scholarly journals O(D, D) and the string α′ expansion: an obstruction

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Stanislav Hronek ◽  
Linus Wulff
Keyword(s):  
Field Theory ◽  
String Theory ◽  
First Order ◽  
Duality Symmetry ◽  
Independent Invariant ◽  
Double Field Theory ◽  
Set Up ◽  
String Theories

Abstract Double Field Theory (DFT) is an attempt to make the O(d, d) T-duality symmetry of string theory manifest, already before reducing on a d-torus. It is known that supergravity can be formulated in an O(D, D) covariant way, and remarkably this remains true to the first order in α′. We set up a systematic way to analyze O(D, D) invariants, working order by order in fields, which we carry out up to order α′3. At order α′ we recover the known Riemann squared invariant, while at order α′2 we find no independent invariant. This is compatible with the α′ expansion in string theory. However, at order α′3 we show that there is again no O(D, D) invariant, in contradiction to the fact that all string theories have quartic Riemann terms with coefficient proportional to ζ (3). We conclude that DFT and similar frameworks cannot capture the full α′ expansion in string theory.

scholarly journals String theory at order α′2 and the generalized Bergshoeff-de Roo identification

2021 ◽  
Vol 2021 (11) ◽  
Author(s):  
Stanislav Hronek ◽  
Linus Wulff
Keyword(s):  
Field Theory ◽  
String Theory ◽  
Strong Evidence ◽  
Degrees Of Freedom ◽  
Heterotic String ◽  
Lorentz Transformations ◽  
Covariant Formalism ◽  
Double Field Theory ◽  
Two Parameter ◽  
Parameter Deformation

Abstract It has been shown by Marques and Nunez that the first α′-correction to the bosonic and heterotic string can be captured in the O(D, D) covariant formalism of Double Field Theory via a certain two-parameter deformation of the double Lorentz transformations. This deformation in turn leads to an infinite tower of α′-corrections and it has been suggested that they can be captured by a generalization of the Bergshoeff-de Roo identification between Lorentz and gauge degrees of freedom in an extended DFT formalism. Here we provide strong evidence that this indeed gives the correct α′2-corrections to the bosonic and heterotic string by showing that it leads to a cubic Riemann term for the former but not for the latter, in agreement with the known structure of these corrections including the coefficient of Riemann cubed.

scholarly journals Dynamics of perturbations in Double Field Theory & non-relativistic string theory

2015 ◽  
Vol 2015 (12) ◽  
pp. 1-33 ◽  
Author(s):  
Sung Moon Ko ◽  
Charles M. Melby-Thompson ◽  
René Meyer ◽  
Jeong-Hyuck Park
Keyword(s):  
Field Theory ◽  
String Theory ◽  
Relativistic String ◽  
Double Field Theory

scholarly journals U-duality in three and four dimensions

2017 ◽  
Vol 32 (27) ◽  
pp. 1750169 ◽  
Author(s):  
Emanuel Malek
Keyword(s):  
Field Theory ◽  
Symmetry Groups ◽  
Duality Group ◽  
Four Dimensions ◽  
Duality Symmetry ◽  
Double Field Theory ◽  
Duality Groups

Using generalised geometry we study the action of U-duality acting in three and four dimensions on the bosonic fields of 11-dimensional supergravity. We compare the U-duality symmetry with the T-duality symmetry of double field theory and see how the [Formula: see text] and [Formula: see text] U-duality groups reduce to the [Formula: see text] and [Formula: see text] T-duality symmetry groups of the type IIA theory. As examples we dualise M2-branes, both black and extreme. We find that uncharged black M2-branes become charged under U-duality, generalising the Harrison transformation, while extreme M2-branes will become new extreme M2-branes. The resulting tension and charges are quantised appropriately if we use the discrete U-duality group [Formula: see text].

scholarly journals Generalized dualities and higher derivatives

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Tomas Codina ◽  
Diego Marqués
Keyword(s):  
Field Theory ◽  
Heterotic Strings ◽  
First Order ◽  
Higher Derivative ◽  
Double Field Theory ◽  
Higher Derivatives

Abstract Generalized dualities had an intriguing incursion into Double Field Theory (DFT) in terms of local O(d, d) transformations. We review this idea and use the higher derivative formulation of DFT to compute the first order corrections to generalized dualities. Our main result is a unified expression that can be easily specified to any generalized T-duality (Abelian, non-Abelian, Poisson-Lie, etc.) or deformations such as Yang-Baxter, in any of the theories captured by the bi-parametric deformation (bosonic, heterotic strings and HSZ theory), in any supergravity scheme related by field redefinitions. The prescription allows further extensions to higher orders. As a check we recover some previously known particular examples.

scholarly journals The OD, D geometry of string theory

2014 ◽  
Vol 29 (15) ◽  
pp. 1450080 ◽  
Author(s):  
David S. Berman ◽  
Chris D. A. Blair ◽  
Emanuel Malek ◽  
Malcolm J. Perry
Keyword(s):  
Field Theory ◽  
String Theory ◽  
Covariant Derivative ◽  
Double Field Theory ◽  
Metric Connection

We construct an action for double field theory using a metric connection that is compatible with both the generalised metric and the OD, D structure. The connection is simultaneously torsionful and flat. Using this connection, one may construct a proper covariant derivative for double field theory. We then write the doubled action in terms of the generalised torsion of this connection. This action then exactly reproduces that required for double field theory and gauged supergravity.

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 Non-Riemannian isometries from double field theory

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Chris D. A. Blair ◽  
Gerben Oling ◽  
Jeong-Hyuck Park
Keyword(s):  
Field Theory ◽  
String Theory ◽  
Relativistic String ◽  
Noether Symmetries ◽  
Dimensional Algebra ◽  
Infinite Dimensional ◽  
Killing Spinors ◽  
Double Field Theory ◽  
Riemannian Geometries ◽  
Killing Equations

Abstract We explore the notion of isometries in non-Riemannian geometries. Such geometries include and generalise the backgrounds of non-relativistic string theory, and they can be naturally described using the formalism of double field theory. Adopting this approach, we first solve the corresponding Killing equations for constant flat non-Riemannian backgrounds and show that they admit an infinite-dimensional algebra of isometries which includes a particular type of supertranslations. These symmetries correspond to known worldsheet Noether symmetries of the Gomis-Ooguri non-relativistic string, which we now interpret as isometries of its non-Riemannian doubled background. We further consider the extension to supersymmetric double field theory and show that the corresponding Killing spinors can depend arbitrarily on the non-Riemannian directions, leading to “supersupersymmetries” that square to supertranslations.

scholarly journals Born sigma model for branes in exceptional geometry

2020 ◽  
Vol 2020 (7) ◽  
Author(s):  
Yuho Sakatani ◽  
Shozo Uehara
Keyword(s):  
Field Theory ◽  
String Theory ◽  
Sigma Model ◽  
Physical Space ◽  
Hermitian Manifold ◽  
Double Field Theory ◽  
M Theory

Abstract In double field theory, the physical space has been understood as a subspace of the doubled space. Recently, the doubled space has been defined as the para-Hermitian manifold and the physical space is realized as a leaf of a foliation of the doubled space. This construction naturally introduces the fundamental 2-form, which plays an important role in a reformulation of string theory known as the Born sigma model. In this paper, we present the Born sigma model for $p$-branes in M-theory and type IIB theory by extending the fundamental 2-form into $U$-duality-covariant $(p+1)$-forms.

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.

scholarly journals Double field theory algebroid and curved L∞-algebras

2021 ◽  
Vol 62 (5) ◽  
pp. 052302
Author(s):  
Clay James Grewcoe ◽  
Larisa Jonke
Keyword(s):  
Field Theory ◽  
Double Field Theory
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