skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Normal ordering and non(anti)commutativity in open super strings

Abstract

Nonanticommutativity in an open super string moving in the presence of a background antisymmetric tensor field B{sub {mu}}{sub {nu}} is investigated in a conformal field theoretic approach, leading to nonanticommutative structures. In contrast to several discussions, in which boundary conditions are taken as Dirac constraints, we first obtain the mode algebra by using the newly proposed normal ordering, which satisfies both equations of motion and boundary conditions. Using these the anticommutator among the fermionic string coordinates is obtained. Interestingly, in contrast to the bosonic case, this new normal ordering plays an important role in uncovering the underlying nonanticommutative structure between the fermionic string coordinates. We feel that our approach is more transparent than the previous ones and the results we obtain match with the existing results in the literature.

Authors:
 [1];  [2]
  1. S. N. Bose National Centre for Basic Sciences, JD Block, Sector III, Salt Lake, Kolkata-700098 (India)
  2. Sundarban Mahavidyalaya, Kakdwip, South 24 Parganas, West-Bengal (India)
Publication Date:
OSTI Identifier:
21020205
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. D, Particles Fields; Journal Volume: 75; Journal Issue: 6; Other Information: DOI: 10.1103/PhysRevD.75.065026; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; ALGEBRA; BOUNDARY CONDITIONS; COMMUTATION RELATIONS; CONFORMAL INVARIANCE; COORDINATES; EQUATIONS OF MOTION; FERMIONS; QUANTUM FIELD THEORY; STRING MODELS; TENSOR FIELDS

Citation Formats

Gangopadhyay, Sunandan, and Hazra, Arindam Ghosh. Normal ordering and non(anti)commutativity in open super strings. United States: N. p., 2007. Web. doi:10.1103/PHYSREVD.75.065026.
Gangopadhyay, Sunandan, & Hazra, Arindam Ghosh. Normal ordering and non(anti)commutativity in open super strings. United States. doi:10.1103/PHYSREVD.75.065026.
Gangopadhyay, Sunandan, and Hazra, Arindam Ghosh. Thu . "Normal ordering and non(anti)commutativity in open super strings". United States. doi:10.1103/PHYSREVD.75.065026.
@article{osti_21020205,
title = {Normal ordering and non(anti)commutativity in open super strings},
author = {Gangopadhyay, Sunandan and Hazra, Arindam Ghosh},
abstractNote = {Nonanticommutativity in an open super string moving in the presence of a background antisymmetric tensor field B{sub {mu}}{sub {nu}} is investigated in a conformal field theoretic approach, leading to nonanticommutative structures. In contrast to several discussions, in which boundary conditions are taken as Dirac constraints, we first obtain the mode algebra by using the newly proposed normal ordering, which satisfies both equations of motion and boundary conditions. Using these the anticommutator among the fermionic string coordinates is obtained. Interestingly, in contrast to the bosonic case, this new normal ordering plays an important role in uncovering the underlying nonanticommutative structure between the fermionic string coordinates. We feel that our approach is more transparent than the previous ones and the results we obtain match with the existing results in the literature.},
doi = {10.1103/PHYSREVD.75.065026},
journal = {Physical Review. D, Particles Fields},
number = 6,
volume = 75,
place = {United States},
year = {Thu Mar 15 00:00:00 EDT 2007},
month = {Thu Mar 15 00:00:00 EDT 2007}
}
  • Boundary conditions play a nontrivial role in string theory. For instance, the rich structure of D-branes is generated by choosing appropriate combinations of Dirichlet and Neumann boundary conditions. Furthermore, when an antisymmetric background is present at the string end points (corresponding to mixed boundary conditions) space time becomes noncommutative there. We show here how to build up normal ordered products for bosonic string position operators that satisfy both equations of motion and open string boundary conditions at the quantum level. We also calculate the equal time commutator of these normal ordered products in the presence of an antisymmetric tensor background.
  • Noncommutativity in an open bosonic string moving in the presence of a background Neveu-Schwarz two-form field B{sub {mu}}{sub {nu}} is investigated in a conformal field theory approach, leading to noncommutativity at the boundaries. In contrast to several discussions, in which boundary conditions are taken as Dirac constraints, we first obtain the mode algebra by using the newly proposed normal ordering, which satisfies both equations of motion and boundary conditions. Using these the commutator among the string coordinates is obtained. Interestingly, this new normal ordering yields the same algebra between the modes as the one satisfying only the equations of motion.more » In this approach, we find that noncommutativity originates more transparently, and our results match with the existing results in the literature.« less
  • Sr 2RuO 4, an unconventional superconductor, is known to possess an incommensurate spin-density wave instability driven by Fermi surface nesting. Here we report a static spin-density wave ordering with a commensurate propagation vector q c = (0.250.250) in Fe-doped Sr 2RuO 4, despite the magnetic fluctuations persisting at the incommensurate wave vectors q ic = (0.30.3L) as in the parent compound. The latter feature is corroborated by the first-principles calculations, which show that Fe substitution barely changes the nesting vector of the Fermi surface. Finally, these results suggest that in addition to the known incommensurate magnetic instability, Sr 2RuO 4more » is also in proximity to a commensurate magnetic tendency that can be stabilized via Fe doping.« less
  • We compute analytically the small-scale temperature fluctuations of the cosmic microwave background from cosmic (super-)strings and study the dependence on the string intercommuting probability P. We develop an analytical model which describes the evolution of a string network and calculate the numbers of string segments and kinks in a horizon volume. Then we derive the probability distribution function (pdf) which takes account of finite angular resolution of observation. The resultant pdf consists of a Gaussian part due to frequent scatterings by long string segments and a non-Gaussian tail due to close encounters with kinks. The dispersion of the Gaussian partmore » is reasonably consistent with that obtained by numerical simulations by Fraisse et al.. On the other hand, the non-Gaussian tail contains two phenomenological parameters which are determined by comparison with the numerical results for P = 1. Extrapolating the pdf to the cases with P < 1, we predict that the non-Gaussian feature is suppressed for small P.« less