Second order higher-derivative corrections in Double Field Theory

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.

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Higher-derivative heterotic Double Field Theory and classical double copy

Journal of High Energy Physics ◽

10.1007/jhep07(2021)072 ◽

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.

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Generalized dualities and higher derivatives

Journal of High Energy Physics ◽

10.1007/jhep10(2020)002 ◽

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.

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Double field theory algebroid and curved L∞-algebras

Journal of Mathematical Physics ◽

10.1063/5.0041479 ◽

2021 ◽

Vol 62 (5) ◽

pp. 052302

Author(s):

Clay James Grewcoe ◽

Larisa Jonke

Keyword(s):

Field Theory ◽

Double Field Theory

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Gauged double field theory as an L∞ algebra

Journal of High Energy Physics ◽

10.1007/jhep06(2021)058 ◽

2021 ◽

Vol 2021 (6) ◽

Author(s):

Eric Lescano ◽

Martín Mayo

Keyword(s):

Field Theory ◽

Algebraic Structure ◽

Classical Field ◽

Field Theories ◽

Lie Derivative ◽

Linear Perturbation ◽

Double Field Theory ◽

Generalized Frame ◽

Symmetry Transformations ◽

Classical Field Theories

Abstract L∞ algebras describe the underlying algebraic structure of many consistent classical field theories. In this work we analyze the algebraic structure of Gauged Double Field Theory in the generalized flux formalism. The symmetry transformations consist of a generalized deformed Lie derivative and double Lorentz transformations. We obtain all the non-trivial products in a closed form considering a generalized Kerr-Schild ansatz for the generalized frame and we include a linear perturbation for the generalized dilaton. The off-shell structure can be cast in an L3 algebra and when one considers dynamics the former is exactly promoted to an L4 algebra. The present computations show the fully algebraic structure of the fundamental charged heterotic string and the $$ {L}_3^{\mathrm{gauge}} $$ L 3 gauge structure of (Bosonic) Enhanced Double Field Theory.

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Non-Riemannian gravity actions from double field theory

Journal of High Energy Physics ◽

10.1007/jhep06(2021)173 ◽

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.

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Singularity Theorems in the Effective Field Theory for Quantum Gravity at Second Order in Curvature

Universe ◽

10.3390/universe6100171 ◽

2020 ◽

Vol 6 (10) ◽

pp. 171

Author(s):

Folkert Kuipers ◽

Xavier Calmet

Keyword(s):

Field Theory ◽

Quantum Gravity ◽

Effective Field Theory ◽

Energy Condition ◽

Null Energy Condition ◽

Effective Field ◽

Second Order ◽

Jordan Frame ◽

Singularity Theorems ◽

Massive Spin

In this paper, we discuss singularity theorems in quantum gravity using effective field theory methods. To second order in curvature, the effective field theory contains two new degrees of freedom which have important implications for the derivation of these theorems: a massive spin-2 field and a massive spin-0 field. Using an explicit mapping of this theory from the Jordan frame to the Einstein frame, we show that the massive spin-2 field violates the null energy condition, while the massive spin-0 field satisfies the null energy condition, but may violate the strong energy condition. Due to this violation, classical singularity theorems are no longer applicable, indicating that singularities can be avoided, if the leading quantum corrections are taken into account.

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