# SISSA Preprints

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Item 1/8 BPS States in Ads/CFT(2006-11-09T11:36:47Z) Gava, Edi; Milanesi, Giuseppe; Narain, Kumar S.; O'Loughlin, Martin; Physics; Elementary Particle TheoryWe study a class of exact supersymmetric solutions of type IIB Supergravity. They have an SO(4) x SU(2) x U(1) isometry and preserve generically 4 of the 32 supersymmetries of the theory. Asymptotically AdS_5 x S^5 solutions in this class are dual to 1/8 BPS chiral operators which preserve the same symmetries in the N=4 SYM theory. They are parametrized by a set of four functions that satisfy certain differential equations. We analyze the solutions to these equations in a large radius asymptotic expansion: they carry charges with respect to two U(1) KK gauge fields and their mass saturates the expected BPS bound.Item 2D Navier-Stokes Equation: Continuity Properties for Controllability(2006-06-13T09:46:31Z) Rodrigues, Sergio S.; Mathematics; Functional Analysis and ApplicationsItem 4D Effective Theory and Geometrical Approach(2006-10-04T10:42:39Z) Salvio, Alberto; Physics; Elementary Particle TheoryWe consider the 4D effective theory for the light Kaluza-Klein (KK) modes. The heavy KK mode contribution is generally needed to reproduce the correct physical predictions: an equivalence, between the effective theory and the D-dimensional (or geometrical) approach to spontaneous symmetry breaking (SSB), emerges only if the heavy mode contribution is taken into account. This happens even if the heavy mode masses are at the Planck scale. In particular, we analyze a 6D Einstein-Maxwell model coupled to a charged scalar and fermions. Moreover, we briefly review non-Abelian and supersymmetric extensions of this theory.Item About quantization of gravity(SISSA Library, 1984) Furlan, Giuseppe; de Alfaro, Vittorio; Fubini, Sergio; Physics; Elementary Particle TheoryItem The Absolute Neutrino Mass Scale, Neutrino Mass Spectrum, Majorana CP-Violation and Neutrinoless Double-Beta Decay(2006-09-25T15:37:55Z) Pascoli, Silvia; Petcov, Serguey T.; Schwetz, Thomas; Physics; Elementary Particle TheoryAssuming 3-$\nu$ mixing, massive Majorana neutrinos and neutrinoless double-beta (\betabeta-) decay generated only by the (V-A) charged current weak interaction via the exchange of the three Majorana neutrinos, we briefly review the predictions for the effective Majorana mass $\meff$ in \betabeta-decay and reanalyse the physics potential of future \betabeta-decay experiments to provide information on the type of neutrino mass spectrum, the absolute scale of neutrino masses, and Majorana CP-violation in the lepton sector. Using as input the most recent experimental results on neutrino oscillation parameters and the prospective precision that can be achieved in future measurements of the latter, we perform a statistical analysis of a \betabeta-decay half-life measurement taking into account experimental and theoretical errors, as well as the uncertainty implied by the imprecise knowledge of the corresponding nuclear matrix element (NME). We show, in particular, how the possibility to dis...Item Adler-Gelfand-Dickey approach to classical W-algebras within the theory of Poisson vertex algebras(SISSA, 2014-01-09) De Sole, Alberto; Kac, Victor G.; Valeri, Daniele; MathematicsWe put the Adler-Gelfand-Dickey approach to classical W-algebras in the framework of Poisson vertex algebras. We show how to recover the bi-Poisson structure of the KP hierarchy, together with its generalizations and reduction to the N-th KdV hierarchy, using the formal distribution calculus and the lambda-bracket formalism. We apply the Lenard-Magri scheme to prove integrability of the corresponding hierarchies. We also give a simple proof of a theorem of Kupershmidt and Wilson in this framework. Based on this approach, we generalize all these results to the matrix case. In particular, we find (non-local) bi-Poisson structures of the matrix KP and the matrix N-th KdV hierarchies, and we prove integrability of the N-th matrix KdV hierarchy.Item Algebra of Operators in AdS-Rindler(2022-08-08) Bahiru, Eyoab D.; physicsWe discuss the algebra of operators in AdS-Rinlder wedge, particularly in AdS5/CFT4. We explicitly construct the algebra at N = 8 limit and discuss its Type III1 nature. We will consider 1/N corrections to the theory and describe how several divergences can be renormalized and the algebra becomes Type II8. This will make it possible to associate a density matrix to any state in the Hilbert space and thus a von Neumann entropy.Item Algebraic structure of Lorentz and diffeomorphism anomalies(1993-04-03) Werneck de Oliveira, M.; Sorella, S.P.; physicsThe Wess-Zumino consistency conditions for Lorentz and diffeomor phism anomalies are discussed by introducing an operator δ whichallows to decompose the exterior space-time derivative as a BRS com mutator.Item Algebraic-geometrical Darboux coordinates in R-matrix formalism(SISSA, 1994) Diener, Paola; Dubrovin, Boris; Mathematics; Mathematical PhysicsItem Almost global existence of solutions for capillarity-gravity water waves equations with periodic spatial boundary conditions(2017) Berti, Massimiliano; Delort, Jean-Marc; MathematicsThe goal of this monograph is to prove that any solution of the Cauchy problem for the capillarity-gravity water waves equations, in one space dimension, with periodic, even in space, initial data of small size ϵ, is almost globally defined in time on Sobolev spaces, i.e. it exists on a time interval of length of magnitude ϵ−N for any N, as soon as the initial data are smooth enough, and the gravity-capillarity parameters are taken outside an exceptional subset of zero measure. In contrast to the many results known for these equations on the real line, with decaying Cauchy data, one cannot make use of dispersive properties of the linear flow. Instead, our method is based on a normal forms procedure, in order to eliminate those contributions to the Sobolev energy that are of lower degree of homogeneity in the solution. Since the water waves equations are a quasi-linear system, usual normal forms approaches would face the well known problem of losses of derivatives in the unbounded transformations. In this monograph, to overcome such a difficulty, after a paralinearization of the capillarity-gravity water waves equations, necessary to obtain energy estimates, and thus local existence of the solutions, we first perform several paradifferential reductions of the equations to obtain a diagonal system with constant coefficients symbols, up to smoothing remainders. Then we may start with a normal form procedure where the small divisors are compensated by the previous paradifferential regularization.The reversible structure of the water waves equations, and the fact that we look for solutions even in x, guarantees a key cancellation which prevents the growth of the Sobolev norms of the solutions.Item Almost Global Stochastic Feedback Stabilization of Conditional Quantum Dynamics(2005) Altafini, Claudio; Ticozzi, Francesco; Mathematics; Functional Analysis and ApplicationsWe propose several parametrization-free solutions to the problem of quantum state reduction control by means of continuous measurement and smooth quantum feedback. In particular, we design a feedback law for which almost global stochastic feedback stabilization can be proved analytically by means of Lyapunov techinques. This synthesis arises very naturally from the physics of the problem, as it relies on the variance associated with the quantum filtering process.Item The alpha-prime stretched horizon in Heterotic string(2006-05-11T11:24:55Z) Exirifard, Ghasem; Physics; Elementary Particle TheoryThe linear alpha-prime corrections and the field redefinition ambiguities are studied for half-BPS singular backgrounds representing a wrapped fundamental string. It is shown that there exist schemes in which the inclusion of all the linear alpha-prime corrections converts these singular solutions to black holes with regular horizon for which the modified Hawking-Bekenstein entropy is in agreement with the statistical entropy.Item Ambrosio-Tortorelli approximation of cohesive fracture models in linearized elasticity(SISSA, 2013-05) Focardi, Matteo; Iurlano, Flaviana; MathematicsWe provide an approximation result in the sense of $\Gamma$-convergence for cohesive fracture energies of the form \[ \int_\Omega \mathscr{Q}_1(e(u))\,dx+a\,\mathcal{H}^{n-1}(J_u)+b\,\int_{J_u}\mathscr{Q}_0^{1/2}([u]\odot\nu_u)\,d\mathcal{H}^{n-1}, \] where $\Omega\subset{\mathbb R}^n$ is a bounded open set with Lipschitz boundary, $\mathscr{Q}_0$ and $\mathscr{Q}_1$ are coercive quadratic forms on ${\mathbb M}^{n\times n}_{sym}$, $a,\,b$ are positive constants, and $u$ runs in the space of fields $SBD^2(\Omega)$ , i.e., it's a special field with bounded deformation such that its symmetric gradient $e(u)$ is square integrable, and its jump set $J_u$ has finite $(n-1)$-Hausdorff measure in ${\mathbb R}^n$. The approximation is performed by means of Ambrosio-Tortorelli type elliptic regularizations, the prototype example being \[ \int_\Omega\Big(v|e(u)|^2+\frac{(1-v)^2}{\varepsilon}+{\gamma\,\varepsilon}|\nabla v|^2\Big)\,dx, \] where $(u,v)\in H^1(\Omega,{\mathbb R}^n){\times} H^1(\Omega)$, $\varepsilon\leq v\leq 1$ and $\gamma>0$.Item Analysis of a dynamic peeling test with speed-dependent toughness(2017) Lazzaroni, Giuliano; Nardini, Lorenzo; MathematicsWe analyse a one-dimensional model of dynamic debonding for a thin film, where the local toughness of the glue between the film and the substrate also depends on the debonding speed. The wave equation on the debonded region is strongly coupled with Griffth's criterion for the evolution of the debonding front. We provide an existence and uniqueness result and find explicitly the solution in some concrete examples. We study the limit of solutions as inertia tends to zero, observing phases of unstable propagation, as well as time discontinuities, even though the toughness diverges at a limiting debonding speed.Item Anomaly-corrected supersymmetry algebra and supersymmetric holographic renormalization(SISSA, 2017-03-16) An, Ok Song; PhysicsWe present a systematic approach to supersymmetric holographic renormalization for a generic 5D N = 2 gauged supergravity theory with matter multiplets, including its fermionic sector, with all gauge fields consistently set to zero. We determine the complete set of supersymmetric local boundary counterterms, including the finite counterterms that parameterize the choice of supersymmetric renormalization scheme. This allows us to derive holographically the superconformal Ward identities on a generic background, including the Weyl and super-Weyl anomalies. Moreover, we show that these anomalies satisfy the Wess-Zumino consistency condition. The super-Weyl anomaly implies that the fermionic operators of the dual field theory, such as the supercurrent, do not transform as tensors under rigid supersymmetry on backgrounds that admit a Killing spinor, and their anticommutator with the conserved supercharge contains anomalous terms. This property is explicitly checked for a toy model. Finally, using the anomalous transformation of the supercurrent, we obtain the anomaly-corrected supersymmetry algebra on curved backgrounds admitting a Killing spinor.Item Another look at elliptic homogenization(2023-06-21) Braides, Andrea; Cosma Brusca, Giuseppe; Donati, Davide; mathematicsWe consider the limit of sequences of normalized (s, 2)-Gagliardo seminorms with an oscillating coefficient as s → 1. In a seminal paper by Bourgain, Brezis and Mironescu (subsequently extended by Ponce) it is proven that if the coefficient is constant then this sequence Γ-converges to a multiple of the Dirichlet integral. Here we prove that, if we denote by ε the scale of the oscillations and we assume that 1−s << ε2, this sequence converges to the homogenized functional formally obtained by separating the effects of s and ε; that is, by the homogenization as ε → 0 of the Dirichlet integral with oscillating coefficient obtained by formally letting s → 1 first.Item An artificial viscosity approach to quasistatic crack growth(2006-07-26T10:13:39Z) Toader, Rodica; Zanini, Chiara; Mathematics; Functional Analysis and ApplicationsWe introduce a new model of irreversible quasistatic crack growth in which the evolution of cracks is the limit of a suitably modified $\epsilon$-gradient flow of the energy functional, as the "viscosity" parameter $\epsilon$ tends to zero.Item Aspects of Finite Temperature Quantum Field Theory in a Black Hole Background(2005) Milanesi, Giuseppe; Mintchev, Mihail; Physics; Elementary Particle TheoryWe quantize a scalar field at finite temperature T in the background of a classical black hole, adopting 't Hooft's "brick wall" model with generic mixed boundary conditions at the brick wall boundary. We first focus on the exactly solvable case of two dimensional space-time. As expected, the energy density is integrable in the limit of vanishing brick wall thickness only for T = TH - the Hawking temperature. Consistently with the most general stress energy tensor allowed in this background, the energy density shows a surface contribution localized on the horizon. We point out that the usual divergences occurring in the entropy of the thermal atmosphere are due to the assumption that the third law of thermodynamics holds for the quantum field in the black hole background. Such divergences can be avoided if we abandon this assumption. The entropy density also has a surface term localized on the horizon, which is open to various interpretations. The extension of these results to higher space-time dimensions is briefly discussed.Item Asymptotic behavior of the dirichlet energy on poisson point clouds(2022-03-23) Braides, Andrea; Caroccia, Marco; mathematicsWe prove that quadratic pair interactions for functions defined on planar Poisson clouds and taking into account pairs of sites of distance up to a certain (large-enough) threshold can be almost surely approximated by the multiple of the Dirichlet energy by a deterministic constant. This is achieved by scaling the Poisson cloud and the corresponding energies and computing a compact discrete-to-continuum limit. In order to avoid the effect of exceptional regions of the Poisson cloud, with an accumulation of sites or with ‘disconnected’ sites, a suitable ‘coarse-grained’ notion of convergence of functions defined on scaled Poisson clouds must be given.Item Asymptotic behaviour of the capacity in two-dimensional heterogeneous media(2022-06-13) Braides, Andrea; Brusca, G.C.; mathematicsWe describe the asymptotic behaviour of the minimal inhomogeneous two-capacity of small sets in the plane with respect to a fixed open set Ω. This problem is gov erned by two small parameters: ε, the size of the inclusion (which is not restrictive to assume to be a ball), and δ, the period of the inhomogeneity modelled by oscillating coefficients. We show that this capacity behaves as C| log ε| −1. The coefficient C is ex plicitly computed from the minimum of the oscillating coefficient and the determinant of the corresponding homogenized matrix, through a harmonic mean with a proportion depending on the asymptotic behaviour of | log δ|/| log ε|.