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We reconsider linear perturbations around general Friedmann - Lemaitre - Robertson - Walker (FLRW) cosmological backgrounds. Exploiting gauge freedom involving only time reparametrizations, we write down classical background solutions analytically, for an arbitrary number of fluid components. We then show that the time evolution of scalar and tensor adiabatic perturbations are governed by Schr\"odinger-like differential equations of generalized Heun type. After recovering known analytic results for a single-component fluid, we discuss more general situations with two and three different fluid components, with special attention to the combination of radiation, matter and vacuum energy, which is supposed to describe the $\Lambda$CDM model. The evolution of linear perturbations of a flat $\Lambda$CDM universe is described by a two-transient model, where the transitions from radiation to matter and matter to vacuum energy are governed by a Heun equation and a Hypergeometric equation, respectively. We discuss an analytic approach to the study of the general case, involving generalized Heun equations, that makes use of (quantum) Seiberg-Witten curves for ${\cal N}=2$ supersymmetric gauge theories and has proven to be very effective in the analysis of Black-Hole, fuzzball and ECO perturbations., Comment: 30 pages, 6 figures, 3 tables

We discuss the dynamics of a (neutral) test particle in Topological Star spacetime undergoing scattering processes by a superposed test radiation field, a situation that in a 4D black hole spacetime is known as relativistic Poynting-Robertson effect, paving the way for future studies involving radiation-reaction effects. Furthermore, we study self-force-driven evolution of a scalar field, perturbing the Top-Star spacetime with a scalar charge current. The latter for simplicity is taken to be circular, equatorial and geodetic. To perform this study, besides solving all the self-force related problem (regularization of all divergences due to the self-field, mode sum regularization, etc.), we had to adapt the 4D Mano-Suzuki-Takasugi formalism to the present 5D situation. Finally, we have compared this formalism with the (quantum) Seiberg-Witten formalism, both related to the solutions of a Heun Confluent Equation, but appearing in different contexts in the literature, black hole perturbation theory the first, quantum curves in super-Yang-Mills theories the second., Comment: 31 pages, 3 figures for 8 eps files, revtex macros used

We propose a novel indicator for chaotic quantum scattering processes, the scattering form factor (ScFF). It is based on mapping the locations of peaks in the scattering amplitude to random matrix eigenvalues, and computing the analog of the spectral form factor (SFF). We compute the spectral and scattering form factors of several non-chaotic systems. We determine the ScFF associated with the phase shifts of the leaky torus, closely related to the distribution of the zeros of Riemann zeta function. We compute the ScFF for the decay amplitude of a highly excited string states into two tachyons. We show that it displays the universal features expected from random matrix theory - a decline, a ramp and a plateau - and is in general agreement with the Gaussian unitary ensemble. It also shows some new features, owning to the special structure of the string amplitude, including a "bump" before the ramp associated with gaps in the average eigenvalue density. The "bump" is removed for highly excited string states with an appropriate state dependent unfolding. We also discuss the SFF for the Gaussian $\beta$- ensemble, writing an interpolation between the known results of the Gaussian orthogonal, unitary, and symplectic ensembles., Comment: 47 pages, 17 figures

We give a detailed (microscopic) description of the geometric and non-geometric fundamental branes and their bound states in Type II superstring compactifications preserving N=6 supersymmetry. We consider general boundary states that couple to the twisted sector and compute the relevant annulus amplitudes. We check consistency of the construction by relating the transverse channel, corresponding to closed-string tree-level exchange, with the direct open-string loop channel. Focussing on the Type IIA frame, we show that D0-D4 have the expected tension for a geometric brane, while the non-geometric D2-D6 boundary states have a tension equal to $1/\sqrt{K}$ the one of a geometric brane for the $\mathbb{Z}_K$ orbifold. This is consistent with Fricke T-duality of the N=6 model., Comment: 25 pages

By exploiting the Kerr-Schild gauge, we study the scattering of a massive (charged) scalar off a Kerr-Newman black hole. In this gauge, the interactions between the probe and the target involve only tri-linear vertices. We manage to write down the tree-level scattering amplitudes in analytic form, from which we can construct an expression for the eikonal phase which is exact in the spin of the black hole at arbitrary order in the Post-Minkowskian expansion. We compute the classical contribution to the cross-section and deflection angle at leading order for a Kerr black hole for arbitrary orientation of the spin. Finally, we test our method by reproducing the classical amplitude for a Schwarzschild black hole at second Post-Minkowskian order and outline how to extend the analysis to the Kerr-Newman case., Comment: 36 pages, 7 figures. v2: typos corrected and refs added. Version published on JHEP

Topological stars, or top stars for brevity, are smooth horizonless static solutions of Einstein-Maxwell theory in 5-d that reduce to spherically symmetric solutions of Einstein-Maxwell-Dilaton theory in 4-d. We study linear scalar perturbations of top stars and argue for their stability and deformability. We tackle the problem with different techniques including WKB approximation, numerical analysis, Breit-Wigner resonance method and quantum Seiberg-Witten curves. We identify three classes of quasi-normal modes corresponding to prompt-ring down modes, long-lived meta-stable modes and what we dub `blind' modes. All mode frequencies we find have negative imaginary parts, thus suggesting linear stability of top stars. Moreover we determine the tidal Love and dissipation numbers encoding the response to tidal deformations and, similarly to black holes, we find zero value in the static limit but, contrary to black holes, we find non-trivial dynamical Love numbers and vanishing dissipative effects at linear order. For the sake of illustration in a simpler context, we also consider a toy model with a piece-wise constant potential and a centrifugal barrier that captures most of the above features in a qualitative fashion.

We perform a detailed study of linear perturbations of the JMaRT family of non-BPS smooth horizonless solutions of type IIB supergravity beyond the near-decoupling limit. In addition to the unstable quasi normal modes (QNMs) responsible for the ergo- region instability, already studied in the literature, we find a new class of `charged' unstable modes with positive imaginary part, that can be interpreted in terms of the emission of charged (scalar) quanta with non zero KK momentum. We use both matched asymptotic expansions and numerical integration methods. Moreover, we exploit the recently discovered correspondence between JMaRT perturbation theory, governed by a Reduced Confluent Heun Equation, and the quantum Seiberg-Witten (SW) curve of $\mathcal{N} = 2$ SYM theory with gauge group SU(2) and $N_f = (0,2)$ flavours.

We analyze the amplitudes of one highly excited string (HES) state with two or three tachyons in open bosonic string theory. We argue that these processes are chaotic by showing that the spacing ratios of successive peaks in the angular dependence of the amplitudes are distributed as predicted by the $\beta$-ensemble of random matrix theory (RMT). We show how the continuous parameter $\beta$ depends on the level and helicity of the scattered HES state. We derive the scattering amplitude of an HES and three tachyons and show that it takes the form of the Veneziano amplitude times a dressing factor, and that the dressing is chaotic as a function of the scattering angle, in the sense that its spacing ratios match with RMT predictions.

We perform a detailed study of perturbations around 2-charge circular fuzz-balls and compare the results with the ones obtained in the case of 'small' BHs. In addition to the photon-sphere modes that govern the prompt ring-down, we find a new branch of long-lived QNMs localised inside the photon-sphere at the (meta)stable minimum of the radial effective potential. The latter are expected to dominate late time signals in the form of 'echoes'. Moreover, contrary to 'small' BHs, some 'static' tidal Love numbers are non-zero and independent of the mass, charges and angular momentum of the fuzz-ball. We rely on the recently established connection between BH or fuzz-ball perturbation theory and quantum Seiberg-Witten curves for N = 2 SYM theories, which in turn are related to Liouville CFT via the AGT correspondence. We test our results against numerical results obtained with Leaver's method of continuous fractions or Breit-Wigner resonance method for direct integration and with the WKB approximation based on geodesic motion. We also exclude rotational super-radiance, due to the absence of an ergo-region, and absorption, due to the absence of a horizon., Comment: 48 pages, 6 figures

We study orientifold projections of families of four-dimensional $\mathcal{N}=1$ toric quiver gauge theories. We restrict to quivers that have the unusual property of being associated with multiple periodic planar diagrams which give rise, in general, to inequivalent models. A suitable orientifold projection relates a subfamily of the latter by conformal duality. That is, there exist exactly marginal deformations that connect the projected models. The deformations take the form of a sign flip in some of the superpotential interactions, similarly to the $\beta$-deformation of $\mathcal{N}=4$ SYM. Our construction generalizes previous results on the orientifold projections of the PdP$_{3b}$ and PdP$_{3c}$ singularities., Comment: 47 pages, 25 figures, 2 appendices. v2: Typos corrected, improved text, 3 tables added

We propose a novel measure of chaotic scattering amplitudes. It takes the form of a log-normal distribution function for the ratios $r_n={\delta_n}/{\delta_{n+1}}$ of (consecutive) spacings $\delta_n$ between two (consecutive) peaks of the scattering amplitude. We show that the same measure applies to the quantum mechanical scattering on a leaky torus as well as to the decay of highly excited string states into two tachyons. Quite remarkably the $r_n$ obey the same distribution that governs the non-trivial zeros of Riemann zeta function., Comment: v2: small corrections, references added; v3: minor improvements to match published version

We study various orientifold projections of 4d $\mathcal{N}=1$ toric gauge theories, associated with CY singularities known as $L^{a,b,a}/\mathbb{Z}_2$, with $a+b$ even. We obtain superconformal chiral theories that have the same central charge, anomalies and superconformal index, whereas they were different before the orientifold. Some of these projections are implemented by a novel type of orientifold without fixed loci, known as glide orientifold. We claim that these theories flow to the same conformal manifold, and they are connected by quadratic exactly marginal deformations. The latter can be written in terms of conjugate pairs of bifundamental fields of $R$-charge one, generalizing previous results for unoriented non-chiral theories., Comment: 42 pages, 33 figures

We analyse the perturbative four-point amplitudes in the simplest string theory examples of T-fold backgrounds, which enjoy N=6 supersymmetries in four dimensions. There are two theories defined as asymmetric orbifolds of order 2 and 3, respectively. The perturbative spectrum and the one-loop four-point amplitudes are shown to be invariant under an arithmetic symplectic group defined over the Hurwitz (respectively Eisenstein) quaternions. The supersymmetry constraints on the low energy effective couplings are determined and we conjecture the U-duality group of the theory and the non-perturbative completion of the six-derivative coupling as a rank one theta series. We discuss the non-perturbative spectrum of BPS states in the light of our analysis., Comment: 60+37 pages

We extend our investigation on Couch-Torrence conformal inversions of BHs and D-branes in various directions. We analyse asymptotically flat rotating charged BHs in $D=4$, in particular extremal rotating BHs in STU supergavity, and find invariance for special choices of the charges. Due to the dependence of the critical radii on the impact parameter(s), the relation between the scattering angle for geodesics outside the photon-halo and the in-spiralling angle for geodesics inside the photon-halo is modified by the inclusion of a boundary term. We also consider rotating BHs in $D=5$ and rotating D3-branes and find invariance under generalised Couch-Torrence inversions for special choices of the angular momenta. Alas we don't find any similar symmetry for smooth horizonless geometries. Moreover, relying on the surprising connection between classical BH perturbation theory and quantum Seiberg-Witten curves for ${\cal N}=2$ SYM theories, we study scalar wave equations in these backgrounds and identify the near super-radiant modes produced in near-extremal BH mergers. Finally, we study scalar fluctuations around Kerr-Newman BHs in AdS$_4$ and find stringent conditions for generalised Couch-Torrence symmetry that are relaxed in the extremal case or by allowing a rescaling of the wave function., Comment: 32 pages and 3 appendices

We study the emergence of partonic behavior in scattering processes at large Mandelstam's variable $s$ from string amplitudes in holographic backgrounds. We generalize the approach of Polchinski and Strassler (2001) in two ways. (i) We analyze several holographic confining backgrounds in particular the hard wall model, the soft wall model and Witten's model. (ii) In addition to deriving the asymptotic behavior of the amplitudes at fixed angle and in the Regge limit, we also expand the amplitudes around their poles, integrate over the holographic direction and then re-sum the expansion. Due to dependence of the string tension on the holographic coordinate, the resulting singularities take the form of branch points rather than poles and the amplitudes display branch cuts and acquire a finite imaginary part. This may signal the failure of the PS prescription to reproduce the correct analytic structure at low energies. We also observe that the peaks are more pronounced in the region of small $s$ but fade away for large $s$. In the fixed angle approximation we find in the hard and soft wall models that ${\cal A}\sim s^{2-\Delta/2}$ whereas in Witten's model ${\cal A} \sim s^{3-\Delta/2}$ and ${\cal A} \sim s^{7/3-2\Delta/3}$ for the 11D and 10D formulations, respectively. In the Regge regime ${\cal A}\sim {s^{2}}\,t^{-2+\alpha}\,(\log{s/ t})^{-1+\alpha}$ where $\alpha$ is the power found in the fixed angle regime. Using the pole expansion the result for each model is $Re[{\cal A}] \sim s^{-1}$, $Im[{\cal A}] \sim s^{\alpha}$. We compute the corresponding amplitudes for mesons using open strings and find qualitatively similar results as for closed strings., Comment: v1: 42 pages. v2: minor corrections, references added, 42 pages. v3: references added, and minor corrections made to text to match published version, 42 pages

Very much as extremal Reissner-Nordst\"om BHs, D3-branes and their intersecting bound-states in lower dimensions enjoy a remarkable symmetry under conformal inversions that exchange the horizon with infinity and keep the photon-sphere fixed. We explore the implications of this symmetry for the dynamics of massless and massive BPS particles. In particular we find a remarkable identity between the scattering angle of a probe impinging from infinity and the in-spiraling angle of a probe with the very same energy and angular momentum falling into the horizon from inside the photon-sphere. We argue for the identity of the radial actions and Shapiro time-delays for the two processes, when a cutoff regulator or an AdS ambient is adopted. We spell out the detailed conditions for the inversion symmetry to hold in the case of large BPS BHs in four dimensions. We address conformal inversions for other BHs and Dp-branes with photon-spheres in various dimensions with flat or AdS asymptotics. We briefly discuss the fate of the symmetry at the quantum level as well as for non spherically symmetric BHs and branes and sketch potential implications for the holographic correspondence., Comment: 26 pages, 6 figures Corrected some misprints, improved discussion on BHs in AdS

We exploit the recently proposed correspondence between gravitational perturbations and quantum Seiberg-Witten curves to compute the spectrum of quasi-normal modes of asymptotically flat Kerr Newman black holes and establish detailed gauge/gravity dictionaries for a large class of black holes, D-branes and fuzzballs in diverse dimensions. QNM frequencies obtained from the quantum periods of $SU(2)$ ${\cal N}=2$ SYM with $N_f=3$ flavours are compared against numerical results, WKB (eikonal) approximation and geodetic motion showing remarkable agreement. Starting from the master example relating quasi-normal modes of Kerr-Newman black holes in AdS$_4$ to $SU(2)$ gauge theory with $N_f=4$, we illustrate the procedure for some simple toy-models that allow analytic solutions. We also argue that the AGT version of the gauge/gravity correspondence may give precious hints as to the physical/geometric origin of the quasi-normal modes/Seiberg-Witten connection and further elucidate interesting properties (such as tidal Love numbers and grey-body factors) that can help discriminating black holes from fuzzballs., Comment: 33 pages plus appendices and 4 figures

We analyze the relevance of the generalized Kronheimer construction for the gauge-gravity correspondence. We study the general structure of IIB supergravity D3-brane solutions on crepant resolutions $Y$ of singularities $\mathbb{C}^3/\Gamma$ with $\Gamma$ a finite subgroup of $SU(3)$. Next we concentrate on another essential item for the D3-brane construction, i.e., the existence of a Ricci-flat metric on $Y$, with particular attention to the case $\Gamma=\mathbb{Z}_4$. We conjecture that on the exceptional divisor the Kronheimer K\"ahler metric and the Ricci-flat one, that is locally flat at infinity, coincide. The conjecture is shown to be true in the case of the Ricci-flat metric on ${\rm tot} K_{{\mathbb WP}[112]}$ that we construct, which is a partial resolution of $\mathbb{C}^3/\mathbb{Z}_4$. For the full resolution we have $Y=\operatorname{tot} K_{\mathbb{F}_{2}}$, where $\mathbb{F}_2$ is the second Hizebruch surface. We try to extend the proof of the conjecture to this case using the one-parameter K\"ahler metric on $\mathbb{F}_2$ produced by the Kronheimer construction as initial datum in a Monge-Amp\`{e}re (MA) equation. We exhibit three formulations of this MA equation, one in terms of the K\"ahler potential, the other two in terms of the symplectic potential; in all cases one can establish a series solution in powers of the fiber variable of the canonical bundle. The main property of the MA equation is that it does not impose any condition on the initial geometry of the exceptional divisor, but uniquely determines all the subsequent terms as local functionals of the initial datum. While a formal proof is still missing, numerical and analytical results support the conjecture. As a by-product of our investigation we have identified some new properties of this type of MA equations that we believe to be so far unknown., Comment: 63 pages, 8 figures. To appear in the Lett. Math. Phys. special issue in memory of Boris A. Dubrovin

We study the orientifold of the ${\mathcal{N}} = 1$ superconformal field theories describing D3-branes probing the Suspended Pinch Point singularity, as well as the orientifolds of non-chiral theories obtained by a specific orbifold $\mathbb{Z}_n$ of SPP. We find that these models realize a mechanism analogous to the one recently found for the orientifold of the complex Calabi-Yau cone over the Pseudo del Pezzo surface PdP$_{3c}$: they all flow to a new IR fixed point such that the value of the $a$-charge is less than half the one of the oriented theory. We also find that the value of $a$ coincides with the charge of specific orientifolds of the toric singularities $L^{(\bar{n},\bar{n},\bar{n})}$ with $\bar{n}=3n/2$ for $n$ even or $L^{(\bar{n},\bar{n}+1,\bar{n})}$ with $\bar{n}=(3n{-}1)/2$ for $n$ odd, suggesting the existence of an IR duality., Comment: 41 pages, 23 figures. v2: Improved text, references added

QNMs govern the linear response to perturbations of BHs, D-branes and fuzzballs and the gravitational wave signals in the ring-down phase of binary mergers. A remarkable connection between QNMs of neutral BHs in 4d and quantum SW geometries describing the dynamics of ${\cal N}=2$ SYM theories has been recently put forward. We extend the gauge/gravity dictionary to a large class of gravity backgrounds including charged and rotating BHs of Einstein-Maxwell theory in $d=4,5$ dimensions, D3-branes, D1D5 `circular' fuzzballs and smooth horizonless geometries; all related to ${\cal N}=2$ SYM with a single $SU(2)$ gauge group and fundamental matter. We find that photon-spheres, a common feature of all examples, are associated to degenerations of the classical elliptic SW geometry whereby a cycle pinches to zero size. Quantum effects resolve the singular geometry and lead to a spectrum of quantized energies, labeled by the overtone number $n$. We compute the spectrum of QNMs using exact WKB quantization, geodetic motion and numerical simulations and show excellent agreement between the three methods. We explicitly illustrate our findings for the case D3-brane QNMs., Comment: 7 pages, 2 figures

Deep conceptual problems associated with classical black holes can be addressed in string theory by the ``fuzzball'' paradigm, which provides a microscopic description of a black hole in terms of a thermodynamically large number of regular, horizonless, geometries with much less symmetry than the corresponding black hole. Motivated by the tantalizing possibility to observe quantum gravity signatures near astrophysical compact objects in this scenario, we perform the first $3+1$ numerical simulations of a scalar field propagating on a large class of multicenter geometries with no spatial isometries arising from ${\cal N}=2$ four-dimensional supergravity. We identify the prompt response to the perturbation and the ringdown modes associated with the photon sphere, which are similar to the black-hole case, and the appearance of echoes at later time, which is a smoking gun of some structure at the horizon scale and of the regular interior of these solutions. The response is in agreement with an analytical model based on geodesic motion in these complicated geometries. Our results provide the first numerical evidence for the dynamical linear stability of fuzzballs, and pave the way for an accurate discrimination between fuzzballs and black holes using gravitational-wave spectroscopy., Comment: Published version, 22 pages, 10 figures, Movies are available in https://web.uniroma1.it/gmunu/fuzzballs-multipole-moments-and-ringdown

We extend and generalise the string corrections to the EM memory to the Type I superstring including spin effects. Very much as in the simpler bosonic string context, the relevant corrections are non-perturbative in $\alpha'$, slowly decaying (as $1/R$) at large distances and modulated in retarded time $u=t-R$. For spin $N$ states in the first Regge trajectory they entail a sequence of $N$ derivatives wrt $u$ on the `parent' $N=0$ amplitude. We also briefly discuss how to include loop effects, that broaden and shift the string resonances, and how to modify our analysis for macroscopic semi-classical quasi-BPS coherent states, whose collisions may lead to detectable string memory signals in viable Type I models., Comment: 24 pages, 5 figures

We study massless geodesics near the photon-spheres of a large family of solutions of Einstein-Maxwell theory in five dimensions, including BHs, naked singularities and smooth horizon-less JMaRT geometries obtained as six-dimensional uplifts of the five-dimensional solution. We find that a light ring of unstable photon orbits surrounding the mass center is always present, independently of the existence of a horizon or singularity. We compute the Lyapunov exponent, characterizing the chaotic behaviour of geodesics near the `photon-sphere' and the time decay of ring-down modes dominating the response of the geometry to perturbations at late times. We show that, for geometries free of naked singularities, the Lyapunov exponent is always bounded by its value for a Schwarzschild BH of the same mass., Comment: 19 pages, 5 figures

The mixing of graviphotons and dark brane photons to the Standard Model hypercharge is analyzed in full generality, in weakly-coupled string theory. Both the direct mixing as well as effective terms that provide mixing after inclusion of SM corrections are estimated to lowest order. The results are compared with Effective Field Theory (EFT) couplings, originating in a hidden large-N theory coupled to the SM. The string theory mixing terms are typically subleading compared with the generic EFT couplings. The case where the hidden theory is a holographic theory is also analyzed, providing also suppressed mixing terms to the SM hypercharge., Comment: 45 pages plus appendices. 36 figures. V3 comments added

We identify string corrections to the EM memory effect. Though largely negligible in the low-energy limit, the effect become relevant in high-energy collisions and in extreme events. We illustrate our findings in a simple unoriented bosonic string model. Thanks to the coherent effect of the infinite tower of open string resonances, the corrections are non-perturbative in $\alpha'$, modulated in retarded time and slowly decaying even at large distances from the source. Remarkably compact expressions obtain for special choices of the kinematics in tree-level 4-point amplitudes. We discuss further corrections occurring at higher-points and the exponential damping resulting from broadening and shifting of the massive poles due to loops. Finally we estimate the range of the parameters and masses for detectability in semi-realistic (Type I) contexts and propose a rationale for this string memory effect., Comment: 16 pages, 5 figures

We discuss stringy ${\alpha'}$ corrections to the gravitational wave signal generated in the merging of two black holes. We model the merging with two BPS compact massive objects in the heterotic string, described by standard vertex operators or coherent states. Despite the expected cubic suppression in ${\alpha'}$ w.r.t. the General Relativity result, at tree level the string corrections seem to leave a footprint or a memory on the gravitational wave signals within the sensitivity region of aLIGO/VIRGO and future interferometers. Including loop effects that broaden and destabilise the string resonances suggests a sort of lost stringy memory effect that can be regained through the analysis of the quasi normal modes in the ring-down phase., Comment: 36 pages

We extend and refine a general method to extract the multipole moments of arbitrary stationary spacetimes and apply it to the study of a large family of regular horizonless solutions to $ {\cal N}{\,=\,}2$ four-dimensional supergravity coupled to four Abelian gauge fields. These microstate geometries can carry angular momentum and have a much richer multipolar structure than the Kerr black hole. In particular they break the axial and equatorial symmetry, giving rise to a large number of nontrivial multipole moments. After studying some analytical examples, we explore the four-dimensional parameter space of this family with a statistical analysis. We find that microstate mass and spin multipole moments are typically (but not always) larger that those of a Kerr black hole with the same mass and angular momentum. Furthermore, we find numerical evidence that some invariants associated with the (dimensionless) moments of these microstates grow monotonically with the microstate size and display a global minimum at the black-hole limit, obtained when all centers collide. Our analysis is relevant in the context of measurements of the multipole moments of dark compact objects with electromagnetic and gravitational-wave probes, and for observational tests to distinguish fuzzballs from classical black holes., Comment: 29 pages, 1 figure

Within General Relativity, the unique stationary solution of an isolated black hole is the Kerr spacetime, which has a peculiar multipolar structure depending only on its mass and spin. We develop a general method to extract the multipole moments of arbitrary stationary spacetimes and apply it to a large family of horizonless microstate geometries. The latter can break the axial and equatorial symmetry of the Kerr metric and have a much richer multipolar structure, which provides a portal to constrain fuzzball models phenomenologically. We find numerical evidence that all multipole moments are typically larger (in absolute value) than those of a Kerr black hole with the same mass and spin. Current measurements of the quadrupole moment of black-hole candidates could place only mild constraints on fuzzballs, while future gravitational-wave detections of extreme mass-ratio inspirals with the space mission LISA will improve these bounds by orders of magnitude., Comment: v3: 5 pages, 1 figure. Fixes grammatical typos. Matches version to appear in PRL

We study the interplay between mass deformations and unoriented projections of super-conformal quiver gauge theories resulting from D3-branes at (toric) Calabi-Yau singularities. We focus on simple orbifold cases ($\mathbb{C}^3/\mathbb{Z}_3$ and $\mathbb{C}^3/\mathbb{Z}_4$) and their non-orbifold descendants. This allows us to generalize the construction rules and clarify points that have been previously overlooked. In particular we spell out the conditions of anomaly cancellations as well as super-conformal invariance that typically require the introduction of flavour branes, which in turn may spoil toric symmetry. Finally, we discuss duality cascades in this context and the interplay between Seiberg/toric duality and unoriented projection with (or without) mass deformations., Comment: 51 pages plus appendices, 36 figures. In version 2, text and figures corrected. Published in JHEP

We reconsider a modification of the N-point amplitude of the Neveu-Schwarz (NS) model in which the tachyon becomes a pion by shifting its mass to zero and keeping the super-projective invariance of the integrand of the amplitude. For the scattering of four particles it reduces to the amplitude written by Lovelace and Shapiro that has Adler zeroes. We confirm that also the N-pion amplitude has Adler zeroes and show that it reduces to that of the non-linear $\sigma$-model for $\alpha' \rightarrow 0$ keeping $F_\pi$ fixed. The four- and six-point flavour-ordered amplitudes satisfy tree-level unitarity since they can be derived from the correspondent amplitudes of the NS model in ten dimensions by suitably choosing the components of the momenta of the external mesons in the six extra dimensions. Negative norm states (ghosts) are shown to appear instead in higher-point amplitudes. We also discuss several amplitudes involving different external mesons., Comment: 21 pages plus appendices and 1 figure

We study the scattering of massless probes in the vicinity of the {\it photon-sphere} of asymptotically AdS black holes and horizon-free microstate geometries (fuzzballs). We find that these exhibit a chaotic behaviour characterised by exponentially large deviations of nearby trajectories. We compute the Lyapunov exponent $\lambda$ governing the exponential growth in $d$ dimensions and show that it is bounded from above by $\lambda_b = \sqrt{d{-}3}/2b_{\rm min}$ where $b_{\rm min}$ is the minimal impact parameter under which a massless particle is swallowed by the black hole or gets trapped in the fuzzball for a very long time. Moreover we observe that $\lambda$ is typically below the advocated bound on chaos $\lambda_H=2\pi \kappa_B T/\hbar$, that in turn characterises the radial fall into the horizon, but the bound is violated in a narrow window near extremality, where the photon-sphere coalesces with the horizon. Finally, we find that fuzzballs are characterised by Lyapunov exponents smaller than those of the corresponding BH's suggesting the possibility of discriminating the existence of micro-structures at horizon scales via the detection of ring-down modes with time scales $\lambda^{-1}$ longer than those expected for a BH of the given mass and spin., Comment: 26 pages, 9 figures

Ultra High Energy Cosmic Rays may include strangelets, a form of Strange Quark Matter, among their components. We briefly review their properties and discuss how they can be accelerated via Penrose process taking place in singular rotating Kerr black holes or in their smooth, horizonless counterparts in string theory, according to the fuzzball proposal. We focus on non-BPS solutions of the JMaRT kind and compute the efficiency of Penrose process that turns out not to be bounded unlike for Kerr BHs., Comment: 26 pages, 7 figures

We study interactions of string coherent states in the DDF (after Di Vecchia, Del Giudice, Fubini) formalism. For simplicity we focus on open bosonic strings. After reviewing basic properties of DDF operators and of excited open strings, we present some classical profiles and show how they become more and more compact as the number of harmonics increases at fixed mass. We then compute various three- and four-point amplitudes with insertions of coherent states, tachyons and vector bosons on the boundary of the disk relying on a convenient choice of reference null momenta. We find that the amplitudes exponentiate in a rather subtle and interesting way. We then study the high-energy fixed-angle limit, dominated by a saddle-point when coherent states are present, and the soft behaviour as the momentum of a vector boson is taken to zero. We briefly comment on generalisation of our analysis to multiple intersecting and magnetised D-branes and to closed strings., Comment: 39 pages, 6 figures

Using soft-graviton theorems a well-known zero-frequency limit (ZFL) for the gravitational radiation flux $dE^{GW}/d \omega$ is re-derived and extended to order ${{\cal O}}(\omega)$ and ${{\cal O}}(\omega^2)$ for arbitrary massless multi-particle collisions. The (angle-integrated, unpolarized) ${{\cal O}}(\omega)$ correction to the flux turns out to be absent in the case of two-particle elastic collisions. The ${{\cal O}}(\omega^2)$ correction is instead non-vanishing and takes a simple general expression which is then applied to bremsstrahlung from two-particle elastic collisions. For a tree-level process the outcome is finite and consistent with expectations. Instead, if the tree-level form of the soft theorems is used at sub-sub-leading order even when the elastic amplitude needs an all-loop (eikonal) resummation, an unphysical infrared singularity occurs. Its origin can be traced to the infinite Coulomb phase of gravitational scattering in four dimensions. We briefly discuss how to get rid, in principle, of the unwanted divergences and indicate --without carrying out-- a possible procedure to find the proper correction to the naive soft theorems. Nevertheless, if a simple recipe recently proposed for handling these divergences is adopted, we find surprisingly good agreement with results obtained independently via the eikonal approach to transplanckian-energy scattering at large (small) impact parameter (deflection angle), where such Coulomb divergences explicitly cancel out., Comment: 37 pages, 1 figure, references added, points clarified

Hidden theories coupled to the SM may provide emergent axions, that are composites/bound-states of the hidden fields. This is motivated by paradigms emerging from the AdS/CFT correspondence but it is a more general phenomenon. We explore the general setup and find that UV-sourced interactions of instanton densities give rise to emergent axions in the IR. We study the general properties of such axions and argue that they are generically different from both fundamental and composite axions that have been studied so far., Comment: 42 pages plus appendices, 5 figures

Black holes absorb any particle impinging with an impact parameter below a critical value. We show that 2- and 3-charge fuzzball geometries exhibit a similar trapping behaviour for a selected choice of the impact parameter of incoming massless particles. This suggests that the blackness property of black holes arises as a collective effect whereby each micro-state absorbs a specific channel., Comment: 23 pages, 3 figures