arXiv subjects

Alvaro Restuccia

Publications and source records attributed to Alvaro Restuccia.

At least 19 recordsLinked to original sources

arXiv2025

QM2-branes and the Swampland Distance Conjecture in nine dimensions

We discuss the relationship between the Swampland program and QM2-branes, which are supersymmetric M2-branes with discrete spectrum. The worldvolume description of these M2-branes is well-known. The global description is given in terms of twisted torus bundles with monodromy in $\mathrm{SL}(2,\mathbb{Z})$. In particular, we show that the towers of states that ensure the Swampland Distance Conjecture for type II maximal supergravity in nine dimensions are directly related to QM2-branes with trivial monodromy on a background that is toroidally compactified.

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arXiv2025

Torsion in M2-brane theory

We determine the role of torsion in the local and global geometrical description of M2-branes with fluxes and parabolic monodromies. The monodromy corresponds to a representation of the fundamental group of the base manifold into the parabolic subgroup of $\mbox{SL}(2,\mathbb{Z})$, the group of isotopy classes of area-preserving diffeomorphisms. These are supersymmetric M2-branes with a quantum discrete spectrum with finite multiplicity. The global description of these QM2-branes is given by twisted torus bundles with monodromy. They are classified by $\mbox{H}^2(\Sigma,\mathbb{Z}_\rho)=\mathbb{Z}\oplus \mathbb{Z}_k$, or equivalently, by the coinvariants associated with the parabolic monodromy subgroup. We generalize previous constructions in two different ways. The first one considers parabolic monodromies with $k>1$. This will allow us to identify torsion cycles of order greater than one. We find that there are well-defined nilmanifolds in three, four, and five dimensions contained in the global description of these M2-branes. These nilmanifolds are in correspondence with the nilpotent Lie algebras $g_{3,1}$, $g_{3,1}\oplus g_1$, and $g_{3,1}\oplus g_2$. All these nilmanifolds have torsion cycles of order $k$ contained in the compact sector of the target space of the M2-brane. The torsion is also manifest in the equivalence classes of M2-brane twisted torus bundles, namely coinvariants. The second one is that we analyze how the torsion acts on the coinvariants of the base manifold. Together with the flux condition, the torsion defines explicitly the number of coinvariants for a given flux and monodromy $k$.

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arXiv2024

U-duality in quantum M2-branes and gauged supergravities

In this paper, we study the relation of the M2-brane with fluxes and monodromy in $SL(2,\mathbb{Z})$, which has a quantum discrete supersymmetric spectrum with finite multiplicity, and type IIB gauged supergravities in nine dimensions. $SL(2,\mathbb{Z})$ is the group of isotopy classes of the area preserving diffeomorphisms. The global description of these M2-branes we are considering is formulated on twisted torus bundles, and they are classified in terms of $H^2(\Sigma,\mathcal{Z}_{\mathcal{\rho}})$, or equivalently, by their coinvariants for a given monodromy subgroup. We find the 'gauge' symmetries between equivalent M2-branes, on torus bundles with monodromy, that leads to $\mathbb{R}$, $SO(2)$ or $SO(1,1)$, the symmetry groups of type IIB gauged supergravities in 9d. We obtain an explicit relation between the equivalent classes of M2-brane bundles and the mass parameters that classify the gaugings of type IIB supergravities in 9d. We also find that the symmetries, between inequivalent M2-branes on twisted torus bundles for a given monodromy, are related with $\mathbb{Z}$, $\mathcal{Z}_3$, $\mathcal{Z}_5$, $\mathcal{Z}_9$ or $\mathcal{Z}_{2n-7}$ for $n\geq 5$, the U-duality symmetry group, a subgroup of $SL(2,\mathbb{Z})$. In distinction, in the case without monodromy, related to type II maximal supergravity at low energies, its U-duality group corresponds to the full $SL(2,\mathbb{Z})$.

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arXiv2023

Gravitational-gauge vector interaction in the Hořava-Lifshitz framework

An anisotropic model describing gravity--vector gauge coupling at all energy scales is presented. The starting point is the 4+1 dimensional non--projectable Hořava--Lifshitz gravity theory subject to a geometrical restriction. Renormalizability arguments require all possible interactions in the potential up to terms with $z=4$ spatial derivatives on the geometrical tensor fields: the Riemann and Weyl tensors. The latter being necessary on a 4+1 dimensional formulation. The dimensional reduction to 3+1 dimensions give rise to a model invariant under {foliation--preserving diffeomorphisms} (FDiff) and $U(1)$ symmetry groups. The reduced theory on the {kinetic conformal} (KC) point ($λ=1/3$), propagates the same spectrum of the Einstein--Maxwell theory. Moreover, at low energies, on the IR point $α=0$, $β=1$, its field equations are exactly the Einstein--Maxwell ones in a particular gauge condition. The Minkowski ground state is stable provided several restrictions on the coupling parameters are satisfied, they are explicitly obtained. The quantum propagators of the physical degrees of freedom are obtained and after an analysis of the first and second class constraints the renormalizability by power counting is proved, provided that the aforementioned restrictions on the coupling parameters are satisfied.

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arXiv2023

Type IIB parabolic ($p,q$)-strings from M2-branes with fluxes

We extend the work of Schwarz [1] to show that bound states of type IIB supersymmetric ($p, q$)-strings on a circle are associated with M2-branes irreducibly wrapped on $T^2$, or equivalently with nontrivial worldvolume fluxes. Beyond this extension we consider the Hamiltonian of an M2-brane with $C_{\pm}$ fluxes formulated on a symplectic torus bundle with monodromy. In particular, we analyze the relevant case when the monodromy is parabolic. We show that the Hamiltonian is defined in terms of the coinvariant module. We also find that the mass operator is invariant under transformations between inequivalent coinvariants. These coinvariants classify the inequivalent classes of twisted torus bundles with nontrivial monodromy for a given flux. We obtain their associated ($p,q$)-strings via double dimensional reduction, which are invariant under a parabolic subgroup of $SL(2,\mathbb{Q})$. This is the origin of the gauge symmetry of the associated gauged supergravity. These bound states could also be related to the parabolic Scherk-Schwarz reductions of type IIB string theory.

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arXiv2021

Wave zone in the Hořava-Lifshitz theory at the kinetic-conformal point in the low energy regime

We show that in the Hořava-Lifshitz theory at the kinetic-conformal point, in the low energy regime, a wave zone for asymptotically flat fields can be consistently defined. In it, the physical degrees of freedom, the transverse traceless tensorial modes, satisfy a linear wave equation. The Newtonian contributions, among which there are terms which manifestly break the relativistic invariance, are non-trivial but do not obstruct the free propagation (radiation) of the physical degrees of freedom. For an appropriate value of the couplings of the theory, the wave equation becomes the relativistic one in agreement with the propagation of the gravitational radiation in the wave zone of General Relativity. Previously to the wave zone analysis, and in general grounds, we obtain the physical Hamiltonian of the Hořava-Lifshitz theory at the kinetic-conformal point in the constrained submanifold. We determine the canonical physical degrees of freedom in a particular coordinate system. They are well defined fuctions of the transverse-traceless modes of the metric and coincide with them in the wave zone and also at linearized level.

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arXiv2021

Charged Throats in the Hořava--Lifshitz Theory

A spherically symmetric solution of the field equations of the Hořava--Lifshitz gravity--gauge vector interaction theory is obtained and analyzed. It describes a charged throat. The solution exists provided a restriction on the relation between the mass and charge is satisfied. The restriction reduces to the Reissner--Nordström one in the limit in which the coupling constants tend to the relativistic values of General Relativity. We introduce the correct charts to describe the solution across the entire manifold, including the throat connecting an asymptotic Minkowski space--time with a singular 3+1 dimensional manifold. The solution external to the throat on the asymptotically flat side tends to the Reissner--Nordström space--time at the limit when the coupling parameter, associated with the term in the low energy Hamiltonian that manifestly breaks the relativistic symmetry, tends to zero. Also, when the electric charge is taken to be zero the solution becomes the spherically symmetric and static solution of the Hořava--Lifshitz gravity.

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arXiv2019

Pure electromagnetic-gravitational interaction in Hořava-Lifshitz theory at the kinetic conformal point

We introduce the electromagnetic-gravitational coupling in the Hořava-Lifshitz framework, in $3+1$ dimensions, by considering the Hořava-Lifshitz gravity theory in $4+1$ dimensions at the kinetic conformal point and then performing a Kaluza-Klein reduction to $3+1$ dimensions. The action of the theory is second order in time derivatives and the potential contains only higher order spacelike derivatives up to $z=4$, $z$ being the critical exponent. These terms include also higher order derivative terms of the electromagnetic field. The propagating degrees of freedom of the theory are exactly the same as in the Einstein-Maxwell theory. We obtain the Hamiltonian, the field equations and show consistency of the constraint system. The kinetic conformal point is protected from quantum corrections by a second class constraint. At low energies the theory depends on two coupling constants, $β$ and $α$. We show that the anisotropic field equations for the gauge vector is a deviation of the covariant Maxwell equations by a term depending on $β-1$. Consequently, for $β=1$, Maxwell equations arise from the anisotropic theory at low energies. We also prove that the anisotropic electromagnetic-gravitational theory at the IR point $β=1$, $α=0$, is exactly the Einstein-Maxwell theory in a gravitational gauge used in the ADM formulation of General Relativity.

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arXiv2019

Classification of M2-brane 2-torus bundles, U-duality invariance and type II gauged supergravities

In this paper we obtain the complete classification of the inequivalent classes of M2-brane symplectic torus bundles with monodromy in $SL(2,Z)$ and their precise U-duality relations among them. There are eight inequivalent classes of bundles whose monodromy groups, at low energies, are in correspondence with the gauging groups of the eight type II gauged supergravities in nine dimensions. Four of those have been previously found and they correspond to the 'type IIB side'. In this paper we provide the explicit realization of the remaining four classes associated to the 'type IIA side'. The precise M2-brane U-duality relations between the eight inequivalent classes of bundles have allowed to identified the remaining four ones. We conjecture that the classes of gaugings -- classifying the eight types of II gauged supergravity in nine dimensions -- are determined by the inequivalent coinvariant classes associated to the base and the fiber of the supermembrane bundles and their duals.

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arXiv2018

The anisotropic coupling of gravity and electromagnetism in Hořava-Lifshitz theory

We analyze the electromagnetic-gravity interaction in a pure Hořava-Lifshitz framework. To do so we formulate the Hořava-Lifshitz gravity in $4+1$ dimensions and perform a Kaluza-Klein reduction to $3+1$ dimensions. We use this reduction as a mathematical procedure to obtain the $3+1$ coupled theory, which at the end is considered as a fundamental, self-consistent, theory. The critical value of the dimensionless coupling constant in the kinetic term of the action is $λ=1/4$. It is the kinetic conformal point for the non-relativistic electromagnetic-gravity interaction. In distinction, the corresponding kinetic conformal value for pure Hořava-Lifshitz gravity in $3+1$ dimensions is $λ=1/3$. We analyze the geometrical structure of the critical and noncritical cases, they correspond to different theories. The physical degrees of freedom propagated by the noncritical theory are the transverse traceless graviton, the transverse gauge vector and two scalar fields. In the critical theory one of the scalars is absent, only the dilaton scalar field is present. The gravity and vector excitations propagate with the same speed, which at low energy can be taken to be the speed of light. The field equations for the gauge vector in the non-relativistic theory have exactly the same form as the relativistic electromagnetic field equations arising from the Kaluza-Klein reduction of General Relativity, and are equal to them for a particular value of one of the coupling constants. The potential in the Hamiltonian is a polynomial of finite degree in the gauge vector and its covariant derivatives.

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arXiv2018

A new integrable equation valued on a Cayley-Dickson algebra

We introduce a new integrable equation valued on a Cayley-Dickson (C-D) algebra. In the particular case in which the algebra reduces to the complex one the new interacting term in the equation cancells and the equation becomes the known Korteweg-de Vries equation. For each C-D algebra the equation has an infinite sequence of local conserved quantities. We obtain a Bäcklund transformation in the sense of Walhquist-Estabrook for the equation for any Cayley-Dickson algebra, and relate it to a generalized Gardner equation. From it, the infinite sequence of conserved quantities follows directly. We give the explicit expression for the first few of them. From the Bäcklund transformation we get the Lax pair and the one-soliton and two-soliton solutions generalizing the known solutions for the quaternion valued KdV equation. From the Gardner equation we obtain the generalized modified KdV equation which also has an infinite sequence of conserved quantities. The new integrable equation is preserved under a subgroup of the automorphisms of the C-D algebra. In the particular case of the algebra of octonions, the equation is invariant under $SU(3)$.

math-ph↗

arXiv2017

On the space of solutions of the Horava theory at the kinetic-conformal point

The nonprojectable Horava theory at the kinetic-conformal point is defined by setting a specific value of the coupling constant of the kinetic term of the Lagrangian. This formulation has two additional second class-constraints that eliminate the extra mode. We show that the space of solutions of this theory in the Hamiltonian formalism is bigger than the space of solutions in the original Lagrangian formalism. In the Hamiltonian formalism there are certain configurations for the Lagrange multupliers that lead to solutions that cannot be found in the original Lagrangian formulation. We show specific examples in vacuum and with a source. The solution with the source has homogeneous and isotropic spatial hypersurfaces. The enhancement of the space of solutions leaves the possibility that new solutions applicable to cosmology, or to other physical systems, can be found in the Hamiltonian formalism.

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arXiv2017

Einstein's quadrupole formula from the kinetic-conformal Horava theory

We analyze the radiative and nonradiative linearized variables in a gravity theory within the familiy of the nonprojectable Horava theories, the Horava theory at the kinetic-conformal point. There is no extra mode in this formulation, the theory shares the same number of degrees of freedom with general relativity. The large-distance effective action, which is the one we consider, can be given in a generally-covariant form under asymptotically flat boundary conditions, the Einstein-aether theory under the condition of hypersurface orthogonality on the aether vector. In the linearized theory we find that only the transverse-traceless tensorial modes obey a sourced wave equation, as in general relativity. The rest of variables are nonradiative. The result is gauge-independent at the level of the linearized theory. For the case of a weak source, we find that the leading mode in the far zone is exactly Einstein's quadrupole formula of general relativity, if some coupling constants are properly identified. There are no monopoles nor dipoles in this formulation, in distinction to the nonprojectable Horava theory outside the kinetic-conformal point. We also discuss some constraints on the theory arising from the observational bounds on Lorentz-violating theories.

gr-qc↗

arXiv2016

Quantization of the Horava theory at the kinetic-conformal point

The Horava theory depends on several coupling constants. The kinetic term of its Lagrangian depends on one dimensionless coupling constant lambda. For the particular value lambda = 1/3 the kinetic term becomes conformal invariant, although the full Lagrangian does not have this symmetry. For any value of lambda the nonprojectable version of the theory has second-class constraints which play a central role in the process of quantization. Here we study the complete nonprojectable theory, including the Blas-Pujolas-Sibiryakov interacting terms, at the kinetic-conformal point lambda = 1/3. The generic counting of degrees of freedom indicates that this theory propagates the same physical degrees of freedom of General Relativity. We analyze this point rigorously taking into account all the z=1,2,3 terms that contribute to the action describing quadratic perturbations around the Minkowski spacetime. We show that the constraints of the theory and equations determining the Lagrange multipliers are strongly elliptic partial differential equations, an essential condition for a constrained phase-space structure in field theory. We show how their solutions lead to the two independent tensorial physical modes propagated by the theory. We also obtain the reduced Hamiltonian. These arguments strengthen the consistency of the theory. We find the restrictions on the space of coupling constants to ensure the positiveness of the reduced Hamiltonian. We obtain the propagator of the physical modes, showing that there are not ghosts and that the propagator effectively acquires the z=3 scaling for all physical degrees of freedom at the high energy regime. By evaluating the superficial degree of divergence, taking into account the second-class constraints, we show that the theory is power-counting renormalizable. ...

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arXiv2015

10D Massive Type IIA Supergravities as the uplift of Parabolic M2-brane Torus bundles

We remark that the two 10D massive deformations of the $N=2$ maximal type IIA supergravity (Romans and HLW supergravity) are associated to the low energy limit of the uplift to 10D of M2-brane torus bundles with parabolic monodromy linearly and non-linearly realized respectively. Romans supergravity corresponds to M2-brane compactified on a twice-punctured torus bundle.

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arXiv2015

Wormholes in Horava gravity with cosmological constant

By combining analytical and numerical methods we find that the solutions of the complete Horava theory with negative cosmological constant that satisfy the conditions of staticity, spherical symmetry and vanishing of the shift function are two kinds of geometry: (i) a wormhole-like solution with two sides joined by a throat and (ii) a single side with a naked singularity at the origin. We study the second-order effective action. We consider the case when the coupling constant of the (partial ln N)^2 term, which is the unique deviation from general relativity in the effective action, is small. At one side the wormhole acquires a kind of deformed AdS asymptotia and at the other side there is an asymptotic essential singularity. The deformation of AdS essentially means that the lapse function N diverges asymptotically a bit faster than AdS. This can also be interpreted as an anisotropic Lifshitz scaling that the solutions acquire asymptotically.

gr-qc↗

arXiv2014

Wormholes and naked singularities in the complete Horava theory

We find the static spherically symmetric solutions (with vanishing shift function) of the complete nonprojectable Horava theory explicitly, writing the space-time metrics as explicit tensors in local coordinate systems. This completes previous works of other authors that have studied the same configurations. The solutions depend on the coupling constant alpha of the (partial_i ln N)^2 term. The lambda = 1/3 case of the theory does not possess any extra mode, hence the range of alpha is in principle not limited by the linear stability of any extra mode. We study the full range of alpha, both in the positive and negative sectors. We find the same wormhole solutions and naked singularities that were found for the Einstein-aether theory in a sector of the space of alpha. There also arise wormholes in other sector of alpha. Our coordinate systems are valid at the throats of the wormholes. We also find the perturbative solutions for small alpha. We give this version of the solutions directly on the original radial coordinate r, which is particularly suitable for representing the exterior region of solutions with localized sources.

gr-qc↗

arXiv2012

Non-perturbative analysis of the gravitational energy in Hořava Theory

We perform a non-perturbative analysis of the constraints of the Hořava Gravitational theory. In distinction to Einstein gravity the theory has constraints of the first class together with second class ones. We analyze the consequences of having to impose second classes constraints at any time in the quantum formulation of the theory. The second class constraints are formulated as strongly elliptic partial differential equations allowing a global analysis on the existence and uniqueness of the solution. We discuss the possibility of formulating the theory in terms of a master action with first class constraints only. In this case the Hořava theory would correspond to a gauged fixed version of the master theory. Finally we obtain, using the non-perturbative solution of the constraints, the explicit expression of the gravitational energy. It is, under some assumptions, always positive and the solution of Hořava field equations at minimal energy is the Minkowski metric.

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