396,812 research outputs found
Free Fields Equations For Space-Time Algebras With Tensorial Momentum
Free field equations, with various spins, for space-time algebras with
second-rank tensor (instead of usual vector) momentum are constructed. Similar
algebras are appearing in superstring/M theories. The most attention is payed
to the gauge invariance properties, particularly the spin two equations with
gauge invariance are constructed for dimensions 2+2 and 2+4 and connection to
Einstein equation and diffeomorphism invariance is established
Nonlinear QED and Physical Lorentz Invariance
The spontaneous breakdown of 4-dimensional Lorentz invariance in the
framework of QED with the nonlinear vector potential constraint
A_{\mu}^{2}=M^{2}(where M is a proposed scale of the Lorentz violation) is
shown to manifest itself only as some noncovariant gauge choice in the
otherwise gauge invariant (and Lorentz invariant) electromagnetic theory. All
the contributions to the photon-photon, photon-fermion and fermion-fermion
interactions violating the physical Lorentz invariance happen to be exactly
cancelled with each other in the manner observed by Nambu a long ago for the
simplest tree-order diagrams - the fact which we extend now to the one-loop
approximation and for both the time-like (M^{2}>0) and space-like (M^{2}<0)
Lorentz violation. The way how to reach the physical breaking of the Lorentz
invariance in the pure QED case taken in the flat Minkowskian space-time is
also discussed in some detail.Comment: 16 pages, 2 Postscript figures to be published in Phys. Rev.
Real Hypersurfaces of Type A in Complex Two-Plane Grassmannians Related to The Reeb Vector Field
Y. J. Suh and H. Lee (Bull. Korean. Math. Soc. 47, 551-561 (2010))
characterized real hypersurfaces of type by the invariance of vector
bundle under the shape operator and the orthogonality of
and , where , and
are the normal bundle of , K\"ahler structure and Quaternionic K\"ahler
structure of respectively. In this paper, we
characterize real hypersurfaces of type A by the invariance of the vector
bundle under the shape operator with the Reeb vector field in
.Comment: 8 page
Quantum String Dynamics in the conformal invariant SL(2,R) WZWN Background: Anti-de Sitter Space with Torsion
We consider classical and quantum strings in the conformally invariant
background corresponding to the SL(2,R) WZWN model. This background is locally
anti-de Sitter spacetime with non-vanishing torsion. Conformal invariance is
expressed as the torsion being parallelized. The precise effect of the
conformal invariance on the dynamics of both circular and generic classical
strings is extracted. In particular, the conformal invariance gives rise to a
repulsive interaction of the string with the background which precisely cancels
the dominant attractive term arising from gravity. We perform both
semi-classical and canonical string-quantization, in order to see the effect of
the conformal invariance of the background on the string mass spectrum. Both
approaches yield that the high-mass states are governed by m sim HN (N,`large
integer'), where m is the string mass and H is the Hubble constant. It follows
that the level spacing grows proportionally to N: d(m^2 alpha')/dN sim N, while
the entropy goes like: S sim sqrt{m}. Moreover, it follows that there is no
Hagedorn temperature,so that the partition function is well defined at any
positive temperature. All results are compared with the analogue results in
Anti- de Sitter spacetime, which is a non conformal invariant background.
Conformal invariance simplifies the mathematics of the problem but the physics
remains mainly unchanged. Differences between conformal and non-conformal
backgrounds only appear in the intermediate region of the string spectrum, but
these differences are minor. For low and high masses, the string mass spectra
in conformal and non-conformal backgrounds are identical. Interestingly enough,
conformal invariance fixes the value of the spacetime curvature to be -69/(26
alpha').Comment: Latex file, 23 pages, no figure
Super-Yang-Mills and M5-branes
We uplift 5-dimensional super-Yang-Mills theory to a 6-dimensional gauge
theory with the help of a space-like constant vector , whose norm
determines the Yang-Mills coupling constant. After the localization of
the 6D gauge theory acquires Lorentzian invariance as well as scale invariance.
We discuss KK states, instantons and the flux quantization. The 6D theory
admits extended solutions like 1/2 BPS `strings' and monopoles.Comment: 15 pages; minor changes, to appear in JHE
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