arXiv subjects

Sergio Luigi Cacciatori

Publications and source records attributed to Sergio Luigi Cacciatori.

33 records · Page 2Linked to original sources

arXiv2021

De Sitter magnetic black hole dipole with a supersymmetric horizon

We find a new non BPS solution in $N=2$ $D=4$ gauged supergravity coupled to $U(1)$ gauge fields and matter. It consists in a closed universe with two extremal black holes of equal size, surrounding two singularities. They have opposite magnetic charges (and no electric charges), but stay in static equilibrium thanks to the positive pressure of a cosmological constant. The geometry is perfectly symmetric under the exchange of the black holes and the flip of the sign of the charges. However the scalar field is non constant and non symmetric, with different values at the horizons, which depend on a real modulus. At one of the horizon the solution becomes $\frac 12$-BPS supersymmetric, while at the other one there is no supersymmetry, but the entropy remains independent from the scalar modulus.

hep-th↗

arXiv2021

Co-homology of Differential Forms and Feynman diagrams

In the present review we provide an extensive analysis of the intertwinement between Feynman integrals and cohomology theories in the light of the recent developments. Feynman integrals enter in several perturbative methods for solving non linear PDE, starting from Quantum Field Theories and including General Relativity and Condensed Matter Physics. Precision calculations involve several loop integrals, one strategy to address which is to bring them back in terms of linear combinations of a complete set of integrals (the Master Integrals). In this sense Feynman integrals can be thought as defining a sort of vector space to be decomposed in term of a basis. Such a task may be simpler if the vector space is endowed with a scalar product. Recently, it has been discovered that, interpreting these spaces in terms of twisted cohomology, the role of a scalar product is played by intersection products. The present review is meant to provide the mathematical tools, usually familiar to mathematicians but often not in the standard baggage of physicists, like singular, simplicial and intersection (co)homologies, hodge structures etc., apt to restate this strategy on precise mathematical grounds. It is thought to be both an introduction for beginners interested to the topic, as well as a general reference providing helpful tools for tackling the several still open problems.

hep-th↗

arXiv2020

Quantization and soliton-like solutions for the $ΦΨ$-model in a optic fiber

In the framework of a mesoscopical model for dielectric media we provide an analytical description for the electromagnetic field confined in a cylindrical cavity containing a finite dielectric sample. This system is apted to simulate the electromagnetic field in a optic fiber, in which two different regions, a vacuum region and a dielectric one, appear. A complete description for the scattering basis is introduced, together with field quantization and the two-point function. Furthermore, we also determine soliton-like solutions in the dielectric, propagating in the sample of nonlinear dielectric medium.

hep-th↗

arXiv2020

Super throats with non trivial scalars

We find new BPS solutions in $N=2$ $D=4$ Fayet-Iliopoulos gauged supergravity with STU prepotential. These are stationary solutions carrying a Kerr-Newman throat spacetime geometry and are everywhere regular. One of the three scalar vector fields is non constant. Moreover, they carry non vanishing magnetic fluxes and dipolar electric fields.

hep-th↗

arXiv2017

Projective Superspaces in Practice

We study the supergeometry of complex projective superspaces $\mathbb{P}^{n|m}$. First, we provide formulas for the cohomology of invertible sheaves of the form $\mathcal{O}_{\mathbb{P}^{n|m}} (\ell)$, that are pull-back of ordinary invertible sheaves on the reduced variety $\mathbb{P}^n$. Next, by studying the even Picard group $\mbox{Pic}_0 (\mathbb{P}^{n|m})$, classifying invertible sheaves of rank $1|0$, we show that the sheaves $\mathcal{O}_{\mathbb {P}^{n|m}} (\ell)$ are not the only invertible sheaves on $\mathbb{P}^{n|m}$, but there are also new genuinely supersymmetric invertible sheaves that are unipotent elements in the even Picard group. We study the $Π$-Picard group $\mbox{Pic}_Π(\mathbb{P}^{n|m})$, classifying $Π$-invertible sheaves of rank $1|1$, proving that there are also non-split $Π$-invertible sheaves on supercurves $\mathbb{P}^{1|m}$. Further, we investigate infinitesimal automorphisms and first order deformations of $\mathbb{P}^{n|m}$, by studying the cohomology of the tangent sheaf using a supersymmetric generalisation of the Euler exact sequence. A special special attention is paid to the meaningful case of supercurves $\mathbb{P}^{1|m}$ and of Calabi-Yau's $\mathbb{P}^{n|n+1}$. Last, with an eye to applications to physics, we show in full detail how to endow $\mathbb{P}^{1|2}$ with the structure of $\mathcal{N}=2$ super Riemann surface and we obtain its SUSY-preserving infinitesimal automorphisms from first principles, that prove to be the Lie superalgebra $\mathfrak{osp} (2|2)$. A particular effort has been devoted to keep the exposition as concrete and explicit as possible.

math.AG↗

arXiv2017

One-Dimensional Super Calabi-Yau Manifolds and their Mirrors

We apply a definition of generalised super Calabi-Yau variety (SCY) to supermanifolds of complex dimension one. One of our results is that there are two SCY's having reduced manifold equal to $\mathbb{P}^1$, namely the projective super space $\mathbb{P}^{1|2} $ and the weighted projective super space $\mathbb{WP}^{1|1}_{(2)}$. Then we compute the corresponding sheaf cohomology of superforms, showing that the cohomology with picture number one is infinite dimensional, while the de Rham cohomology, which is what matters from a physical point of view, remains finite dimensional. Moreover, we provide the complete real and holomorphic de Rham cohomology for generic projective super spaces $\mathbb P^{n|m}$. We also determine the automorphism groups: these always match the dimension of the projective super group with the only exception of $\mathbb{P}^{1|2} $, whose automorphism group turns out to be larger than the projective general linear supergroup. By considering the cohomology of the super tangent sheaf, we compute the deformations of $\mathbb{P}^{1|m}$, discovering that the presence of a fermionic structure allows for deformations even if the reduced manifold is rigid. Finally, we show that $\mathbb{P}^{1|2} $ is self-mirror, whereas $\mathbb{WP} ^{1|1}_{(2)}$ has a zero dimensional mirror. Also, the mirror map for $\mathbb{P}^{1|2}$ naturally endows it with a structure of $N=2$ super Riemann surface.

hep-th↗

arXiv2014

Iwasawa nilpotency degree of non compact symmetric cosets in N-extended Supergravity

We analyze the polynomial part of the Iwasawa realization of the coset representative of non compact symmetric Riemannian spaces. We start by studying the role of Kostant's principal SU(2)_P subalgebra of simple Lie algebras, and how it determines the structure of the nilpotent subalgebras. This allows us to compute the maximal degree of the polynomials for all faithful representations of Lie algebras. In particular the metric coefficients are related to the scalar kinetic terms while the representation of electric and magnetic charges is related to the coupling of scalars to vector field strengths as they appear in the Lagrangian. We consider symmetric scalar manifolds in N-extended supergravity in various space-time dimensions, elucidating various relations with the underlying Jordan algebras and normed Hurwitz algebras. For magic supergravity theories, our results are consistent with the Tits-Satake projection of symmetric spaces and the nilpotency degree turns out to depend only on the space-time dimension of the theory. These results should be helpful within a deeper investigation of the corresponding supergravity theory, e.g. in studying ultraviolet properties of maximal supergravity in various dimensions.

hep-th↗

arXiv2014

Perturbative photon production in a dispersive medium

We investigate photon pair-creation in a dispersive dielectric medium induced by the presence of a spacetime varying dielectric constant. Our aim is to examine the possibility to observe new phenomena of pair creation induced by travelling dielectric perturbations e.g. created by laser pulses by means of the Kerr effect. In this perspective, we adopt a semi-phenomenological version of the Hopfield model in which a space-time dependent dielectric susceptibility appears. We focus our attention on perturbation theory, and provide general formulas for the photon production induced by a local but arbitrarily spacetime dependent refractive index perturbation. As an example, we further explore the case of an uniformly travelling perturbation, and provide examples of purely time-dependent perturbations.

quant-ph↗

arXiv2013

The Physical Mirror Equivalence for the Local P^2

In this paper we consider the total space of the canonical bundle of P^2 and we use a proposal by Hosono, together with results in Seidel and Auroux-Katzarkov-Orlov, to deduce the right physical mirror equivalence between D^b(K_{P^2}) and the derived Fukaya category of its mirror. By construction, our equivalence is compatible with the mirror map between moduli spaces and with the computation of Gromov--Witten invariants.

math-ph↗

arXiv2012

Adams-Iwasawa N=8 Black Holes

We study some of the properties of the geometry of the exceptional Lie group E7(7), which describes the U-duality of the N=8, d=4 supergravity. In particular, based on a symplectic construction of the Lie algebra e7(7) due to Adams, we compute the Iwasawa decomposition of the symmetric space M=E7(7)/(SU(8)/Z_2), which gives the vector multiplets' scalar manifold of the corresponding supergravity theory. The explicit expression of the Lie algebra is then used to analyze the origin of M as scalar configuration of the "large" 1/8-BPS extremal black hole attractors. In this framework it turns out that the U(1) symmetry spanning such attractors is broken down to a discrete subgroup Z_4, spoiling their dyonic nature near the origin of the scalar manifold. This is a consequence of the fact that the maximal manifest off-shell symmetry of the Iwasawa parametrization is determined by a completely non-compact Cartan subalgebra of the maximal subgroup SL(8,R) of E7(7), which breaks down the maximal possible covariance SL(8,R) to a smaller SL(7,R) subgroup. These results are compared with the ones obtained in other known bases, such as the Sezgin-van Nieuwenhuizen and the Cremmer-Julia /de Wit-Nicolai frames.

hep-th↗

arXiv2012

The E^3/Z3 orbifold, mirror symmetry, and Hodge structures of Calabi-Yau type

Starting from the Kähler moduli space of the rigid orbifold Z=E^3/\mathbb{Z}_3 one would expect for the cohomology of the generalized mirror to be a Hodge structure of Calabi-Yau type (1,9,9,1). We show that such a structure arises in a natural way from rational Hodge structures on Λ^3 \mathbb{K}^6, \mathbb{K}=\mathbb{Q}[ω], where ωis a primitive third root of unity. We do not try to identify an underlying geometry, but we show how special geometry arises in our abstract construction. We also show how such Hodge structure can be recovered as a polarized substructure of a bigger Hodge structure given by the third cohomology group of a six-dimensional Abelian variety of Weil type.

hep-th↗

arXiv2012

Emission of correlated photon pairs from superluminal perturbations in dispersive media

We develop a perturbative theory that describes a superluminal refractive perturbation propagating in a dispersive medium and the subsequent excitation of the quantum vacuum zero-point fluctuations. We find a process similar to the anomalous Doppler effect: photons are emitted in correlated pairs and mainly within a Cerenkov-like cone, one on the forward and the other in backward directions. The number of photon pairs emitted from the perturbation increases strongly with the degree of superluminality and under realizable experimental conditions, it can reach up to ~0.01 photons per pulse. Moreover, it is in principle possible to engineer the host medium so as to modify the effective group refractive index. In the presence of "fast light" media, e.g. a with group index smaller than unity, a further ~10x enhancement may be achieved and the photon emission spectrum is characterized by two sharp peaks that, in future experiments would clearly identify the correlated emission of photon pairs.

quant-ph↗

arXiv2010

Classical theta constants vs. lattice theta series, and super string partition functions

Recently, various possible expressions for the vacuum-to-vacuum superstring amplitudes has been proposed at genus $g=3,4,5$. To compare the different proposals, here we will present a careful analysis of the comparison between the two main technical tools adopted to realize the proposals: the classical theta constants and the lattice theta series. We compute the relevant Fourier coefficients in order to relate the two spaces. We will prove the equivalence up to genus 4. In genus five we will show that the solutions are equivalent modulo the Schottky form and coincide if we impose the vanishing of the cosmological constant.

hep-th↗

arXiv2010

On the geometry of C^3/D_27 and del Pezzo surfaces

We clarify some aspects of the geometry of a resolution of the orbifold X = C3/D_27, the noncompact complex manifold underlying the brane quiver standard model recently proposed by Verlinde and Wijnholt. We explicitly realize a map between X and the total space of the canonical bundle over a degree 1 quasi del Pezzo surface, thus defining a desingularization of X. Our analysis relys essentially on the relationship existing between the normalizer group of D_27 and the Hessian group and on the study of the behaviour of the Hesse pencil of plane cubic curves under the quotient.

hep-th↗

arXiv2008

D-Branes on C^3_6 part I: prepotential and GW-invariants

This is the first of a set of papers having the aim to provide a detailed description of brane configurations on a family of noncompact threedimensional Calabi-Yau manifolds. The starting point is the singular manifold C^3/Z_6, which admits five distinct crepant resolutions. Here we apply local mirror symmetry to partially determine the prepotential encoding the GW-invariants of the resolved varieties. It results that such prepotential provides all numbers but the ones corresponding to curves having null intersection with the compact divisor. This is realized by means of a conjecture, due to S. Hosono, so that our results provide a check confirming at least in part the conjecture.

hep-th↗