arXiv subjects

Camilo las Heras

Publications and source records attributed to Camilo las Heras.

5 recordsLinked to original sources

arXiv2026

Bordisms between 9d type IIB supergravities and commutator widths of duality groups

We study the topological properties of bordisms interpolating between different 9d gauged supergravities obtained from compactification of type IIB string theory on $\mathbb{S}^1$ with a non-trivial $\mathsf{SL}(2,\mathbb{Z})$ bundle. We describe how such bordisms implement the needed monodromies through stacks of $[p,q]$ 7-branes or gravitational solitons of non-trivial topology. For the later mechanism, we see that the topology of the bordism becomes increasingly complicated for large monodromies, which results in the associated bordisms being arbitrarily suppressed, against expectations on the breaking of global symmetries in Quantum Gravity. Motivated by this, we propose a refinement of the Swampland Cobordism Conjecture for the first bordism group $Ω_1({\rm B}G)$ with a $G$ duality bundle. We argue that even if gravitational solitons can realize the monodromies associated with elements of the commutator subgroup of $G$, if the number of needed commutators is unbounded (in other words, the commutator width of $G$ diverges) then an infinite number of duality defects realizing elements in $G$ need to be included. We test this proposal for different duality groups $G$, and see that our expectations are realized, often in non-trivial ways.

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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 $\mbox{H}^2(Σ,\mathbb{Z}_ρ)=\mathbb{Z}\oplus \mathbb{Z}_k$, 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 $H^2(Σ,\mathcal{Z}_{\mathcalρ})$, 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

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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