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Diego Marques

Publications and source records attributed to Diego Marques.

At least 37 records · Page 2Linked to original sources
arXiv2024

Hidden symmetries from extra dimensions

In Kaluza-Klein compactifications, some symmetries of the higher dimensional theory are preserved in lower dimensions, others are broken, and occasionally, there are symmetry enhancements. The symmetries that are enhanced by toroidal compactifications were recently shown to define a symmetry principle with constrained parameters that fixes the action before dimensional reduction. Here we show the opposite: symmetries of the higher dimensional theory that are broken in the reduction process, can actually be realized after dimensional reduction as a global symmetry principle with constrained parameters that fixes couplings in the lower dimensional theory. We implement this principle in pure gravity, half-maximal supergravity and the circle reduction of 11 dimensional supergravity to Type IIA superstring theory. As a further application, we show that it can be used to constrain the quartic Ramond-Ramond couplings in Type IIA superstring theory from the four-point $ζ(3)\, α'{}^3\, t_8 t_8 R^{(-) 4}$ interactions.

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arXiv2024

On Non Invertible Symmetries in Type IIB Supergravity

In this work, we uncover a collection of non invertible topological operators linked to the 0-, 2-, 4- and 6-form symmetries related to the type IIB superstring effective theory. By pinpointing the $\text{SL}(2,\mathbb{Z})$-covariant conserved currents corresponding to these symmetries, we first derive a set of $\text{SL}(2,\mathbb{Z})$ invariant invertible topological operators that encapsulate the integer BPS charges inherent to the theory. Moving forward, by incorporating fractional charges while maintaining gauge invariance, we introduce the non invertible topological operators for each generalized symmetry, and in particular for the $\text{SL}(2,\mathbb{Z})$ 0-form symmetry. Identifying them as a novel kind of symmetries reminiscent of fractional quantum Hall effect (FQHE)-like non invertible operators, we study their action on charged objects and their associated SymTFTs obtained via half (higher) gauging.

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arXiv2023

Exploring the $β$ symmetry of supergravity

Kaluza-Klein reductions of low energy string effective actions possess a continuous $O(d,d) $ symmetry. The non-geometric elements of this group, parameterized by a bi-vector $β$, are not inherited from the symmetries of the higher-dimensional theory, but constitute instead a symmetry enhancement produced by the isometries of the background. The realization of this enhancement in the parent theory was recently defined as $β$ symmetry, a powerful tool that allows to avoid the field reparameterizations of the Kaluza-Klein procedure. In this paper we further explore this symmetry and its impact on the first order $α'$-corrections. We derive the $β$ transformation rules from the frame formulation of Double Field Theory (DFT), and connect them to the corresponding rules in the Metsaev-Tseytlin and Bergshoeff-de Roo supergravity schemes. It follows from our results that $β$ symmetry is a necessary condition for the uplift of string $α'$-expansions to DFT.

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arXiv2023

On the Exceptional Set of Transcendental Entire Functions in Several Variables

In this paper, among other things, we prove that any subset of $\overline{\mathbb{Q}}^m$ (closed under complex conjugation and which contains the origin) is the exceptional set of uncountable many transcendental entire functions over $\mathbb{C}^m$ with rational coefficients. This result solves a several variables version of a question posed by Mahler for transcendental entire functions.

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arXiv2023

A Note On Transcendental Analytic Functions With Rational Coefficients Mapping $\mathbb{Q}$ Into Itself

In this note, the main focus is on a question about transcendental entire functions mapping $\mathbb{Q}$ into $\mathbb{Q}$ (which is related to a Mahler's problem). In particular, we prove that, for any $t>0$, there is no a transcendental entire function $f\in\mathbb{Q}[[z]]$ such that $f(\mathbb{Q})\subseteq\mathbb{Q}$ and whose denominator of $f(p/q)$ is $O(q^{t})$, for all rational numbers $p/q$, with $q$ sufficiently large.

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arXiv2022

An $α'$-complete theory of cosmology and its tensionless limit

We explore the exactly duality invariant higher-derivative extension of double field theory due to Hohm, Siegel and Zwiebach (HSZ) specialized to cosmological backgrounds. Despite featuring a finite number of derivatives in its original formulation, this theory encodes infinitely many $α'$ corrections for metric, B-field and dilaton, which are obtained upon integrating out certain extra fields. We perform a cosmological reduction with fields depending only on time and show consistency of this truncation. We compute the $α'^4$ coefficients of the general cosmological classification. As a possible model for how to deal with all $α'$ corrections in string theory we give a two-derivative reformulation in which the extra fields are kept. The corresponding Friedmann equations are then ordinary second order differential equations that capture all $α'$ corrections. We explore the tensionless limit $α'\rightarrow \infty$, which features string frame de Sitter vacua, and we set up perturbation theory in $\frac{1}{α'}$.

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arXiv2022

The $β$-symmetry of supergravity

Continuous O$(d,d)$ global symmetries emerge in Kaluza-Klein reductions of $D$-dimensional string supergravities to $D-d$ dimensions. We show that the non-geometric elements of this group effectively act in the $D$-dimensional parent theory as a hidden bosonic symmetry that fixes its couplings: the $β$-symmetry. We give the explicit $β$-transformations to first order in $α'$ and verify the invariance of the action as well as the closure of the transformation rules.

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arXiv2021

General String Cosmologies at Order $α'{}^{\,3}$

We compute the cosmological reduction of general string theories, including bosonic, heterotic and type II string theory to order $α'^{3}$, i.e., with up to eight derivatives. To this end we refine recently introduced methods that allow one to bring the reduced theory in one dimension to a canonical form with only first-order time derivatives. The resulting theories are compatible with a continuous $O(d,d,\mathbb{R})$ invariance, which in turn fixes the B-field couplings.

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arXiv2021

String Dualities at Order $α'^{\,3}$

We compute the cosmological reduction of the fourth powers of the Riemann tensor claimed to arise in string theory at order $α'^{\,3}$, with overall coefficient proportional to $ζ(3)$, and show that it is compatible with an $O(9,9)$ symmetry. This confirms the general result in string theory, due to Sen, that classical string theory with $d$-dimensional translation invariance admits an $O(d,d)$ symmetry to all orders in $α'$.

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arXiv2020

Generalized Dualities and Higher Derivatives

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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arXiv2019

On the Arithmetic Behavior of Liouville Numbers under Rational Maps

In 1972, Alniaçik proved that every strong Liouville number is mapped into the set of $U_m$-numbers, for any non-constant rational function with coefficients belonging to an $m$-degree number field. In this paper, we generalize this result by providing a larger class of Liouville numbers (which, in particular, contains the strong Liouville numbers) with this same property (this set is sharp is a certain sense).

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arXiv2019

$L_\infty$ algebras and Tensor Hierarchies in Exceptional Field Theory and Gauged Supergravity

We show how the gauge and field structure of the tensor hierarchies in Double and $E_{7(7)}$ Exceptional Field Theory fits into $L_\infty$ algebras. Special attention is paid to redefinitions, the role of covariantly constrained fields and intertwiners. The results are connected to Gauged Supergravities through generalized Scherk-Schwarz reductions. We find that certain gauging-dependent parameters generate trivial gauge transformations, giving rise to novel symmetries for symmetries that are absent in their ungauged counterparts.

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arXiv2018

On a question proposed by K. Mahler concerning Liouville numbers

In 1906, Maillet proved that given a non-constant rational function $f$, with rational coefficients, if $ξ$ is a Liouville number, then so is $f(ξ)$. Motivated by this fact, in 1984, Mahler raised the question about the existence of transcendental entire functions with this property. In this work, we provide an uncountable subset of Liouville numbers for which there exists a transcendental entire function taking this set into the set of the Liouville numbers.

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arXiv2018

Generalized Cullen Numbers in Linear Recurrence Sequences

A Cullen number is a number of the form $m2^m+1$, where $m$ is a positive integer. In 2004, Luca and St\u anic\u a proved, among other things, that the largest Fibonacci number in the Cullen sequence is $F_4=3$. Actually, they searched for generalized Cullen numbers among some binary recurrence sequences. In this paper, we will work on higher order recurrence sequences. For a given linear recurrence $(G_n)_n$, under weak assumptions, and a given polynomial $T(x)\in \mathbb{Z}[x]$, we shall prove that if $G_n=mx^m+T(x)$, then \[ m\ll\log \log |x|\log^2(\log \log |x|)\ \mbox{and}\ n\ll\log |x|\log\log |x|\log^2(\log \log |x|), \] where the implied constant depends only on $(G_n)_n$ and $T(x)$.

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arXiv2017

A stronger version of a question proposed by K. Mahler

In 1902, P. Stäckel proved the existence of a transcendental function $f(z)$, analytic in a neighbourhood of the origin, and with the property that both $f(z)$ and its inverse function assume, in this neighbourhood, algebraic values at all algebraic points. Based on this result, in 1976, K. Mahler raised the question of the existence of such functions which are analytic in $\mathbb{C}$. Recently, the authors answered positively this question. In this paper, we prove a much stronger version of this result by considering other subsets of $\mathbb{C}$.

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arXiv2017

A question proposed by K. Mahler on exceptional sets of transcendental functions with integer coefficients: solution of a Mahler's problem

In this paper, we shall prove that any subset of $\overline{\mathbb Q}\cap B(0,1)$, which is closed under complex conjugation and which contains the element $0$, is the exceptional set of uncountably many transcendental functions, analytic in the unit ball, with integer coefficients. This solves a strong version of an old question proposed by K. Mahler (1976).

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arXiv2017

The Odd story of $α'$-corrections

The $α'$-deformed frame-like Double Field Theory (DFT) is a T-duality and gauge invariant extension of DFT in which generalized Green-Schwarz transformations provide a gauge principle that fixes the higher-derivative corrections. It includes all the first order $α'$-corrections of the bosonic and heterotic string low energy effective actions and of the Hohm-Siegel-Zwiebach $α'$-geometry. Here we gauge this theory and parameterize it in terms of a frame, a two-form, a dilaton, gauge vectors and scalar fields. This leads to a unified framework that extends the previous construction by including all duality constrained interactions in generic (gauged/super)gravity effective field theories in arbitrary number of dimensions, to first order in $α'$.

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