Direct Product ◽  
Equations Of Motion ◽  
Space Time ◽  
Vector Representation ◽  
First Order ◽  
Duality Relations ◽  
The One

Following arXiv:hep-th/0412336 we use the nonlinear realisation of the semi-direct product of [Formula: see text] and its vector representation to construct brane dynamics. The brane moves through a space-time which arises in the nonlinear realisation from the vector representation and it contains the usual embedding coordinates as well as the worldvolume fields. The resulting equations of motion are first order in derivatives and can be thought of as duality relations. Each brane carries the full [Formula: see text] symmetry and so the Cremmer–Julia duality symmetries. We apply this theory to find the dynamics of the IIA and IIB strings, the M2 and M5 branes, the IIB D3 brane as well as the one and two branes in seven dimensions.

FURTHER TOPOLOGICAL PROOFS OF GRIBOV AMBIGUITIES

1992 ◽  
Vol 07 (10) ◽  
pp. 849-853 ◽  
Author(s):  
GERARD JUNGMAN
Keyword(s):  
Gauge Group ◽  
Space Time ◽  
Large Classes ◽  
Four Dimensions ◽  
Gauge Fixing ◽  
Gribov Ambiguity

We show the existence of Gribov ambiguity for gauge group SU (N) and large classes of space-time manifolds with dimension less than or equal to four, working in the continuous category, extending previous results of Singer. In lower dimensions, and in four dimensions with gauge group SU (N), N≥3, we require only that the manifold be compact and orientable. In four dimensions with gauge group SU (2) there is a slight complification due to the fact that π4( SU (2)) does not vanish, though we are still able to state a useful result for that case. Some discussion of motivation is presented, in particular as regards to recent gauge-fixing proposals which arise in work that attempts to relate the Gribov ambiguity to confinement.

scholarly journals A MAXWELL-LIKE FORMULATION OF GRAVITATIONAL THEORY IN MINKOWSKI SPACE–TIME

2007 ◽  
Vol 16 (06) ◽  
pp. 1027-1041 ◽  
Author(s):  
EDUARDO A. NOTTE-CUELLO ◽  
WALDYR A. RODRIGUES
Keyword(s):  
Gravitational Field ◽  
Minkowski Space ◽  
Gravitational Theory ◽  
Space Time ◽  
Lorentzian Geometry ◽  
Field Equations ◽  
Yang Mills ◽  
Minkowski Space Time ◽  
Clifford Bundle ◽  
Gauge Fixing

Using the Clifford bundle formalism, a Lagrangian theory of the Yang–Mills type (with a gauge fixing term and an auto interacting term) for the gravitational field in Minkowski space–time is presented. It is shown how two simple hypotheses permit the interpretation of the formalism in terms of effective Lorentzian or teleparallel geometries. In the case of a Lorentzian geometry interpretation of the theory, the field equations are shown to be equivalent to Einstein's equations.

scholarly journals A NEW APPROACH TO BLACK HOLE MICROSTATES

1998 ◽  
Vol 13 (23) ◽  
pp. 1875-1879 ◽  
Author(s):  
RICHARD J. EPP ◽  
R. B. MANN
Keyword(s):  
Black Hole ◽  
Degrees Of Freedom ◽  
Black Hole Entropy ◽  
Space Time ◽  
Orthonormal Frame ◽  
Great Promise ◽  
Frame Field ◽  
New Approach ◽  
Four Dimensions ◽  
First Order

If one encodes the gravitational degrees of freedom in an orthonormal frame field, there is a very natural first-order action one can write down (which in four dimensions is known as the Goldberg action). In this letter we will show that this action contains a boundary action for certain microscopic degrees of freedom living at the horizon of a black hole, and argue that these degrees of freedom hold great promise for explaining the microstates responsible for black hole entropy, in any number of space–time dimensions. This approach faces many interesting challenges, both technical and conceptual.

scholarly journals Klein-Gordon Equation and Wave Function in Robertson-Walker and Schwarzschild space-tim

2021 ◽  
Author(s):  
Sangwha Yi
Keyword(s):  
Wave Function ◽  
Wave Equations ◽  
Gordon Equation ◽  
Space Time ◽  
Wave Functions ◽  
Relativity Theory ◽  
General Relativity Theory ◽  
Gauge Fixing ◽  
Klein Gordon ◽  
Klein Gordon Equation

In the general relativity theory, we find Klein-Gordon wave functions in Robertson-Walker and Schwarzschild space-time. Specially, this article is that Klein-Gordon wave equations is treated by gauge fixing equations in Robertson-Walker space-time and Schwarzschild space-time.

scholarly journals Construction of Real Space{Time from Complex Linear Metric Connections

1997 ◽  
Vol 50 (4) ◽  
pp. 793
Author(s):  
P. K. Smrz
Keyword(s):  
Complex Manifold ◽  
Real Space ◽  
Space Time ◽  
Cartan Geometry ◽  
Four Dimensions ◽  
Linear Connections ◽  
Real Submanifold ◽  
Complex Linear ◽  
Case Based ◽  
Construction Works

A construction of real space-time based on metric linear connections in a complex manifold is described. The construction works only in two or four dimensions. The four-dimensional case based on a connection reducible to group U(2, 2) can generate Riemann-Cartan geometry on the real submanifold of the original complex manifold. The possibility of connecting the appearance of Dirac fields with anholonomic complex frames is discussed.

Sign in / Sign up

Export Citation Format

Share Document