scholarly journals T-DUALITY OF NSR SUPERSTRING: THE WORLDSHEET PERSPECTIVE

2012 ◽  
Vol 27 (23) ◽  
pp. 1250140 ◽  
Author(s):  
JNANADEVA MAHARANA
Keyword(s):  
Equations Of Motion ◽  
Bosonic String ◽  
Target Space ◽  
Vertex Operators ◽  
Covariant Form ◽  
Dimensional Torus ◽  
Duality Symmetry ◽  
Superspace Formalism ◽  
Closed Bosonic String ◽  
Equations Of Motions

We formulate target space duality symmetry of NSR superstring from the perspectives of worldsheet. The worldsheet action is presented in the superspace formalism in the presence of massless backgrounds. We start from a [Formula: see text]-dimensional target space worldsheet action and compactify the theory on a d-dimensional torus, Td. It is assumed that the backgrounds are independent of compact (super)coordinates. We adopt the formalism of our earlier work to introduce dual supercoordinates along compact directions and introduce the corresponding dual backgrounds. It is demonstrated that combined equations of motion of the two sets of coordinates can be expressed in a manifestly O(d, d) covariant form analogous to the equations of motions for closed bosonic string derived by us. Furthermore, we show that the vertex operators associated with excited massive levels of NSR string can be expressed in an O(d, d) invariant form generalizing earlier result for closed bosonic string.

scholarly journals THE WORLDSHEET PERSPECTIVE OF T-DUALITY SYMMETRY IN STRING THEORY

2013 ◽  
Vol 28 (07) ◽  
pp. 1330011 ◽  
Author(s):  
JNANADEVA MAHARANA
Keyword(s):  
String Theory ◽  
Equations Of Motion ◽  
Closed String ◽  
Invariant Form ◽  
Antisymmetric Tensor ◽  
Vertex Operators ◽  
Dimensional Torus ◽  
Duality Symmetry

The purpose of this paper is to present a pedagogical review of T-duality in string theory. The evolution of the closed string is envisaged on the worldsheet in the presence of its massless excitations. The duality symmetry is studied when some of the spacial coordinates are compactified on d-dimensional torus, Td. The known results are reviewed to elucidate that equations of motion for the compact coordinates are O(d, d) covariant, d being the number of compact directions. Next, the vertex operators of excited massive levels are considered in a simple compactification scheme. It is shown that the vertex operators for each massive level can be cast in a T-duality invariant form in such a case. Subsequently, the duality properties of superstring is investigated in the NSR formulation for the massless backgrounds such as graviton and antisymmetric tensor. The worldsheet superfield formulation is found to be very suitable for our purpose. The Hassan–Sen compactification is adopted and it is shown that the worldsheet equations of motion for compact superfields are O(d, d) covariant when the backgrounds are independent of superfields along compact directions. The vertex operators for excited levels are presented in the NS–NS sector and it is shown that they can be cast in T-duality invariant form for the case of Hassan–Sen compactification scheme. An illustrative example is presented to realize our proposal.

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.

VERTEX OPERATORS FOR THE CLOSED BOSONIC STRING THEORY AT ARBITRARY GENUS IN THE OPERATOR FORMALISM

1990 ◽  
Vol 05 (12) ◽  
pp. 2391-2409 ◽  
Author(s):  
ADRIAN R. LUGO
Keyword(s):  
String Theory ◽  
Bosonic String ◽  
Integral Approach ◽  
Vertex Operators ◽  
Operator Formalism ◽  
Covariant Derivatives ◽  
Bosonic String Theory ◽  
Dilaton Coupling ◽  
Derivatives Of ◽  
Closed Bosonic String

A systematic procedure for constructing vertex operators for the physical states of the closed bosonic string theory at genus g in the operator formalism is presented. The method is based on imposing suitable commutation relations with the generators of the conformal transformations required by unitarity of scattering amplitudes. An Arakelov-type metric on the Riemann surface naturally arises in the case of the tachyon, which allows to define vertex operators at higher levels via covariant derivatives. They involve covariant derivatives of the curvature with respect to this metric as it happens in the path integral approach. As a particular result, the Fradkin-Tseytlin dilaton coupling is obtained.

scholarly journals CLOSED BOSONIC STRING PARTITION FUNCTION IN TIME INDEPENDENT EXACT pp-WAVE BACKGROUND

2006 ◽  
Vol 21 (05) ◽  
pp. 995-1013
Author(s):  
AGAPITOS HATZINIKITAS ◽  
IOANNIS SMYRNAKIS
Keyword(s):  
Partition Function ◽  
Light Cone ◽  
Free Field ◽  
Bosonic String ◽  
Covariant Form ◽  
Modular Invariant ◽  
Light Cone Gauge ◽  
Axion Field ◽  
Pp Wave ◽  
Closed Bosonic String

The modular invariance of the one-loop partition function of the closed bosonic string in four dimensions in the presence of certain homogeneous exact pp -wave backgrounds is studied. In the absence of an axion field, the partition function is found to be modular invariant and equal to the free field partition function. The partition function remains unchanged also in the presence of a fixed axion field. However, in this case, the covariant form of the action suggests summation over all possible twists generated by the axion field. This is shown to modify the partition function. In the light-cone gauge, the axion field generates twists only in the worldsheet σ-direction, so the resulting partition function is not modular invariant, hence wrong. To obtain the correct partition function one needs to sum over twists in the t-direction as well, as suggested by the covariant form of the action away from the light-cone gauge.

scholarly journals O(D,D)-covariant two-loop β-functions and Poisson-Lie T-duality

2021 ◽  
Vol 2021 (10) ◽  
Author(s):  
Falk Hassler ◽  
Thomas B. Rochais
Keyword(s):  
Lie Symmetry ◽  
Bosonic String ◽  
Covariant Form ◽  
Quantum Regime ◽  
The One ◽  
Closed Bosonic String

Abstract We show that the one- and two-loop β-functions of the closed, bosonic string can be written in a manifestly O(D,D)-covariant form. Based on this result, we prove that1) Poisson-Lie symmetric σ-models are two-loop renormalisable and2) their β-functions are invariant under Poisson-Lie T-duality.Moreover, we identify a distinguished scheme in which Poisson-Lie symmetry is manifest. It simplifies the calculation of two-loop β-functions significantly and thereby provides a powerful new tool to advance into the quantum regime of integrable σ-models and generalised T-dualities. As an illustrating example, we present the two-loop β-functions of the integrable λ- and η-deformation.

Vertex operators of closed bosonic string

1986 ◽  
Vol 175 (4) ◽  
pp. 423-427 ◽  
Author(s):  
Ikuo Ichinose ◽  
B. Sakita
Keyword(s):  
Bosonic String ◽  
Vertex Operators ◽  
Closed Bosonic String

scholarly journals Type II DFT solutions from Poisson–Lie $T$-duality/plurality

2019 ◽  
Vol 2019 (7) ◽  
Author(s):  
Yuho Sakatani
Keyword(s):  
Field Theory ◽  
General Class ◽  
Isometry Group ◽  
Equations Of Motion ◽  
Target Space ◽  
Transformation Rule ◽  
Type Ii ◽  
Duality Transformation ◽  
Duality Symmetry ◽  
Double Field Theory

Abstract String theory has $T$-duality symmetry when the target space has Abelian isometries. A generalization of $T$-duality, where the isometry group is non-Abelian, is known as non-Abelian $T$-duality, which works well as a solution-generating technique in supergravity. In this paper we describe non-Abelian $T$-duality as a kind of $\text{O}(D,D)$ transformation when the isometry group acts without isotropy. We then provide a duality transformation rule for the Ramond–Ramond fields by using the technique of double field theory (DFT). We also study a more general class of solution-generating technique, the Poisson–Lie (PL) $T$-duality or $T$-plurality. We describe the PL $T$-plurality as an $\text{O}(n,n)$ transformation and clearly show the covariance of the DFT equations of motion by using the gauged DFT. We further discuss the PL $T$-plurality with spectator fields, and study an application to the $\text{AdS}_5\times\text{S}^5$ solution. The dilaton puzzle known in the context of the PL $T$-plurality is resolved with the help of DFT.

GENERALIZED CANONICAL QUANTIZATION OF BOSONIC STRING IN BACKGROUND FIELDS

1991 ◽  
Vol 06 (07) ◽  
pp. 1211-1231 ◽  
Author(s):  
I.L. BUCHBINDER ◽  
E.S. FRADKIN ◽  
S.L. LYAKHOVICH ◽  
V.D. PERSHIN
Keyword(s):  
Quantum Correction ◽  
Equations Of Motion ◽  
Canonical Quantization ◽  
Virasoro Algebra ◽  
Bosonic String ◽  
Classical Formulation ◽  
Weyl Ordering ◽  
Wick Ordering ◽  
Background Fields ◽  
Closed Bosonic String

The theory of a closed bosonic string interacting with background fields, namely, with metric, antisymmetric tensor of second rank and dilaton, is considered. The classical formulation of the constrained theory is developed and the canonical quantization is carried out. The combined symbols of the Virasoro operators corresponding to the Weyl ordering of zero string modes and to the Wick ordering of oscillating ones are constructed. The quantum Virasoro algebra is formulated by means of star-commutators corresponding to these symbols and the nonlocal first quantum correction in the algebra is calculated. The local part of the correction linear in curvature is derived and effective equations of motion for background fields are obtained in the lowest order.

scholarly journals Relating the b ghost and the vertex operators of the pure spinor superstring

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Osvaldo Chandia ◽  
Brenno Carlini Vallilo
Keyword(s):  
Vertex Operator ◽  
Bosonic String ◽  
Vertex Operators ◽  
Pure Spinor ◽  
Double Pole ◽  
Lorenz Gauge

Abstract The OPE between the composite b ghost and the unintegrated vertex operator for massless states of the pure spinor superstring is computed and shown to reproduce the structure of the bosonic string result. The double pole vanishes in the Lorenz gauge and the single pole is shown to be equal to the corresponding integrated vertex operator.

scholarly journals HETEROTIC T-DUALITY AND THE RENORMALIZATION GROUP

1999 ◽  
Vol 14 (14) ◽  
pp. 2257-2271 ◽  
Author(s):  
KASPER OLSEN ◽  
RICARDO SCHIAPPA
Keyword(s):  
Renormalization Group ◽  
Sigma Models ◽  
Sigma Model ◽  
Beta Function ◽  
Target Space ◽  
Loop Order ◽  
Duality Transformations ◽  
Duality Symmetry ◽  
The One ◽  
Renormalization Group Flows

We consider target space duality transformations for heterotic sigma models and strings away from renormalization group fixed points. By imposing certain consistency requirements between the T-duality symmetry and renormalization group flows, the one-loop gauge beta function is uniquely determined, without any diagram calculations. Classical T-duality symmetry is a valid quantum symmetry of the heterotic sigma model, severely constraining its renormalization flows at this one-loop order. The issue of heterotic anomalies and their cancellation is addressed from this duality constraining viewpoint.

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