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 Higher-derivative heterotic Double Field Theory and classical double copy

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Eric Lescano ◽  
Jesús A. Rodríguez
Keyword(s):  
Field Theory ◽  
Exact Solutions ◽  
Maxwell Equations ◽  
Action Principle ◽  
Low Energy ◽  
Gauge Fields ◽  
Metric Tensor ◽  
Higher Derivative ◽  
Double Field Theory ◽  
Double Copy

Abstract The generalized Kerr-Schild ansatz (GKSA) is a powerful tool for constructing exact solutions in Double Field Theory (DFT). In this paper we focus in the heterotic formulation of DFT, considering up to four-derivative terms in the action principle, while the field content is perturbed by the GKSA. We study the inclusion of the generalized version of the Green-Schwarz mechanism to this setup, in order to reproduce the low energy effective heterotic supergravity upon parametrization. This formalism reproduces higher-derivative heterotic background solutions where the metric tensor and Kalb-Ramond field are perturbed by a pair of null vectors. Next we study higher-derivative contributions to the classical double copy structure. After a suitable identification of the null vectors with a pair of U(1) gauge fields, the dynamics is given by a pair of Maxwell equations plus higher derivative corrections in agreement with the KLT relation.

On the Decomposition of Spinor Fields which satisfy a Nonlinear Higher Order Equation

1983 ◽  
Vol 38 (12) ◽  
pp. 1293-1295
Author(s):  
D. Großer
Keyword(s):  
Field Theory ◽  
Higher Order ◽  
Order Equation ◽  
Field Theories ◽  
First Order ◽  
Spinor Fields ◽  
Fermion Fields ◽  
Higher Derivatives ◽  
Derivatives Of ◽  
Higher Order Equation

Abstract A field theory which is based entirely on fermion fields is non-renormalizable if the kinetic energy contains only derivatives of first order and therefore higher derivatives have to be included. Such field theories may be useful for describing preons and their interaction. In this note we show that a spinor field which satisfies a higher order field equation with an arbitrary nonlinear selfinteraction can be written as a sum of fields which satisfy first order equations.

scholarly journals Quantum Ostrogradsky theorem

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Hayato Motohashi ◽  
Teruaki Suyama
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Field ◽  
First Order ◽  
Higher Derivative ◽  
Original Theorem ◽  
Classical Lagrangian

Abstract The Ostrogradsky theorem states that any classical Lagrangian that contains time derivatives higher than the first order and is nondegenerate with respect to the highest-order derivatives leads to an unbounded Hamiltonian which linearly depends on the canonical momenta. Recently, the original theorem has been generalized to nondegeneracy with respect to non-highest-order derivatives. These theorems have been playing a central role in construction of sensible higher-derivative theories. We explore quantization of such non-degenerate theories, and prove that Hamiltonian is still unbounded at the level of quantum field theory.

scholarly journals Classical and quantum dynamics of higher-derivative systems

2017 ◽  
Vol 32 (33) ◽  
pp. 1730025 ◽  
Author(s):  
Andrei Smilga
Keyword(s):  
Field Theory ◽  
Classical Solution ◽  
Ground State ◽  
Quantum Dynamics ◽  
Higher Derivative ◽  
Higher Dimensional ◽  
Special Cases ◽  
Theory Of Everything ◽  
Higher Derivatives

A brief review of the physics of systems including higher derivatives in the Lagrangian is given. All such systems involve ghosts, i.e. the spectrum of the Hamiltonian is not bounded from below and the vacuum ground state is absent. Usually, this leads to collapse and loss of unitarity. In certain special cases, this does not happen, however, ghosts are benign. We speculate that the Theory of Everything is a higher-derivative field theory, characterized by the presence of such benign ghosts and defined in a higher-dimensional bulk. Our Universe then represents a classical solution in this theory, having the form of a 3-brane embedded in the bulk.

scholarly journals ON HIGHER DERIVATIVES AS CONSTRAINTS IN FIELD THEORY: A GEOMETRIC PERSPECTIVE

2011 ◽  
Vol 08 (08) ◽  
pp. 1687-1693 ◽  
Author(s):  
L. VITAGLIANO
Keyword(s):  
Field Theory ◽  
Hamiltonian Formulation ◽  
First Derivative ◽  
Higher Derivative ◽  
Lagrangian Field Theory ◽  
Higher Derivatives

We formalize geometrically the idea that the (de Donder) Hamiltonian formulation of a higher derivative Lagrangian field theory can be constructed understanding the latter as a first derivative theory subjected to constraints.

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 The generalized Bergshoeff-de Roo identification. Part II

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
W. Baron ◽  
D. Marques
Keyword(s):  
Field Theory ◽  
Second Order ◽  
Parameter Family ◽  
Heterotic String ◽  
Bosonic String ◽  
Invariant Action ◽  
Higher Derivative ◽  
Double Field Theory ◽  
Two Parameter

Abstract We recently introduced a T-duality covariant mechanism to compute all-order higher-derivative interactions in the heterotic string. Here we extend the formalism to account for a two-parameter family of corrections that also include the bosonic string and HSZ theory. 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.

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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