# Calin Iuliu Lazaroiu

## Contact Details

NameCalin Iuliu Lazaroiu |
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## Pub CategoriesHigh Energy Physics - Theory (20) Mathematics - Differential Geometry (10) General Relativity and Quantum Cosmology (2) Cosmology and Nongalactic Astrophysics (2) Mathematics - Complex Variables (1) |

## Publications Authored By Calin Iuliu Lazaroiu

We study generalized $\alpha$-attractor models whose rescaled scalar manifold is the triply-punctured Riemann sphere $Y(2)$ endowed with its complete hyperbolic metric. Using an explicit embedding into the end compactification, we compute solutions of the cosmological evolution equations for a few globally well-behaved scalar potentials, displaying particular trajectories with inflationary behavior. In such models, the orientation-preserving isometry group of the scalar manifold is isomorphic with the permutation group on three elements, acting on $Y(2)$ as the group of anharmonic transformations. Read More

We consider generalized $\alpha$-attractor models whose scalar potentials are globally well-behaved and whose scalar manifolds are elementary hyperbolic surfaces. Beyond the Poincare disk $\mathbb{D}$, such surfaces include the hyperbolic punctured disk $\mathbb{D}^\ast$ and the hyperbolic annuli $\mathbb{A}(R)$ of modulus $\mu=2\log R>0$. For each elementary surface, we discuss its decomposition into canonical end regions and give an explicit construction of the embedding into the Kerekjarto-Stoilow compactification (which in all cases is the unit sphere), showing how this embedding allows for a universal treatment of globally well-behaved scalar potentials upon expanding their extension in real spherical harmonics. Read More

We consider the bulk algebra and topological D-brane category arising from the differential model of the open-closed B-type topological Landau-Ginzburg theory defined by a pair $(X,W)$, where $X$ is a non-compact Calabi-Yau manifold and $W$ has compact critical set. When $X$ is a Stein manifold (but not restricted to be a domain of holomorphy), we extract equivalent descriptions of the bulk algebra and of the category of topological D-branes which are constructed using only the analytic space associated to $X$. In particular, we show that the D-brane category is described by projective matrix factorizations defined over the ring of holomorphic functions of $X$. Read More

We propose a family of differential models for B-type open-closed topological Landau-Ginzburg theories defined by a pair $(X,W)$, where $X$ is any non-compact Calabi-Yau manifold and $W$ is any holomorphic complex-valued function defined on $X$ whose critical set is compact. The models are constructed at cochain level using smooth data, including the twisted Dolbeault algebra of polyvector valued forms and a twisted Dolbeault category of holomorphic factorizations of $W$. We give explicit proposals for cochain level versions of the bulk and boundary traces and for the bulk-boundary and boundary-bulk maps of the Landau-Ginzburg theory. Read More

We obtain the topological obstructions to existence of a bundle of irreducible real Clifford modules over a pseudo-Riemannian manifold $(M,g)$ of arbitrary dimension and signature and prove that bundles of Clifford modules are associated to so-called real Lipschitz structures. The latter give a generalization of spin structures based on certain groups which we call real Lipschitz groups. In the fiberwise-irreducible case, we classify the latter in all dimensions and signatures. Read More

We study stratified G-structures in ${\cal N}=2$ compactifications of M-theory on eight-manifolds $M$ using the uplift to the auxiliary nine-manifold ${\hat M}=M\times S^1$. We show that the cosmooth generalized distribution ${\hat {\cal D}}$ on ${\hat M}$ which arises in this formalism may have pointwise transverse or non-transverse intersection with the pull-back of the tangent bundle of $M$, a fact which is responsible for the subtle relation between the spinor stabilizers arising on $M$ and ${\hat M}$ and for the complicated stratified G-structure on $M$ which we uncovered in previous work. We give a direct explanation of the latter in terms of the former and relate explicitly the defining forms of the $\mathrm{SU}(2)$ structure which exists on the generic locus ${\cal U}$ of $M$ to the defining forms of the $\mathrm{SU}(3)$ structure which exists on an open subset ${\hat {\cal U}}$ of ${\hat M}$, thus providing a dictionary between the eight- and nine-dimensional formalisms. Read More

We consider spaces of "virtual" constrained generalized Killing spinors, i.e. spaces of Majorana spinors which correspond to "off-shell" $s$-extended supersymmetry in compactifications of eleven-dimensional supergravity based on eight-manifolds $M$. Read More

We summarize our geometric and topological description of compact eight-manifolds which arise as internal spaces in ${\cal N}=1$ flux compactifications of M-theory down to $\mathrm{AdS}_3$, under the assumption that the internal part of the supersymmetry generator is everywhere non-chiral. Specifying such a supersymmetric background is {\em equivalent} with giving a certain codimension one foliation defined by a closed one-form and which carries a leafwise $G_2$ structure, a foliation whose topology and geometry we characterize rigorously. Read More

Using a reconstruction theorem, we prove that the supersymmetry conditions for a certain class of flux backgrounds are equivalent with a tractable subsystem of relations on differential forms which encodes the full set of contraints arising fom Fierz identities and from the differential and algebraic conditions on the internal part of the supersymmetry generators. The result makes use of the formulation of such problems through K\"{a}hler-Atiyah bundles, which we developed in previous work. Applying this to the most general ${\cal N}=2$ flux compactifications of 11-dimensional supergravity on 8-manifolds, we can extract the conditions constraining such backgrounds and give an overview of the resulting geometry, which generalizes that of Calabi-Yau fourfolds. Read More

We use the theory of singular foliations to study ${\cal N}=1$ compactifications of eleven-dimensional supergravity on eight-manifolds $M$ down to $\mathrm{AdS}_3$ spaces, allowing for the possibility that the internal part $\xi$ of the supersymmetry generator is chiral on some locus ${\cal W}$ which does not coincide with $M$. We show that the complement $M\setminus {\cal W}$ must be a dense open subset of $M$ and that $M$ admits a singular foliation ${\bar {\cal F}}$ endowed with a longitudinal $G_2$ structure and defined by a closed one-form $\boldsymbol{\omega}$, whose geometry is determined by the supersymmetry conditions. The singular leaves are those leaves which meet ${\cal W}$. Read More

We characterize compact eight-manifolds M which arise as internal spaces in N=1 flux compactifications of M-theory down to AdS3 using the theory of foliations, for the case when the internal part of the supersymmetry generator is everywhere non-chiral. We prove that specifying such a supersymmetric background is equivalent with giving a codimension one foliation of M which carries a leafwise G2 structure, such that the O'Neill-Gray tensors, non-adapted part of the normal connection and torsion classes of the G2 structure are given in terms of the supergravity four-form field strength by explicit formulas which we derive. We discuss the topology of such foliations, showing that the C star algebra of the foliation is a noncommutative torus of dimension given by the irrationality rank of a certain cohomology class constructed from the four-form field strength, which must satisfy the Latour obstruction. Read More

We summarize a unified and computationally efficient treatment of Fierz identities for form-valued pinor bilinears in various dimensions and signatures, using concepts and techniques borrowed from a certain approach to spinors known as geometric algebra. Our formulation displays the real, complex and quaternionic structures in a conceptually clear manner, which is moreover amenable to implementation in various symbolic computation systems. Read More

We show how supersymmetry conditions for flux compactifications of supergravity and string theory can be described in terms of a flat subalgebra of the Kahler-Atiyah algebra of the compactification space, a description which has wide-ranging applications. As a motivating example, we consider the most general M-theory compactifications on eight-manifolds down to AdS3 spaces which preserve N=2 supersymmetry in 3 dimensions. We also give a brief sketch of the lift of such equations to the cone over the compactification space and of the geometric algebra approach to `constrained generalized Killing pinors', which forms the technical and conceptual core of our investigation. Read More

Motivated by open problems in F-theory, we reconsider warped compactifications of M theory on 8-manifolds to AdS3 spaces in the presence of a non-trivial field strength of the M-theory 3-form, studying the most general conditions under which such backgrounds preserve N=2 supersymmetry in three dimensions. In contrast with previous studies, we allow for the most general pair of Majorana generalized Killing pinors on the internal 8-manifold, without imposing any chirality conditions on those pinors. We also show how such pinors can be lifted to the 9-dimensional metric cone over the compactification 8-manifold. Read More

We study constrained generalized Killing spinors over the metric cone and cylinder of a (pseudo-)Riemannian manifold, developing a toolkit which can be used to investigate certain problems arising in supersymmetric flux compactifications of supergravity theories. Using geometric algebra techniques, we give conceptually clear and computationally effective methods for translating supersymmetry conditions for the metric and fluxes of the unit section of such cylinders and cones into differential and algebraic constraints on collections of differential forms defined on the cylinder or cone. In particular, we give a synthetic description of Fierz identities, which are an important ingredient of such problems. Read More

We study `constrained generalized Killing (s)pinors', which characterize supersymmetric flux compactifications of supergravity theories. Using geometric algebra techniques, we give conceptually clear and computationally effective methods for translating supersymmetry conditions into differential and algebraic constraints on collections of differential forms. In particular, we give a synthetic description of Fierz identities, which are an important ingredient of such problems. Read More

We review various generalizations of the notion of Lie algebras, in particular those appearing in the recently proposed Bagger-Lambert-Gustavsson model, and study their interrelations. We find that Filippov's n-Lie algebras are a special case of strong homotopy Lie algebras. Furthermore, we define a class of homotopy Maurer-Cartan equations, which contains both the Nahm and the Basu-Harvey equations as special cases. Read More

We extend the construction of generalized Berezin and Berezin-Toeplitz quantization to the case of compact Hodge supermanifolds. Our approach is based on certain super-analogues of Rawnsley's coherent states. As applications, we discuss the quantization of affine and projective superspaces. Read More

We study extended Berezin and Berezin-Toeplitz quantization for compact Kaehler manifolds, two related quantization procedures which provide a general framework for approaching the construction of fuzzy compact Kaehler geometries. Using this framework, we show that a particular version of generalized Berezin quantization, which we baptize "Berezin-Bergman quantization", reproduces recent proposals for the construction of fuzzy Kaehler spaces. We also discuss how fuzzy Laplacians can be defined in our general framework and study a few explicit examples. Read More

We study D-brane moduli spaces and tachyon condensation in B-type topological minimal models and their massive deformations. We show that any B-type brane is isomorphic with a direct sum of `minimal' branes, and that its moduli space is stratified according to the type of such decompositions. Using the Landau-Ginzburg formulation, we propose a closed formula for the effective deformation potential, defined as the generating function of tree-level open string amplitudes in the presence of D-branes. Read More