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 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 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 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.

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 1+1 DIMENSIONAL NCOS AND ITS U(N) GAUGE THEORY DUAL

2001 ◽  
Vol 16 (05) ◽  
pp. 922-935 ◽  
Author(s):  
IGOR R. KLEBANOV ◽  
JUAN MALDACENA
Keyword(s):  
Gauge Theory ◽  
Electric Field ◽  
Electric Fields ◽  
Degrees Of Freedom ◽  
Finite Energy ◽  
Open String ◽  
Closed String ◽  
Dual Theory ◽  
Open Strings ◽  
Electric Flux

We study some aspects of open string theories on D-branes with critical electric fields. We show that the massless open string modes that move in the direction of the electric field decouple. In the 1+1 dimensional case the dual theory is U(N) SYM with electric flux, and the decoupling of massless open strings is dual to the decoupling of the U(1) degrees of freedom. We also show that, if the direction along the electric field is compact, then there are finite energy winding closed string modes. They are dual to Higgs branch excitations of the SYM theory, and their energetics works accordingly. These properties provide new non-trivial evidence for the duality.

scholarly journals ACTION FOR (FREE) OPEN STRING MODES IN AdS SPACE USING THE LOOP VARIABLE APPROACH

2007 ◽  
Vol 22 (02) ◽  
pp. 107-117 ◽  
Author(s):  
B. SATHIAPALAN
Keyword(s):  
Equations Of Motion ◽  
Flat Space ◽  
Open String ◽  
Closed String ◽  
Group Method ◽  
Open Strings ◽  
Variable Approach ◽  
Massive Spin ◽  
Complete Treatment ◽  
Space Case

The loop variable technique (for open strings in flat space) is a gauge-invariant generalization of the renormalization group method for obtaining equations of motion. Unlike the beta functions, which are only proportional to the equations of motion, here it gives the full equation of motion. In an earlier paper, a technique was described for adapting this method to open strings in gravitational backgrounds. However, unlike the flat space case, these equations cannot be derived from an action and are therefore not complete. This is because there are ambiguities in the method that involve curvature couplings that cannot be fixed by appealing to gauge invariance alone but need a more complete treatment of the closed string background. An indirect method to resolve these ambiguities is to require symmetricity of the second derivatives of the action. In general this will involve modifying the equations by terms with arbitrarily high powers of curvature tensors. This is illustrated for the massive spin-two field. It is shown that in the special case of an AdS or dS background, the exact action can easily be determined in this way.

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.

scholarly journals NONCOMMUTATIVE HOMOTOPY ALGEBRAS ASSOCIATED WITH OPEN STRINGS

2007 ◽  
Vol 19 (01) ◽  
pp. 1-99 ◽  
Author(s):  
HIROSHIGE KAJIURA
Keyword(s):  
Algebraic Structure ◽  
Minimal Model ◽  
Decomposition Theorem ◽  
Open String ◽  
Closed String ◽  
Field Theories ◽  
Homotopy Algebras ◽  
General Properties ◽  
Open Strings

We discuss general properties of A∞-algebras and their applications to the theory of open strings. The properties of cyclicity for A∞-algebras are examined in detail. We prove the decomposition theorem, which is a stronger version of the minimal model theorem, for A∞-algebras and cyclic A∞-algebras and discuss various consequences of it. In particular, it is applied to classical open string field theories and it is shown that all classical open string field theories on a fixed conformal background are cyclic A∞-isomorphic to each other. The same results hold for classical closed string field theories, whose algebraic structure is governed by cyclic L∞-algebras.

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