Exact classical solution of the equation of motion for the Rarita-Schwinger Majorana field and topology of flat space in supergravity

Tensor models can be interpreted as theory of dynamical fuzzy spaces. In this paper, I study numerically the fluctuation spectra around a Gaussian classical solution of a tensor model, which represents a fuzzy flat space in arbitrary dimensions. It is found that the momentum distribution of the low-lying low-momentum spectra is in agreement with that of the metric tensor modulo the general coordinate transformation in the general relativity at least in the dimensions studied numerically, i.e. one to four dimensions. This result suggests that the effective field theory around the solution is described in a similar manner as the general relativity.

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WEAK FIELD EXPANSION OF GRAVITY: GRAPHS, MATRICES AND TOPOLOGY

International Journal of Modern Physics A ◽

10.1142/s0217751x99001366 ◽

1999 ◽

Vol 14 (17) ◽

pp. 2705-2743

Author(s):

SHOICHI ICHINOSE ◽

NORIAKI IKEDA

Keyword(s):

Graphical Representation ◽

Young Tableau ◽

Flat Space ◽

Weak Field ◽

Main Theme ◽

Leading Order ◽

Group Approach ◽

And Topology ◽

Diagram Approach ◽

Scalar Gravity

We present some approaches to the perturbative analysis of the classical and quantum gravity. First we introduce a graphical representation for a global SO (n) tensor (∂)dhαβ, which generally appears in the weak field expansion around the flat space: gμν=δμν+hμν. Making use of this representation, we explain (1) Generating function of graphs (Feynman diagram approach), (2) Adjacency matrix (Matrix approach), (3) Graphical classification in terms of "topology indices" (Topology approach), (4) The Young tableau (Symmetric group approach). We systematically construct the global SO (n) invariants. How to show the independence and completeness of those invariants is the main theme. We explain it taking simple examples of ∂∂h-, and (∂∂h)2-invariants in the text. The results are applied to the analysis of the independence of general invariants and (the leading order of) the Weyl anomalies of scalar-gravity theories in "diverse" dimensions (2,4,6,8,10 dimensions).

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ON SPIN-STATISTICS AND BOGOLIUBOV TRANSFORMATIONS IN FLAT SPACE–TIME WITH ACCELERATION CONDITIONS

International Journal of Modern Physics A ◽

10.1142/s0217751x13500085 ◽

2013 ◽

Vol 28 (02) ◽

pp. 1350008 ◽

Cited By ~ 14

Author(s):

MICHAEL R. R. GOOD

Keyword(s):

Gordon Equation ◽

Flat Space ◽

Equation Of Motion ◽

Space Time ◽

Unruh Effect ◽

Constant Acceleration ◽

Klein Gordon ◽

External Conditions ◽

Bogoliubov Transformations ◽

Far Future

A single real scalar field of spin zero obeying the Klein–Gordon equation in flat space–time under external conditions is considered in the context of the spin-statistics connection. An imposed accelerated boundary on the field is made to become, in the far future, (1) asymptotically inertial and (2) asymptotically noninertial (with an infinite acceleration). The constant acceleration Unruh effect is also considered. The systems involving nontrivial Bogoliubov transformations contain dynamics which point to commutation relations. Particles described by in-modes obey the same statistics as particles described by out-modes. It is found in the nontrivial systems that the spin-statistics connection can be manifest from the acceleration. The equation of motion for the boundary which forever emits thermal radiation is revealed.

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EXACT SOLUTIONS IN OPEN BOSONIC STRING FIELD THEORY AND MARGINAL DEFORMATION IN CFT

International Journal of Modern Physics A ◽

10.1142/s0217751x04019329 ◽

2004 ◽

Vol 19 (27) ◽

pp. 4695-4713 ◽

Cited By ~ 12

Author(s):

J. KLUSOŇ

Keyword(s):

Field Theory ◽

Exact Solution ◽

Conformal Field Theory ◽

Exact Solutions ◽

Classical Solution ◽

String Field Theory ◽

Equation Of Motion ◽

Bosonic String ◽

Conformal Field ◽

Marginal Deformation

In this paper we continue our study of the exact solution in open bosonic string field theory. We present new solution in the string field theory defined on the background corresponding to the boundary conformal field theory describing D25-brane. Then we will study the fluctuation modes around this solution and we determine their basic properties from the linearized equation of motion of the string field theory defined above the classical solution.

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