## What is/are Double Field?

Double Field - org/1998/Math/MathML" display="inline">^{[1]}Based on the results presented in this paper it is concluded that the race for the vaccine has had repercussions in a double field of power that was permeated by conflicting and cooperative geopolitical and geoeconomic vectors responsible for generating an asymmetrical pattern of power in which vaccines became predominantly private goods whose internalization is accessible to a restricted group of countries with medium and high per capita income.

^{[2]}We consider an $O(d,d;\mathbb{Z})$ invariant massive deformation of double field theory at the level of free theory.

^{[3]}The generalized Kerr-Schild ansatz (GKSA) is a powerful tool for constructing exact solutions in Double Field Theory (DFT).

^{[4]}We generalize the field transformations to the setting with non-anticommuting fermionic isometries and show that the resulting backgrounds are solutions of double field theory.

^{[5]}We use our result to compute the full second order Double Field Theory (DFT) for generic values of the parameters, including the generalized Green-Schwarz transformation and its invariant action.

^{[6]}A double field theory algebroid (DFT algebroid) is a special case of the metric (or Vaisman) algebroid, shown to be relevant in understanding the symmetries of double field theory.

^{[7]}A hardened HEMT structure with the gate and drain double field plates is proposed correspondingly.

^{[8]}We study target space theory on a torus for the states with NL + NR = 2 through Double Field Theory.

^{[9]}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.

^{[10]}To minimize the degradation in detection and mass resolution of spectrometer due to the wide angular and energy spared of the ions in the plasma plume, optimization of the TOF spectrometer in different configurations, single as well as a double field, is also discussed.

^{[11]}We examine various properties of double field theory and the doubled string sigma model in the context of geometric quantisation.

^{[12]}Within the framework of the flux formulation of Double Field Theory (DFT) we employ a generalised Scherk-Schwarz ansatz and discuss the classification of the twists that in the presence of the strong constraint give rise to constant generalised fluxes interpreted as gaugings.

^{[13]}This can be thought of as the worldsheet realization of the strong constraint of double field theory.

^{[14]}In this short paper, we will review the proposal of a correspondence between the doubled geometry of Double Field Theory and the higher geometry of bundle gerbes.

^{[15]}In this work we analyze the algebraic structure of Gauged Double Field Theory in the generalized flux formalism.

^{[16]}Upon treating the whole closed-string massless NS-NS sector as stringy graviton fields, Double Field Theory may evolve into `Stringy Gravity'.

^{[17]}We investigate the cosmological solutions coming from the double field theory equations of motion after coupling a matter source to them.

^{[18]}This gives rise to what is known as exceptional field theory or double field theory.

^{[19]}This generalises previous work by Morand and Park in the context of double field theory.

^{[20]}We argue that Double Field Theory (DFT) and Exceptional Field Theory (EFT) are the prime setting in which to examine such objects.

^{[21]}In this paper, firstly, an analytical model of the fringe field of deflector plates with double field input is given.

^{[22]}Birch saplings with the bar gene were resistant to a double field dose (10 L/ha), but the expression of the GS1 gene only slightly increased resistance compared to the control.

^{[23]}We show how the Wess-Zumino terms of the different branes in string theory can be embedded within double field theory.

^{[24]}We first present the classical double copy as a perturbative construction, similar to its formulation for scattering amplitudes, and then present it as an exact map, with a novel generalisation of the Kerr-Schild double copy motivated by double field theory.

^{[25]}Besides making calculations significantly easier, this approach gives a natural embedding of NATD in Double Field Theory (DFT), which provides an O(d,d) covariant formulation for effective string actions.

^{[26]}We review how a similar construction shows that locally the gauge structure of Double Field Theory corresponds to degree-2 symplectic pre-NQ manifolds.

^{[27]}The metric algebroid proposed by Vaisman (the Vaisman algebroid) governs the gauge symmetry algebra generated by the C-bracket in double field theory (DFT).

^{[28]}By doubling the target space of a canonical Courant algebroid and subsequently projecting down to a specific subbundle, we identify the data of double field theory (DFT) and hence define its algebroid structure.

^{[29]}Double Field Theory (DFT) and Exceptional Field Theory (EFT), collectively called ExFTs, have proven to be a remarkably powerful new framework for string and M-theory.

^{[30]}For the particular case of the abelian gerbe of Kalb-Ramond field, this Higher Kaluza-Klein geometry provides a natural global formulation for Double Field Theory (DFT).

^{[31]}This paper proposes how to execute the unpredictable number of math under prime field and double field utilizing java BigInteger class.

^{[32]}We then provide a duality transformation rule for the Ramond-Ramond fields by using the technique of double field theory (DFT).

^{[33]}Taking $$\mathbf {O}(D,D)$$ O ( D , D ) covariant field variables as its truly fundamental constituents, Double Field Theory can accommodate not only conventional supergravity but also non-Riemannian gravities that may be classified by two non-negative integers, $$(n,\bar{n})$$ ( n , n ¯ ).

^{[34]}If math pedagogy suffers from the lack of engaging strategies, the pedagogy of mathematical music theory must deal with the additional difficulty of double fields and double vocabulary.

^{[35]}The $\mathcal{E}$-model shares many similarities with Double Field Theory (DFT).

^{[36]}In recent work, we proposed a doubled membrane sigma-model that establishes the corresponding connection to double field theory and its algebroid structure.

^{[37]}By combining a model of teaching profession with a Bourdieu-based analysis in the interpretation of 70 interviews with secondary school teachers, we show that a double field structure has emerged in some schools, where a field of traditional teaching competes with one of new professional field teaching.

^{[38]}We study AKSZ constructions for the A and B sigma-models of topological string theory within a double field theory formulation that incorporates backgrounds with geometric and non-geometric fluxes.

^{[39]}We show that generalized supergravity can be reproduced from double field theory with the dilaton depending on a linear dual coordinate.

^{[40]}The construction extends to backgrounds for which there is no Lagrangian description -- namely magnetically charged backgrounds or those violating the strong constraint of double field theory -- at the cost of violating the Jacobi identity of the current algebra.

^{[41]}In Double Field Theory, the mass-squared of doubled fields associated with bosonic closed string states is proportional to NL + NR − 2.

^{[42]}The section condition of Double Field Theory has been argued to mean that doubled coordinates are gauged: a gauge orbit represents a single physical point.

^{[43]}Besides making calculations significantly easier, this approach gives a natural embedding of NATD in Double Field Theory (DFT), a framework which provides an O(d,d) covariant formulation for effective string actions.

^{[44]}

## double field theory

org/1998/Math/MathML" display="inline">^{[1]}We consider an $O(d,d;\mathbb{Z})$ invariant massive deformation of double field theory at the level of free theory.

^{[2]}The generalized Kerr-Schild ansatz (GKSA) is a powerful tool for constructing exact solutions in Double Field Theory (DFT).

^{[3]}We generalize the field transformations to the setting with non-anticommuting fermionic isometries and show that the resulting backgrounds are solutions of double field theory.

^{[4]}We use our result to compute the full second order Double Field Theory (DFT) for generic values of the parameters, including the generalized Green-Schwarz transformation and its invariant action.

^{[5]}A double field theory algebroid (DFT algebroid) is a special case of the metric (or Vaisman) algebroid, shown to be relevant in understanding the symmetries of double field theory.

^{[6]}We study target space theory on a torus for the states with NL + NR = 2 through Double Field Theory.

^{[7]}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.

^{[8]}We examine various properties of double field theory and the doubled string sigma model in the context of geometric quantisation.

^{[9]}Within the framework of the flux formulation of Double Field Theory (DFT) we employ a generalised Scherk-Schwarz ansatz and discuss the classification of the twists that in the presence of the strong constraint give rise to constant generalised fluxes interpreted as gaugings.

^{[10]}This can be thought of as the worldsheet realization of the strong constraint of double field theory.

^{[11]}In this short paper, we will review the proposal of a correspondence between the doubled geometry of Double Field Theory and the higher geometry of bundle gerbes.

^{[12]}In this work we analyze the algebraic structure of Gauged Double Field Theory in the generalized flux formalism.

^{[13]}Upon treating the whole closed-string massless NS-NS sector as stringy graviton fields, Double Field Theory may evolve into `Stringy Gravity'.

^{[14]}We investigate the cosmological solutions coming from the double field theory equations of motion after coupling a matter source to them.

^{[15]}This gives rise to what is known as exceptional field theory or double field theory.

^{[16]}This generalises previous work by Morand and Park in the context of double field theory.

^{[17]}We argue that Double Field Theory (DFT) and Exceptional Field Theory (EFT) are the prime setting in which to examine such objects.

^{[18]}We show how the Wess-Zumino terms of the different branes in string theory can be embedded within double field theory.

^{[19]}We first present the classical double copy as a perturbative construction, similar to its formulation for scattering amplitudes, and then present it as an exact map, with a novel generalisation of the Kerr-Schild double copy motivated by double field theory.

^{[20]}Besides making calculations significantly easier, this approach gives a natural embedding of NATD in Double Field Theory (DFT), which provides an O(d,d) covariant formulation for effective string actions.

^{[21]}We review how a similar construction shows that locally the gauge structure of Double Field Theory corresponds to degree-2 symplectic pre-NQ manifolds.

^{[22]}The metric algebroid proposed by Vaisman (the Vaisman algebroid) governs the gauge symmetry algebra generated by the C-bracket in double field theory (DFT).

^{[23]}By doubling the target space of a canonical Courant algebroid and subsequently projecting down to a specific subbundle, we identify the data of double field theory (DFT) and hence define its algebroid structure.

^{[24]}Double Field Theory (DFT) and Exceptional Field Theory (EFT), collectively called ExFTs, have proven to be a remarkably powerful new framework for string and M-theory.

^{[25]}For the particular case of the abelian gerbe of Kalb-Ramond field, this Higher Kaluza-Klein geometry provides a natural global formulation for Double Field Theory (DFT).

^{[26]}We then provide a duality transformation rule for the Ramond-Ramond fields by using the technique of double field theory (DFT).

^{[27]}Taking $$\mathbf {O}(D,D)$$ O ( D , D ) covariant field variables as its truly fundamental constituents, Double Field Theory can accommodate not only conventional supergravity but also non-Riemannian gravities that may be classified by two non-negative integers, $$(n,\bar{n})$$ ( n , n ¯ ).

^{[28]}The $\mathcal{E}$-model shares many similarities with Double Field Theory (DFT).

^{[29]}In recent work, we proposed a doubled membrane sigma-model that establishes the corresponding connection to double field theory and its algebroid structure.

^{[30]}We study AKSZ constructions for the A and B sigma-models of topological string theory within a double field theory formulation that incorporates backgrounds with geometric and non-geometric fluxes.

^{[31]}We show that generalized supergravity can be reproduced from double field theory with the dilaton depending on a linear dual coordinate.

^{[32]}The construction extends to backgrounds for which there is no Lagrangian description -- namely magnetically charged backgrounds or those violating the strong constraint of double field theory -- at the cost of violating the Jacobi identity of the current algebra.

^{[33]}In Double Field Theory, the mass-squared of doubled fields associated with bosonic closed string states is proportional to NL + NR − 2.

^{[34]}The section condition of Double Field Theory has been argued to mean that doubled coordinates are gauged: a gauge orbit represents a single physical point.

^{[35]}Besides making calculations significantly easier, this approach gives a natural embedding of NATD in Double Field Theory (DFT), a framework which provides an O(d,d) covariant formulation for effective string actions.

^{[36]}