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Title: Noncommutativity of closed string zero modes

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Publication Date:
Sponsoring Org.:
OSTI Identifier:
Grant/Contract Number:
SC0015655; FG02-13ER41917
Resource Type:
Journal Article: Publisher's Accepted Manuscript
Journal Name:
Physical Review D
Additional Journal Information:
Journal Volume: 96; Journal Issue: 6; Related Information: CHORUS Timestamp: 2017-09-05 16:35:15; Journal ID: ISSN 2470-0010
American Physical Society
Country of Publication:
United States

Citation Formats

Freidel, Laurent, Leigh, Robert G., and Minic, Djordje. Noncommutativity of closed string zero modes. United States: N. p., 2017. Web. doi:10.1103/PhysRevD.96.066003.
Freidel, Laurent, Leigh, Robert G., & Minic, Djordje. Noncommutativity of closed string zero modes. United States. doi:10.1103/PhysRevD.96.066003.
Freidel, Laurent, Leigh, Robert G., and Minic, Djordje. 2017. "Noncommutativity of closed string zero modes". United States. doi:10.1103/PhysRevD.96.066003.
title = {Noncommutativity of closed string zero modes},
author = {Freidel, Laurent and Leigh, Robert G. and Minic, Djordje},
abstractNote = {},
doi = {10.1103/PhysRevD.96.066003},
journal = {Physical Review D},
number = 6,
volume = 96,
place = {United States},
year = 2017,
month = 9

Journal Article:
Free Publicly Available Full Text
This content will become publicly available on September 5, 2018
Publisher's Accepted Manuscript

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  • We investigate, in the low-energy limit of the closed bosonic string theory, the role of the toroidal compactification, in which the extra spatial coordinates are circular with radius [ital R]. We explicitly show that the double limit [alpha][prime][r arrow]0 and [ital R][r arrow]0, performed on the tree scattering amplitude of four massless scalar particles, leads to four-dimensional amplitudes describing a diffusion due to the exchange of a scalar, spin-1, and spin-2 particle and that it is not influenced by the compactification procedure adopted.
  • A new Lagrangian description that interpolates between the Nambu-Goto and Polyakov version of interacting strings is given. Certain essential modifications in the Poisson bracket structure of this interpolating theory generates noncommutativity among the string coordinates for both free and interacting strings. The noncommutativity is shown to be a direct consequence of the nontrivial boundary conditions. A thorough analysis of the gauge symmetry is presented taking into account the new modified constraint algebra, which follows from the noncommutative structures and finally a smooth correspondence between gauge symmetry and reparametrization is established.
  • To study noncommutativity properties of the open string with constant B field, we construct a mechanical action that reproduces classical dynamics of the string sector under consideration. It allows one to apply the Dirac quantization procedure for constrained systems in a direct and unambiguous way. The mechanical action turns out to be the first order system without taking the strong field limit B{yields}{infinity}. In particular, it is true for the zero mode of the string coordinate, which means that the noncommutativity is an intrinsic property of this mechanical system. We describe the arbitrariness in the relation existing between the mechanicalmore » and the string variables and show that noncommutativity of the string variables on the boundary can be removed. This is in correspondence with the result of Seiberg and Witten on the relation among noncommutative and ordinary Yang-Mills theories. The recently developed soldering formalism helps us to establish a connection between the original open string action and the Polyakov action.« less
  • One of the questions concerning the covariant open string field theory is why there are two distinct BRST theories and why the four-string interaction appears in one version but not the other. The authors solve this mystery by showing that both theories are gauge-fixed versions of a higher gauge theory, called the geometric string field theory, with a new field, a string verbein e{sub {mu}{sigma}}{sup {nu}{rho}}, which allows us to gauge the string length and {sigma} parametrization. By fixing the gauge, the authors can derive the endpoint gauge (the covariantized light cone gauge), the midpoint gauge of Witten, or themore » interpolating gauge with arbitrary string length. The authors show explicitly that the four-string interaction is a gauge artifact of the geometric theory (the counterpart of the four-fermion instantaneous Coulomb term of QED). By choosing the interpolating gauge, they produce a new class of four-string interactions which smoothly interpolate between the endpoint gauge and the midpoint gauge (where it vanishes). Similarly, they can extract the closed string as a bound state of the open string, which appears in the endpoint gauge but vanishes in the midpoint gauge. Thus, the four-string and open-closed string interactions do not have to be added to the action as long as the string vierbein is included.« less
  • In this paper, a set of relative variables for the closed string with P[sup 2] [gt] O is found, which has Wigner covariance properties. They allow one to obtain global Lorentz-invariant abelianizations of the constraints, like for the open string, and then global Lorentz-invariant canonically conjugated gauge variables are found. But now there are two extra zero modes in the constraints and in the gauge variables, related to the gauge arbitrariness of the origin [sigma][sub o] of the circle [sigma][epsilon] ([minus] [pi], [pi]) embedded in Minkowski space, [sigma] [yields] x[sup [mu][sigma]]. By means of the multitemporal approach a noncanonical redundantmore » set of Dirac observables for the left and right modes is defined; they transform as spin-1 Wigner vectors and satisfy constraints of the same kind as in [sigma] models. The quantization is not made, because a canonical basis of observables is still lacking, but the program to be followed to find them is just the same as the one delineated for the case of the open string.« less