arXiv subjects

Eric Lescano

Publications and source records attributed to Eric Lescano.

31 records · Page 2Linked to original sources

arXiv2023

O$(D,D)$-covariant formulation of perfect and imperfect fluids in the double geometry

We study generic matter coupled to a $D$-dimensional supergravity using a formulation of Double Field Theory (DFT), where all the fields are encoded in O$(D,D)$ multiplets. We study both the case when the matter comes from a variational principle, as well as the case where the matter comes from a statistical or thermodynamic approach. For the latter, we construct the distribution function for the perfect fluid and its entropy current, which is a conserved quantity. We then include general viscous and elastic terms in the generalized energy-momentum tensor which, in the general case, lead to entropy production. We consistently deform the conservation law of the generalized entropy current and identify a particular non-dissipative deformation. Using the generalized fluid model, we revisit the issue of non-covariance of perfect fluids under T-dualities and we show how to resolve it in our DFT model with matter.

hep-th↗

arXiv2023

Double Field Theory with matter and the generalized Bergshoeff-de Roo identification

The scalar field-perfect fluid (sf-pf) correspondence shows that the energy-momentum tensor of a scalar field is in correspondence with the dynamics of a perfect fluid. In this work we generalize this concept to study the higher-derivative structure of Double Field Theory with statistical matter. Using the generalized Bergshoeff-de Roo identification we find nontrivial higher-derivative corrections for the generalized scalar field Lagrangian. However, these contributions are removed to any desired order using field redefinitions at the supergravity level. By virtue of the generalized sf-pf correspondence we obtain the higher-derivative dynamics for the perfect fluid in the double geometry, which is also trivialized at the supergravity level. These results imply that the well-known $α'$-corrections obtained by this procedure only correct the effective vacuum Lagrangian, while the sf-pf Lagrangian coupled to the supergravity background remains uncorrected to all orders. Our findings apply for a general (Bosonic-Heterotic-Type II-HSZ) supergravity background.

hep-th↗

arXiv2022

${\cal N}=1$ supersymmetry and Non-Riemannian Double Field Theory

We construct the ${\cal N}=1$ supersymmetric extension of Double Field Theory for Riemannian and the non-Riemannian in a unified approach. The inclusion of fermions in the double geometry force us to use the generalized frame formalism to construct the generalized flux components for these geometries. We focus on the most general prescription required to get the $D=10$ minimal supergravity model. We study how to consistently avoid the gauge fixing procedure of the double Lorentz symmetry when $n=\bar n$ and $0\le n \le 5$, which gives rise to a bigravity structure (pair of vielbeins producing the same non-Riemannian degrees of freedom). As an example we show how to to include fermionic degrees of freedom in the type I torsional Newton-Cartan (TNC) theory ($n=\bar n=1$) which is related to Carrollian geometries and stringy Newton Cartan through duality rotations and/or null reductions/uplifts.

hep-th↗

arXiv2022

${\cal N}=1$ supersymmetry in $4D$ gravity with torsion and non-metricity

We study the inclusion of fermionic degrees of freedom and ${\cal N}=1$ supersymmetry in 4-dimensional manifolds with arbitrary torsion and non-metricity tensors deforming the connection. We inspect the closure of local diffeomorphism, Lorentz and supersymmetric transformations on the vielbein and gravitino at leading order in fermions. The closure of a pair of supersymmetric transformations acting on the vielbein restricts the form of the spin connection. The dependency of the latter on the fundamental fields is exclusively given by the vielbein, up to Lorentz and/or diffeomorphisms brackets, independently of the torsion or non-metricity deformations of the affine connection, which is not restricted by supersymmetry at this order. We have then studied the couple of the Rarita-Schwinger theory to a generic gravitational Lagrangian; the supersymmetric variation of the former restricts the form of the bosonic Lagrangian in order to accomplish invariance. Special cases where $R_{μν}{}^{ab}=0$, $Q_{μνρ}=0$ or $T_{μν}{}^ρ=0$ are provided.

gr-qc↗

arXiv2022

Double Field Theory with matter and its cosmological application

The phase space formulation of Double Field Theory (DFT) indicates that statistical matter can be included in terms of (T-)duality multiplets. We propose the inclusion of a perfect fluid in the geometry of DFT through a generalized energy-momentum tensor written in terms of a DFT pressure, energy density and velocity. The latter is an $O(D,D)$ vector and satisfies two invariant constraints, in agreement with the on-shell constraints for the generalized momentum. We compute the conservation laws associated to the energy-momentum tensor considering general DFT backgrounds. Then we study cosmological backgrounds using a space-time split, and we find an expression for the DFT cosmological dynamics with the perfect fluid coupled. This proposal reproduces the equations of string cosmology upon parametrization of the DFT Einstein equations.

hep-th↗

arXiv2022

Heterotic Kerr-Schild Double Field Theory and its double Yang-Mills formulation

We present a formulation of heterotic Double Field Theory (DFT), where the fundamental fields are in $O(D,D)$ representations. The theory is obtained splitting an $O(D,D+K)$ duality invariant DFT. This procedure produces a Green-Schwarz mechanism for the generalized metric, and a fundamental gauge field which transforms as a gauge connection only to leading order. After parametrization, the former induces a non-covariant transformation on the metric tensor, which can be removed considering field redefinitions, and an ordinary Green-Schwarz mechanism on the b-field. Within this framework we explore perturbative properties of heterotic DFT. We use a relaxed version of the generalized Kerr-Schild ansatz (GKSA), where the generalized background metric is perturbed up to quadratic order considering a single null vector and the gauge field is linearly perturbed before parametrization. Finally we compare the dynamics of the gauge field and the generalized metric in order to inspect the behavior of the classical double copy correspondence at the DFT level.

hep-th↗

arXiv2021

$α'$-corrections and their double formulation

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.

hep-th↗

arXiv2021

Supersymmetry, T-duality and Heterotic $α'$-corrections

Higher-derivative interactions and transformation rules of the fields in the effective field theories of the massless string states are strongly constrained by space-time symmetries and dualities. Here we use an exact formulation of ten dimensional ${\cal N}=1$ supergravity coupled to Yang-Mills with manifest T-duality symmetry to construct the first order $α'$-corrections of the heterotic string effective action. The theory contains a supersymmetric and T-duality covariant generalization of the Green-Schwarz mechanism that determines the modifications to the leading order supersymmetry transformation rules of the fields. We compute the resulting field-dependent deformations of the coefficients in the supersymmetry algebra and construct the invariant action, with up to and including four-derivative terms of all the massless bosonic and fermionic fields of the heterotic string spectrum.

hep-th↗

arXiv2021

Higher-derivative Heterotic Double Field Theory and Classical Double Copy

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.

hep-th↗

arXiv2021

Gauged Double Field Theory as an $L_{\infty}$ algebra

$L_{\infty}$ 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 $L_{3}$ algebra and when one considers dynamics the former is exactly promoved to an $L_{4}$ algebra. The present computations show the fully algebraic structure of the fundamental charged heterotic string and the $L^{\rm{gauge}}_{3}$ structure of (Bosonic) Enhanced Double Field Theory.

hep-th↗

arXiv2020

On the phase space in Double Field Theory

We present a model of (double) kinetic theory which paves the way to describe matter in a Double Field Theory background. Generalized diffeomorphisms acting on double phase space tensors are introduced. The generalized covariant derivative is replaced by a generalized Liouville operator as it happens in relativistic kinetic theory. The section condition is consistently extended and the closure of the generalized transformations is still given by the C-bracket. In this context we propose a generalized Boltzmann equation and compute the moments of the latter, obtaining an expression for the generalized energy-momentum tensor and its conservation law.

hep-th↗

arXiv2020

$\mathcal{N}=1$ Supersymmetric Double Field Theory and the generalized Kerr-Schild Ansatz

We construct the $\mathcal{N} = 1$ supersymmetric extension of the generalized Kerr-Schild ansatz in the flux formulation of Double Field Theory. We show that this ansatz is compatible with $\mathcal{N} = 1$ supersymmetry as long as it is not written in terms of generalized null vectors. Supersymmetric consistency is obtained through a set of conditions that imply linearity of the generalized gravitino perturbation and unrestricted perturbations of the generalized background dilaton and dilatino. As a final step we parametrize the previous theory in terms of the field content of the low energy effective $10$-dimensional heterotic supergravity and we find that the perturbation of the $10$-dimensional vielbein, Kalb-Ramond field and gravitino can be written in terms of a pair of null vectors, as expected.

hep-th↗

arXiv2016

Second order higher-derivative corrections in Double Field Theory

HSZ Double Field Theory is a higher-derivative theory of gravity with exact and manifest T-duality symmetry. The first order corrections in the massless sector were shown to be governed solely by Chern-Simons deformations of the three-form field strength. We compute the full action with up to six derivatives ${\cal O} (α'{}^2)$ for the universal sector containing the metric, two-form and dilaton fields. The Green-Schwarz transformation of the two-form field remains uncorrected to second order. In addition to the expected Chern-Simons-squared and Riemann-cubed terms the theory contains a cubic Gauss-Bonnet interaction, plus other six-derivative unambiguous terms involving the three-form field strength whose presence indicates that the theory must contain further higher-derivative corrections.

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