scholarly journals More stringy effects in target space from Double Field Theory

2020 ◽  
Vol 2020 (8) ◽  
Author(s):  
Chen-Te Ma ◽  
Franco Pezzella
Keyword(s):  
Field Theory ◽  
Space Dimension ◽  
Mass Term ◽  
Closed String ◽  
Target Space ◽  
Gauge Transformations ◽  
Double Field Theory ◽  
Quadratic Action ◽  
Lower Dimensional ◽  
Compactified Space

Abstract In Double Field Theory, the mass-squared of doubled fields associated with bosonic closed string states is proportional to NL + NR− 2. Massless states are therefore not only the graviton, anti-symmetric, and dilaton fields with (NL = 1, NR = 1) such theory is focused on, but also the symmetric traceless tensor and the vector field relative to the states (NL = 2, NR = 0) and (NL = 0, NR = 2) which are massive in the lower-dimensional non-compactified space. While they are not even physical in the absence of compact dimensions, they provide a sample of states for which both momenta and winding numbers are non-vanishing, differently from the states (NL = 1, NR = 1). A quadratic action is therefore here built for the corresponding doubled fields. It results that its gauge invariance under the linearized double diffeomorphisms is based on a generalization of the usual weak constraint, giving rise to an extra mass term for the symmetric traceless tensor field, not otherwise detectable: this can be interpreted as a mere stringy effect in target space due to the simultaneous presence of momenta and windings. Furthermore, in the context of the generalized metric formulation, a non-linear extension of the gauge transformations is defined involving the constraint extended from the weak constraint that can be uniquely defined in triple products of fields. Finally, we show that the above mentioned stringy effect does not appear in the case of only one compact doubled space dimension.

scholarly journals On the quantization of folded strings in non-critical dimensions

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Jacob Sonnenschein ◽  
Dorin Weissman
Keyword(s):  
Scalar Curvature ◽  
Space Dimension ◽  
Massive Particle ◽  
Open String ◽  
Closed String ◽  
Target Space ◽  
Critical Dimensions ◽  
Complete Set ◽  
Rotating String ◽  
Folding Point

Abstract Classical rotating closed string are folded strings. At the folding points the scalar curvature associated with the induced metric diverges. As a consequence one cannot properly quantize the fluctuations around the classical solution since there is no complete set of normalizable eigenmodes. Furthermore in the non-critical effective string action of Polchinski and Strominger, there is a divergence associated with the folds. We overcome this obstacle by putting a massive particle at each folding point which can be used as a regulator. Using this method we compute the spectrum of quantum fluctuations around the rotating string and the intercept of the leading Regge trajectory. The results we find are that the intercepts are a = 1 and a = 2 for the open and closed string respectively, independent of the target space dimension. We argue that in generic theories with an effective string description, one can expect corrections from finite masses associated with either the endpoints of an open string or the folding points on a closed string. We compute explicitly the corrections in the presence of these masses.

ADVANCES IN TERNARY AND OCTONIONIC GAUGE FIELD THEORIES

2011 ◽  
Vol 26 (18) ◽  
pp. 2997-3012 ◽  
Author(s):  
CARLOS CASTRO
Keyword(s):  
Field Theory ◽  
Gauge Field ◽  
Lie Algebra ◽  
Space Time ◽  
Time Dependent ◽  
Gauge Field Theory ◽  
Gauge Fields ◽  
Gauge Transformations ◽  
Quadratic Action ◽  
Rigid Transformations

A ternary gauge field theory is explicitly constructed based on a totally antisymmetric ternary-bracket structure associated with a 3-Lie algebra. It is shown that the ternary infinitesimal gauge transformations do obey the key closure relations [δ1, δ2] = δ3. Invariant actions for the 3-Lie algebra-valued gauge fields and scalar fields are displayed. We analyze and point out the difficulties in formulating a nonassociative octonionic ternary gauge field theory based on a ternary-bracket associated with the octonion algebra and defined earlier by Yamazaki. It is shown that a Yang–Mills-like quadratic action is invariant under global (rigid) transformations involving the Yamazaki ternary octonionic bracket, and that there is closure of these global (rigid) transformations based on constant antisymmetric parameters Λab = - Λba. Promoting the latter parameters to space–time dependent ones Λab(xμ) allows one to build an octonionic ternary gauge field theory when one imposes gauge covariant constraints on the latter gauge parameters leading to field-dependent gauge parameters and nonlinear gauge transformations. In this fashion one does not spoil the gauge invariance of the quadratic action under this restricted set of gauge transformations and which are tantamount to space–time dependent scalings (homothecy) of the gauge fields.

scholarly journals STOCHASTIC QUANTIZATION APPROACH FOR CAUSAL DYNAMICAL TRIANGULATION STRING FIELD THEORY

2013 ◽  
Vol 28 (06) ◽  
pp. 1350013 ◽  
Author(s):  
HIROSHI KAWABE
Keyword(s):  
Field Theory ◽  
String Field Theory ◽  
Continuum Limit ◽  
Geodesic Distance ◽  
Closed String ◽  
Target Space ◽  
Stochastic Quantization ◽  
Additional Interaction ◽  
Dynamical Triangulation ◽  
Baby Universe

We construct a two-dimensional (2D) causal dynamical triangulation (CDT) model from a matrix model which represents the loop gas model of closed string. The target-space index is reinterpreted as time or geodesic distance. We apply stochastic quantization method to the model to obtain the Generalized CDT (GCDT), which has additional interaction of creating baby universe. If we take a specific scaling in continuum limit, we realize an extended GCDT model characterized by the noncritical string field theory.

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.

scholarly journals α′-corrections and their double formulation

2021 ◽  
Author(s):  
Eric Lescano
Keyword(s):  
Field Theory ◽  
Graduate Students ◽  
String Theory ◽  
Closed String ◽  
Basic Knowledge ◽  
Santiago De Compostela ◽  
Double Field Theory

Abstract The present notes are based on three lectures, each ninety minutes long, prepared for the school “Integrability, Dualities and Deformations”, that ran from 23 to 27 August 2021 in Santiago de Compostela and virtually. These lectures, aimed at graduate students, require only a basic knowledge of string theory. The main goal is to introduce α′-corrections to the gravitational sector of different formulations of closed string theory and to reformulate them using novel techniques based on double field theory.

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