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.

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.

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.

scholarly journals KLT factorization of winding string amplitudes

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Jaume Gomis ◽  
Ziqi Yan ◽  
Matthew Yu
Keyword(s):  
Scattering Amplitudes ◽  
Open String ◽  
Closed String ◽  
Open Strings ◽  
Toroidal Compactifications ◽  
Quantum Numbers ◽  
String Amplitudes

Abstract We uncover a Kawai-Lewellen-Tye (KLT)-type factorization of closed string amplitudes into open string amplitudes for closed string states carrying winding and momentum in toroidal compactifications. The winding and momentum closed string quantum numbers map respectively to the integer and fractional winding quantum numbers of open strings ending on a D-brane array localized in the compactified directions. The closed string amplitudes factorize into products of open string scattering amplitudes with the open strings ending on a D-brane configuration determined by closed string data.

scholarly journals GAUGE INVARIANT ACTION FOR THE OPEN BOSONIC STRING

2008 ◽  
Vol 23 (07) ◽  
pp. 1001-1017 ◽  
Author(s):  
B. SATHIAPALAN
Keyword(s):  
Partition Function ◽  
Gauge Invariance ◽  
Taylor Expansion ◽  
Bosonic String ◽  
Point Function ◽  
Gauge Invariant ◽  
Invariant Action ◽  
Pole Structure ◽  
Zero Momentum ◽  
String Amplitudes

The issue of space–time gauge invariance for the bosonic string has been earlier addressed using the loop variable formalism. In this paper the question of obtaining a gauge invariant action for the open bosonic string is discussed. The derivative with respect to ln a (where a is a worldsheet cutoff) of the partition function — which is first normalized by dividing by the integral of the two-point function of a marginal operator — is a candidate for the action. Applied to the zero-momentum tachyon it gives a tachyon potential that is similar to those that have been obtained using Witten's background independent formalism. This procedure is easily made gauge invariant in the loop variable formalism by replacing ln a by Σ which is the generalization of the Liouville mode that occurs in this formalism. We also describe a method of resumming the Taylor expansion that is done in the loop variable formalism. This allows one to see the pole structure of string amplitudes that would not be visible in the original loop variable formalism.

A FUNCTIONAL LIGHT-CONE GAUGE CONSTRUCTION OF A BOSONIC STRING COMPACTIFIED ON A TORUS

1988 ◽  
Vol 03 (02) ◽  
pp. 451-486 ◽  
Author(s):  
P.C. BRESSLOFF ◽  
J.G. TAYLOR ◽  
A. RESTUCCIA
Keyword(s):  
Open String ◽  
Bosonic String ◽  
Complex Conjugate ◽  
World Sheet ◽  
Light Cone Gauge ◽  
Open Strings ◽  
The World ◽  
Left And Right ◽  
Quantized Field ◽  
String Amplitudes

The closed bosonic string compactified on a torus is decomposed into two open strings corresponding to left and right movers respectively. Multiloop amplitudes are expressed as a product of a holomorphic and an anti-holomorphic function of the moduli of the world-sheet Riemann surface. Such a product is obtained by analytically continuing left and right open string amplitudes such that one is the complex conjugate of the other. A justification for this analytic continuation is provided using a second quantized field theory of strings. The extra parameters needed for complexification are shown to arise from the constraint expressing invariance under choice of origin for string parametrization. The chiral string is discussed.

scholarly journals Single-Valued Integration and Superstring Amplitudes in Genus Zero

2021 ◽  
Vol 382 (2) ◽  
pp. 815-874
Author(s):  
Francis Brown ◽  
Clément Dupont
Keyword(s):  
Open String ◽  
Closed String ◽  
Laurent Expansion ◽  
Tree Level ◽  
Multiple Zeta Values ◽  
Genus Zero ◽  
Period Map ◽  
Multiple Zeta ◽  
Zeta Values ◽  
String Amplitudes

AbstractWe study open and closed string amplitudes at tree-level in string perturbation theory using the methods of single-valued integration which were developed in the prequel to this paper (Brown and Dupont in Single-valued integration and double copy, 2020). Using dihedral coordinates on the moduli spaces of curves of genus zero with marked points, we define a canonical regularisation of both open and closed string perturbation amplitudes at tree level, and deduce that they admit a Laurent expansion in Mandelstam variables whose coefficients are multiple zeta values (resp. single-valued multiple zeta values). Furthermore, we prove the existence of a motivic Laurent expansion whose image under the period map is the open string expansion, and whose image under the single-valued period map is the closed string expansion. This proves the recent conjecture of Stieberger that closed string amplitudes are the single-valued projections of (motivic lifts of) open string amplitudes. Finally, applying a variant of the single-valued formalism for cohomology with coefficients yields the KLT formula expressing closed string amplitudes as quadratic expressions in open string amplitudes.

scholarly journals Closed string deformations in open string field theory. Part I. Bosonic string

2021 ◽  
Vol 2021 (9) ◽  
Author(s):  
Carlo Maccaferri ◽  
Jakub Vošmera
Keyword(s):  
Field Theory ◽  
Star Product ◽  
Open String ◽  
Closed String ◽  
Field Theories ◽  
Tree Level ◽  
Bulk Deformation ◽  
Gauge Invariant ◽  
First Order ◽  
String Background

Abstract This is the first of a series of three papers on open string field theories based on Witten star product deformed with a gauge invariant open/closed coupling. This de- formation is a tree-level tadpole which destabilizes the initial perturbative vacuum. We discuss the existence of vacuum-shift solutions which cancel the tadpole and represent a new configuration where the initial D-brane system has adapted to the change in the closed string background. As an example we consider the bulk deformation which changes the compactification radius and, to first order in the deformation, we reproduce the shift in the mass of the open string KK modes from the new kinetic operator after the vacuum shift. We also discuss the possibility of taming closed string degenerations with the open string propagator in the simplest amplitude corresponding to two closed strings off a disk.

scholarly journals LOOP VARIABLES AND THE INTERACTING OPEN STRING IN A CURVED BACKGROUND

2005 ◽  
Vol 20 (14) ◽  
pp. 1037-1045
Author(s):  
B. SATHIAPALAN
Keyword(s):  
Gauge Invariance ◽  
Equations Of Motion ◽  
Interaction Strength ◽  
Flat Space ◽  
Open String ◽  
Target Space ◽  
Gauge Invariant ◽  
Free Case ◽  
New Feature ◽  
Generally Covariant

Applying the loop variable proposal to a sigma model (with boundary) in a curved target space, we give a systematic method for writing the gauge and generally covariant interacting equations of motion for the modes of the open string in a curved background. As in the free case described in an earlier paper, the equations are obtained by covariantizing the flat space (gauge invariant) interacting equations and then demanding gauge invariance in the curved background. The resulting equation has the form of a sum of terms that would individually be gauge invariant in flat space or at zero interaction strength, but mix amongst themselves in curved space when interactions are turned on. The new feature is that the loop variables are deformed so that there is a mixing of modes. Unlike the free case, the equations are coupled, and all the modes of the open string are required for gauge invariance.

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