scholarly journals Canonical approach to the closed string non-commutativity

2014 ◽  
Vol 12 (2) ◽  
pp. 101-110
Author(s):  
Ljubica Davidovic ◽  
Bojan Nikolic ◽  
Branislav Sazdovic
Keyword(s):  
Dual Space ◽  
Closed String ◽  
Bosonic String ◽  
Poisson Brackets ◽  
Dual Theory ◽  
Duality Transformation ◽  
Original Theory ◽  
Canonical Variables ◽  
Canonical Approach ◽  
Closed Bosonic String

We consider the propagation of the closed bosonic string in the weakly curved background. We show that the closed string non-commutativity is essentially connected to the T-duality and nontrivial background. From the T-duality transformation laws, connecting the canonical variables of the original and T-dual theory, we find the structure of the Poisson brackets in the T-dual space corresponding to the fundamental Poisson brackets in the original theory. We find that the commutative original theory is equivalent to the non-commutative T-dual theory, in which Poisson brackets close on winding and momenta numbers and the coefficients are proportional to the background fluxes.

scholarly journals DUALITY OF THE SUPERSTRING IN SUPERSPACE

1994 ◽  
Vol 09 (15) ◽  
pp. 1361-1368 ◽  
Author(s):  
ASHOK DAS ◽  
JNANADEVA MAHARANA
Keyword(s):  
Explicit Form ◽  
Tensor Field ◽  
Bosonic String ◽  
Dual Theory ◽  
Duality Transformation ◽  
First Order ◽  
Duality Transformations ◽  
Antisymmetric Tensor Field ◽  
Closed Bosonic String ◽  
Model Action

The evolution of a closed NSR string is considered in the background of constant graviton and antisymmetric fields. The σ-model action is written in a manifestly supersymmetric form in terms of superfields. The first order formalism adopted for the closed bosonic string is generalized to implement duality transformations and the constant dual backgrounds are obtained for the dual theory. We recover the G→G−1 duality for the case when antisymmetric tensor field is set to zero. Next, the case when the backgrounds depend on one superfield, is also analyzed. This scenario is similar to the cosmological case envisaged for the bosonic string. The explicit form of the duality transformation is given for this case.

TOROIDAL COMPACTIFICATION OF OPEN AND CLOSED BOSONIC STRINGS

1988 ◽  
Vol 03 (06) ◽  
pp. 571-579 ◽  
Author(s):  
DAVID C. DUNBAR
Keyword(s):  
Bosonic Strings ◽  
Open String ◽  
Closed String ◽  
Bosonic String ◽  
Duality Transformation ◽  
Open Strings ◽  
Closed Bosonic String

Using the duality transformation between open string loops and closed string exchanges, the known compactifications of the closed bosonic string on tori described by even self-dual lattices are coupled to similarly compactified open strings.

OPEN STRINGS AS Z2-ORBIFOLDS OF CLOSED STRINGS

1991 ◽  
Vol 06 (27) ◽  
pp. 2483-2496
Author(s):  
GREG NAGAO
Keyword(s):  
Open String ◽  
Closed String ◽  
Bosonic String ◽  
Modular Invariant ◽  
Open Strings ◽  
Loop Expansion ◽  
Invariant Formulation ◽  
Closed Bosonic String ◽  
String Theories

We present a modular invariant formulation of the open string in terms of the closed string. Chan–Paton factors are understood as multiplicities which arise from a factorization of the closed string. This interpretation of the Chan–Paton factors suggests that the SO (2D/2) open string is consistent to all orders of the loop expansion. We show that the open string may be viewed as a Z2-orbifold of the closed string. Relations are found between various string theories which seem to reinforce an earlier suggestion by Freund that all string theories are derivable from the D = 26 orientable closed bosonic string.

scholarly journals LOOP VARIABLES AND GAUGE INVARIANCE IN CLOSED BOSONIC STRING THEORY

2004 ◽  
Vol 19 (38) ◽  
pp. 2857-2870 ◽  
Author(s):  
B. SATHIAPALAN
Keyword(s):  
Gauge Invariance ◽  
Open String ◽  
Closed String ◽  
Bosonic String ◽  
Tree Level ◽  
Gauge Invariant ◽  
Open Strings ◽  
Invariant Description ◽  
String Amplitudes ◽  
Closed Bosonic String

We extend an earlier proposal for a gauge-invariant description of off-shell open strings (at tree level), using loop variables, to off-shell closed strings (at tree level). The basic idea is to describe the closed string amplitudes as a product of two open string amplitudes (using the technique of Kawai, Lewellen and Tye). The loop variable techniques that were used earlier for open strings can be applied here mutatis mutandis. It is a proposal for a theory whose on-shell amplitudes coincide with those of the closed bosonic string in 26 dimensions. It is also gauge-invariant off-shell. As was the case with the open string, the interacting closed string looks like a free closed string thickened to a band.

scholarly journals Effective theories of two T-dual theories are also T-dual

2019 ◽  
Vol 79 (9) ◽  
Author(s):  
Ljubica Davidović ◽  
Branislav Sazdović
Keyword(s):  
Boundary Conditions ◽  
Dirichlet Boundary ◽  
Open String ◽  
Closed String ◽  
Bosonic String ◽  
Dirichlet Boundary Conditions ◽  
Dual Theory ◽  
Effective Theories ◽  
String Theories

Abstract We investigate how T-duality and solving the boundary conditions of the open bosonic string are related. We start by considering the T-dualization of the open string moving in the constant background. We take that the coordinates of the initial theory satisfy either Neumann or Dirichlet boundary conditions. It follows that the coordinates of T-dual theory satisfy exactly the opposite set of boundary conditions. We treat the boundary conditions of both theories as constraints, and apply the Dirac procedure to them, which results in forming $$\sigma $$σ-dependent constraints. We solve these constraints and obtain the effective theories for the solution. We show that the effective closed string theories are also T-dual.

STRING EQUATIONS OF MOTION FROM VANISHING CURVATURE

1991 ◽  
Vol 06 (08) ◽  
pp. 1319-1333 ◽  
Author(s):  
MARK J. BOWICK ◽  
KONG-QING YANG
Keyword(s):  
Vector Bundles ◽  
Adiabatic Approximation ◽  
Equations Of Motion ◽  
Bosonic String ◽  
Complex Structures ◽  
Closed Bosonic String

The equations of motion for the massless modes of the closed bosonic string are obtained in the adiabatic approximation from the requirement of the vanishing of the curvature of appropriate vector bundles over the space of complex structures Diff S1/S1. This vanishing is required for physical states to be independent of string parametrization.

scholarly journals STRING-LOOP CORRECTIONS TO EFFECTIVE ACTION AND BLACK HOLE INSTABILITIES

1995 ◽  
Vol 10 (07) ◽  
pp. 575-585
Author(s):  
V. V. BELOKUROV ◽  
M. Z. IOFA
Keyword(s):  
Black Hole ◽  
String Theory ◽  
Effective Action ◽  
Black Hole Solution ◽  
Bosonic String ◽  
Superstring Theory ◽  
Integration Measure ◽  
String Loop ◽  
Bosonic String Theory ◽  
Closed Bosonic String

Following the ideas of Ref. 3, to account for instability of 2-D black hole solution, we discuss possible imaginary string-loop corrections to the coefficient at the Einstein term in string effective action (EA). In closed bosonic string theory, such corrections appear because of the tachyon contribution to the integration measure over the moduli. In superstring theory, several possible sources of complex one-string-loop contributions to the EA are considered. It is argued that none of them can account for complex corrections to the Einstein term in the effective action.

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