scholarly journals Non-Riemannian gravity actions from double field theory

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
A. D. Gallegos ◽  
U. Gürsoy ◽  
S. Verma ◽  
N. Zinnato
Keyword(s):  
Field Theory ◽  
Quantum Gravity ◽  
Condensed Matter ◽  
Equations Of Motion ◽  
Technical Note ◽  
Action Principle ◽  
Relativistic Symmetry ◽  
Gravitational Theories ◽  
Double Field Theory

Abstract Non-Riemannian gravitational theories suggest alternative avenues to understand properties of quantum gravity and provide a concrete setting to study condensed matter systems with non-relativistic symmetry. Derivation of an action principle for these theories generally proved challenging for various reasons. In this technical note, we employ the formulation of double field theory to construct actions for a variety of such theories. This formulation helps removing ambiguities in the corresponding equations of motion. In particular, we embed Torsional Newton-Cartan gravity, Carrollian gravity and String Newton-Cartan gravity in double field theory, derive their actions and compare with the previously obtained results in literature.

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.

Equations of motion in double field theory: From particles to scale factors

2011 ◽  
Vol 84 (12) ◽  
Author(s):  
Nahomi Kan ◽  
Koichiro Kobayashi ◽  
Kiyoshi Shiraishi
Keyword(s):  
Field Theory ◽  
Equations Of Motion ◽  
Scale Factors ◽  
Double Field Theory

scholarly journals Perturbative quantum gravity in double field theory

2016 ◽  
Vol 2016 (4) ◽  
pp. 1-38 ◽  
Author(s):  
Rutger H. Boels ◽  
Christoph Horst
Keyword(s):  
Field Theory ◽  
Quantum Gravity ◽  
Double Field Theory ◽  
Perturbative Quantum

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 Effective field theory approach to modified gravity including Horndeski theory and Hořava–Lifshitz gravity

2014 ◽  
Vol 23 (13) ◽  
pp. 1443008 ◽  
Author(s):  
Ryotaro Kase ◽  
Shinji Tsujikawa
Keyword(s):  
Field Theory ◽  
Effective Field Theory ◽  
Modified Gravity ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Power Spectra ◽  
Effective Field ◽  
Theory Approach ◽  
Gravitational Theories ◽  
Wide Range

In this paper, we review the effective field theory of modified gravity in which the Lagrangian involves three-dimensional geometric quantities appearing in the 3+1 decomposition of spacetime. On the flat isotropic cosmological background, we expand a general action up to second-order in the perturbations of geometric scalars, by taking into account spatial derivatives higher than two. Our analysis covers a wide range of gravitational theories — including Horndeski theory/its recent generalizations and the projectable/nonprojectable versions of Hořava–Lifshitz gravity. We derive the equations of motion for linear cosmological perturbations and apply them to the calculations of inflationary power spectra as well as the dark energy dynamics in Galileon theories. We also show that our general results conveniently recover stability conditions of Hořava–Lifshitz gravity already derived in the literature.

scholarly journals Least action principle and gravitational double layer

2020 ◽  
Vol 35 (02n03) ◽  
pp. 2040002 ◽  
Author(s):  
Victor Berezin ◽  
Vyacheslav Dokuchaev ◽  
Yury Eroshenko ◽  
Alexei Smirnov
Keyword(s):  
Shock Wave ◽  
Double Layer ◽  
Equations Of Motion ◽  
Action Principle ◽  
Least Action Principle ◽  
Least Action ◽  
The Least Action Principle ◽  
Higher Derivative ◽  
Gravitational Theories ◽  
New Phenomena

The higher derivative gravitational theories exhibit new phenomena absent in General Relativity. One of them is the possible formation of the so called double layer which is the pure gravitational phenomenon and can be interpreted, in a sense, as the gravitational shock wave. In this paper we show how some very important features of the double layer equations of motion can be extracted straight from the least action principle.

scholarly journals GLOBAL DEFECTS IN FIELD THEORY WITH APPLICATIONS TO CONDENSED MATTER

2005 ◽  
Vol 19 (17) ◽  
pp. 801-819 ◽  
Author(s):  
D. BAZEIA ◽  
J. MENEZES ◽  
R. MENEZES
Keyword(s):  
Field Theory ◽  
Condensed Matter ◽  
Equations Of Motion ◽  
Scalar Fields ◽  
Higher Dimensions ◽  
Spatial Dimension ◽  
Specific Form ◽  
First Order ◽  
Real Scalar ◽  
First Order Differential Equations

We review investigations on defects in systems described by real scalar fields in (D, 1) space-time dimensions. We first work in one spatial dimension, with models described by one and two real scalar fields, and in higher dimensions. We show that when the potential assumes specific form, there are models which support stable global defects for D arbitrary. We also show how to find first-order differential equations that solve the equations of motion, and how to solve models in D dimensions via soluble problems in D = 1. We illustrate the procedure examining specific models and showing how they may be used in applications in different contexts in condensed matter physics, and in other areas.

scholarly journals Supergravity solution-generating techniques and canonical transformations of σ-models from O(D, D)

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Riccardo Borsato ◽  
Sibylle Driezen
Keyword(s):  
Field Theory ◽  
Equations Of Motion ◽  
Canonical Transformations ◽  
Strong Constraint ◽  
Duality Transformations ◽  
Double Field Theory ◽  
Supergravity Solution

Abstract 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. We analyse the various possibilities of turning on the fluxes Hijk, Fijk, Qijk and Rijk, and the solutions for the twists allowed in each case. While we do not impose the DFT (or equivalently supergravity) equations of motion, our results provide solution-generating techniques in supergravity when applied to a background that does solve the DFT equations. At the same time, our results give rise also to canonical transformations of 2-dimensional σ-models, a fact which is interesting especially because these are integrability-preserving transformations on the worldsheet. Both the solution-generating techniques of supergravity and the canonical transformations of 2-dimensional σ-models arise as maps that leave the generalised fluxes of DFT and their flat derivatives invariant. These maps include the known abelian/non-abelian/Poisson-Lie T-duality transformations, Yang-Baxter deformations, as well as novel generalisations of them.

Integrability: From Statistical Systems to Gauge Theory

2019 ◽  
Keyword(s):  
Field Theory ◽  
Gauge Theory ◽  
Summer School ◽  
Condensed Matter ◽  
Theoretical Physics ◽  
Conformal Field ◽  
The Past ◽  
Background Material ◽  
Supersymmetric Gauge ◽  
Statistical Systems

This volume contains lectures delivered at the Les Houches Summer School ‘Integrability: from statistical systems to gauge theory’ held in June 2016. The School was focussed on applications of integrability to supersymmetric gauge and string theory, a subject of high and increasing interest in the mathematical and theoretical physics communities over the past decade. Relevant background material was also covered, with lecture series introducing the main concepts and techniques relevant to modern approaches to integrability, conformal field theory, scattering amplitudes, and gauge/string duality. The book will be useful not only to those working directly on integrablility in string and guage theories, but also to researchers in related areas of condensed matter physics and statistical mechanics.

Sign in / Sign up

Export Citation Format

Share Document