arXiv subjects

A. Sagnotti

Publications and source records attributed to A. Sagnotti.

At least 19 recordsLinked to original sources

arXiv2026

On Cosmologies and Vacua Driven by Tension and Curvatures

We investigate the effects of the exponential potentials typical of non-supersymmetric strings in cosmologies whose spatial and internal slices are maximally symmetric spaces with curvatures labeled by a pair of integers $k$ and $k'$ ($=\pm 1$). We classify the solutions according to their singularity structure and asymptotic behavior and present a semi-quantitative picture of the generic dynamics in the physically most relevant cases with flat spatial slices. The analysis relies on exact solutions emerging when one of the effects dominates, special solutions arising when two or more effects are comparable, scaling asymptotics, and some numerical tests.

hep-th↗

arXiv2025

Supersymmetry Breaking with Fields, Strings and Branes

The first part of this review tries to provide a self-contained view of supersymmetry breaking from the bottom-up perspective. We thus describe N=1 supersymmetry in four dimensions, the Standard Model and the MSSM, with emphasis on the ``soft terms'' that can link it to supergravity. The second part deals with the top-down perspective. It addresses, insofar as possible in a self-contained way, the basic setup provided by ten-dimensional strings and their links with supergravity, toroidal orbifolds, Scherk-Schwarz deformations and Calabi-Yau reductions, before focusing on a line of developments that is closely linked to our own research. Its key input is drawn from ten-dimensional non-tachyonic string models where supersymmetry is absent or non-linearly realized, and runaway ``tadpole potentials'' deform the ten-dimensional Minkowski vacua. We illustrate the perturbative stability of the resulting most symmetrical setups, which are the counterparts of circle reduction but involve internal intervals. We then turn to a discussion of fluxes in Calabi-Yau vacua and the KKLT setup, and conclude with some aspects of Cosmology, emphasizing some intriguing clues that the tadpole potentials can provide for the onset of inflation. The appendices collect some useful material on global and local N=1 supersymmetry, in components and in superspace, on string vacuum amplitudes, and on convenient tools used to examine the fluctuations of non-supersymmetric string vacua.

hep-th↗

arXiv2025

On Pre-Inflationary non Gaussianities

We explore the three-point amplitude of curvature perturbations in scenarios suggested by high-scale supersymmetry breaking in String Theory, where the inflaton is forced to climb a steep exponential potential. We can do it at the price of some simplifications, and more importantly with some assumptions on the softening effects of String Theory. These suggest a scenario proposed long ago by Gasperini and Veneziano, where the initial singularity is replaced by a bounce, and the resulting analysis rests on a scale $\Delta$ that leaves some signs in the angular power spectrum of the CMB. The amplitude comprises two types of contribution: the first oscillates around the original result of Maldacena and gives no further prospects to detect a non-Gaussian signal, but the second, which is subtly tied to the turning point at the end of the climbing phase, within the window 62<N<66 for the inflationary e-folds could be compatible with Planck constraints and potentially observable. The amplitudes involving the tensor modes contain only the first type of contribution.

hep-th↗

arXiv2024

Brane Profiles of Non-Supersymmetric Strings

We connect the indications of 2D CFT for branes in non-supersymmetric strings to actual spacetime profiles, taking the bulk tadpole potentials into account. We find exact solutions for the uncharged branes that spread in the internal intervals of Dudas-Mourad vacua for non-tachyonic orientifolds and heterotic strings. These solutions involve suitable dressings of the uncharged branes of the nine-dimensional tadpole-free theory. Similar exact results for uncharged branes that are transverse to the internal space, or for charged branes, appear more challenging. Nevertheless, we identify their large-distance behavior, which is determined by linearized equations, and show that it is compatible with the CFT analysis in all expected cases. We also provide some hints on the leading back-reaction of the form-fields.

hep-th↗

arXiv2024

Brane-Like Solutions and Other Non-Supersymmetric Vacua

After recasting the standard charged and uncharged brane profiles in the harmonic gauge, we explore solutions with the same isometries where the potentials $V = T \,e^{γ\,ϕ}$ of ten-dimensional non-supersymmetric strings are taken into account. Combining a detailed catalog of the possible asymptotics with some numerical results suggests that these spherically symmetric backgrounds terminate at singularities within finite proper distances.

hep-th↗

arXiv2023

Effective Orientifolds from Broken Supersymmetry

We recently proposed a class of type IIB vacua that yield, at low energies, four--dimensional Minkowski spaces with broken supersymmetry and a constant string coupling. They are compactifications with an internal five-torus bearing a five--form flux $Φ$ and warp factors depending on a single coordinate. The breaking of supersymmetry occurs when the internal space includes a finite interval. A probe-brane analysis revealed a gravitational repulsion and a charge attraction of equal magnitude from the left end of the interval, and a singularity at the other end. Here we complete the analysis revealing the presence, at one end, of an effective $O3$ of negative tension and positive five--form charge. We also determine the values of these quantities, and show that $T = -\, Q = Φ$, and characterize the singularity present at the other end of the interval, which hosts an opposite charge. Finally, we discuss various forms of the gravity action in the presence of a boundary and identify a self--adjoint form for its fluctuations.

hep-th↗

arXiv2023

A 4D IIB Flux Vacuum and Supersymmetry Breaking. II. Bosonic Spectrum and Stability

We recently constructed type-IIB compactifications to four dimensions depending on a single additional coordinate, where a five-form flux $Φ$ on an internal torus leads to a constant string coupling. Supersymmetry is fully broken when the internal manifold includes a finite interval of length $\ell$, which is spanned by a conformal coordinate in a finite range $0 < z < z_m$. Here we examine the low-lying bosonic spectra and their classical stability, paying special attention to self-adjoint boundary conditions. Special boundary conditions result in the emergence of zero modes, which are determined exactly by first-order equations. The different sectors of the spectrum can be related to Schrödinger operators on a finite interval, characterized by pairs of real constants $μ$ and $\tildeμ$, with $μ$ equal to ${1}/{3}$ or ${2}/{3}$ in all cases and different values of $\tildeμ$. The potentials behave as $\frac{μ^2-1/4}{z^2}$ and $\frac{\tildeμ^2-1/4}{\left(z_m-z\right)^2}$ near the ends and can be closely approximated by exactly solvable trigonometric ones. With vanishing internal momenta, one can thus identify a wide range of boundary conditions granting perturbative stability, despite the intricacies that emerge in some sectors. For the Kaluza--Klein excitations of non-singlet vectors and scalars the Schrödinger systems couple pairs of fields, and the stability regions, which depend on the background, widen as the ratio $Φ/{\ell^4}$ decreases.

hep-th↗

arXiv2023

Non-Supersymmetric Vacua and Self-Adjoint Extensions

Internal intervals spanned by finite ranges of a conformal coordinate $z$ and terminating at a pair of singularities are a common feature of many string compactifications with broken supersymmetry. The squared masses emerging in lower-dimensional Minkowski spaces are then eigenvalues of Schrödinger-like operators, whose potentials have double poles at the ends of the intervals. For one-component systems, the possible self-adjoint extensions of Schrödinger operators are described by points in $AdS_3 \times S^1$, and those corresponding to independent boundary conditions at the ends of the intervals by points on the boundary of $AdS_3$. The perturbative stability of compactifications to Minkowski space time depends, in general, on these choices of self-adjoint extensions. We apply this setup to the orientifold vacua driven by the ``tadpole potential'' $V=T \ e^{\,\frac{3}{2}\,ϕ}$ and find, in nine dimensions, a massive scalar spectrum, a unique choice of boundary conditions with stable tensor modes and a massless graviton, and a wide range of choices leading to massless and/or massive vector modes.

hep-th↗

arXiv2022

A 4D IIB Flux Vacuum and Supersymmetry Breaking. I. Fermionic Spectrum

We consider the type-IIB supergravity vacua that include an internal $T^5$, depend on a single coordinate $r$ and respect a four-dimensional Poincaré symmetry, with the aim of highlighting low-energy spectra with broken supersymmetry and a bounded string coupling. These vacua are characterized by the flux $Φ$ of the self-dual five form in the internal torus, the length $\ell$ of the interval described by the coordinate $r$, a dilaton profile that is inevitably constant and a strictly positive dimensionless parameter $h$. As $\ell\rightarrow\infty$ while retaining finite values for $Φ$ and $\ell \,h^{-\,\frac{5}{4}}$, half of the original ten-dimensional supersymmetry is recovered, while finite values of $\ell$ break it completely. In the large-$\ell$ limit one boundary disappears but the other is still present, and is felt as a BPS orientifold by a probe brane. In this paper we focus on the fermionic zero modes and show that, although supersymmetry is broken for finite values of $\ell$, they are surprisingly those of four-dimensional $N=4$ supergravity coupled to five vector multiplets. The gravitini can acquire masses via radiative corrections, absorbing four of the massless spin-$\frac{1}{2}$ modes.

hep-th↗

arXiv2021

On Warped String Vacuum Profiles and Cosmologies, II. Non-Supersymmetric Strings

We investigate the effects of the leading tadpole potentials of 10D tachyon-free non-supersymmetric strings in warped products of flat geometries of the type M(p+1) x R x T(10-p-2) depending on a single coordinate. In the absence of fluxes and for p<8, there are two families of these vacua for the orientifold disk-level potential, both involving a finite internal interval. Their asymptotics are surprisingly captured by tadpole-free solutions, isotropic for one family and anisotropic at one end for the other. In contrast, for the heterotic torus-level potential there are four types of vacua. Their asymptotics are always tadpole-dependent and isotropic at one end lying at a finite distance, while at the other end, which can lie at a finite or infinite distance, they can be tadpole-dependent isotropic or tadpole-free anisotropic. We then elaborate on the general setup for including symmetric fluxes, and present the three families of exact solutions that emerge when the orientifold potential and a seven-form flux are both present. These solutions include a pair of boundaries, which are always separated by a finite distance. In the neighborhood of one, they all approach a common supersymmetric limit, while the asymptotics at the other boundary can be tadpole-free isotropic, tadpole-free anisotropic or again supersymmetric. We also discuss corresponding cosmologies, with emphasis on their climbing or descending behavior at the initial singularity. In some cases the toroidal dimensions can contract during the cosmological expansion.

hep-th↗

arXiv2021

On Warped String Vacuum Profiles and Cosmologies, I. Supersymmetric Strngs

We investigate in detail solutions of supergravity that involve warped products of flat geometries of the type M(p+1) x R x T(D-p-2) depending on a single coordinate. In the absence of fluxes, the solutions include flat space and Kasner-like vacua that break all supersymmetries. In the presence of a symmetric flux, there are three families of solutions that are characterized by a pair of boundaries and have a singularity at one of them, the origin. The first family comprises supersymmetric vacua, which capture a universal limiting behavior at the origin. The first and second families also contain non--supersymmetric solutions whose behavior at the other boundary, which can lie at a finite or infinite distance, is captured by the no--flux solutions. The solutions of the third family have a second boundary at a finite distance where they approach again the supersymmetric backgrounds. These vacua exhibit a variety of interesting scenarios, which include compactifications on finite intervals and (p+1)-dimensional effective theories where the string coupling has an upper bound. We also build corresponding cosmologies, and in some of them the string coupling can be finite throughout the evolution.

hep-th↗

arXiv2021

String (In)Stability Issues with Broken Supersymmetry

We review the main results of our investigations motivated by the tadpole potentials of ten-dimensional strings with broken supersymmetry. While these are at best partial indications, it is hard to resist the feeling that they do capture some lessons of String Theory. For example, these very tadpole potentials lead to weak-string-coupling cosmologies that appear to provide clues on the onset of the inflation from an initial fast roll. The transition, if accessible to us, would offer a natural explanation for the lack of power manifested by the CMB at large angular scales. In addition, the same tadpole potentials can drive spontaneous compactifications to lower-dimensional Minkowski spaces at corresponding length scales. Furthermore, the cosmological solutions exhibit an intriguing "instability of isotropy" that, if taken at face value, would point to an accidental origin of compactification. Finally, symmetric static AdS x S solutions driven by the tadpole potentials also exist, but they are unstable due to mixings induced by their internal fluxes. On the other hand, the original Dudas-Mourad solution is perturbatively stable, and we have gathered some detailed evidence that instabilities induced by internal fluxes can be held under control in a similar class of weak-coupling type-IIB compactifications to Minkowski space.

hep-th↗

arXiv2021

Integrable Models and Supersymmetry Breaking

We elaborate on integrable dynamical systems from scalar-gravity Lagrangians that include the leading dilaton tadpole potentials of broken supersymmetry. In the static Dudas-Mourad compactifications from ten to nine dimensions, which rest on these leading potentials, the string coupling and the space-time curvature become unbounded in some regions of the internal space. On the other hand, the string coupling remains bounded in several corresponding solutions of these integrable models. One can thus identify corrected potential shapes that could grant these features generically when supersymmetry is absent or non-linearly realized. On the other hand, large scalar curvatures remain present in all our examples. However, as in other contexts, the combined effects of the higher-derivative corrections of String Theory could tame them.

hep-th↗

arXiv2020

On Boundaries, Charges and Fermi Fields

We address some general issues related to torsion and Noether currents for Fermi fields in the presence of boundaries, with emphasis on the conditions that guarantee charge conservation. We also describe exact solutions of these boundary conditions and some implications for string vacua with broken supersymmetry.

hep-th↗

arXiv2019

On Classical Stability with Broken Supersymmetry

We study the perturbative stability of four settings that arise in String Theory, when dilaton potentials accompany the breaking of Supersymmetry, in the USp(32) and U(32) orientifold models, and also in the heterotic SO(16)xSO(16) model. The first two settings are a family of AdS3xS7 orientifold vacua and a family of AdS7xS3 heterotic vacua, supported by form fluxes, with small world-sheet and string-loop corrections within wide ranges of parameters. In both cases we find some unstable scalar perturbations, as a result of mixings induced by fluxes, confirming for the first class of vacua a previous result. However, in the second class they only affect the l=1 modes, so that a Z2 projection induced by an overall internal parity suffices to eliminate them, leading to perturbative stability. Moreover, the constant dilaton profiles of these vacua allow one to extend the analysis to generic potentials, thus exploring the possible effects of higher-order corrections, and we exhibit wide nearby regions of perturbative stability. The solutions in the third setting have nine-dimensional Poincare' symmetry. They include regions with large world-sheet or string-loop corrections, but we show that these vacua have no perturbative instabilities. Finally, the last setting concerns cosmological solutions in ten dimensions where the "climbing" phenomenon takes place: they have bounded string-loop corrections but large world-sheet ones close to the initial singularity. We find that perturbations generally decay, but homogeneous tensor modes exhibit an interesting logarithmic growth that signals a breakdown of isotropy. If the Universe then proceeds to lower dimensions, milder potentials from other branes force all perturbations to remain bounded.

hep-th↗

arXiv2018

The Evens and Odds of CMB Anomalies

The lack of power of large--angle CMB anisotropies is known to increase its statistical significance at higher Galactic latitudes, where a string--inspired pre--inflationary scale $Δ$ can also be detected. Considering the Planck 2015 data, and relying largely on a Bayesian approach, we show that the effect is mostly driven by the \emph{even}--$\ell$ harmonic multipoles with $\ell \lesssim 20$, which appear sizably suppressed in a way that is robust with respect to Galactic masking, along with the corresponding detections of $Δ$. On the other hand, the first \emph{odd}--$\ell$ multipoles are only suppressed at high Galactic latitudes. We investigate this behavior in different sky masks, constraining $Δ$ through even and odd multipoles, and we elaborate on possible implications. We include low--$\ell$ polarization data which, despite being noise--limited, help in attaining confidence levels of about 3 $σ$ in the detection of $Δ$. We also show by direct forecasts that a future all--sky $E$--mode cosmic--variance--limited polarization survey may push the constraining power for $Δ$ beyond 5 $σ$.

astro-ph.CO↗

arXiv2017

An Update on Brane Supersymmetry Breaking

"Brane supersymmetry breaking" is a peculiar phenomenon that can occur in perturbative orientifold vacua. It results from the simultaneous presence, in the vacuum, of non-mutually BPS sets of BPS branes and orientifolds, which leave behind a net tension and thus a runaway potential, but no tachyons. In the simplest ten-dimensional realization, the low-lying modes combine the closed sector of type-I supergravity with an open sector including USp(32) gauge bosons, fermions in the antisymmetric 495 and an additional singlet playing the role of a goldstino. We review some properties of this system and of other non-tachyonic models in ten dimensions with broken supersymmetry, and we illustrate some puzzles that their very existence raises, together with some applications that they have stimulated.

hep-th↗

arXiv2017

A superfield constraint for N=2 --> N=0 breaking

We identify a cubic holomorphic constraint that subtends the total breaking of N=2 supersymmetry in a vector multiplet and exhibit its microscopic origin. The new constraint leaves behind, at low energies, a vector and the two goldstini, in a non-linear Lagrangian that generalizes the N=2 Volkov-Akulov model.

hep-th↗