2,846 research outputs found
Domain walls of gauged supergravity, M-branes, and algebraic curves
We provide an algebraic classification of all supersymmetric domain wall
solutions of maximal gauged supergravity in four and seven dimensions, in the
presence of non-trivial scalar fields in the coset SL(8,R)/SO(8) and
SL(5,R)/SO(5) respectively. These solutions satisfy first-order equations,
which can be obtained using the method of Bogomol'nyi. From an
eleven-dimensional point of view they correspond to various continuous
distributions of M2- and M5-branes. The Christoffel-Schwarz transformation and
the uniformization of the associated algebraic curves are used in order to
determine the Schrodinger potential for the scalar and graviton fluctuations on
the corresponding backgrounds. In many cases we explicitly solve the
Schrodinger problem by employing techniques of supersymmetric quantum
mechanics. The analysis is parallel to the construction of domain walls of
five-dimensional gauged supergravity, with scalar fields in the coset
SL(6,R)/SO(6), using algebraic curves or continuous distributions of D3-branes
in ten dimensions. In seven dimensions, in particular, our classification of
domain walls is complete for the full scalar sector of gauged supergravity. We
also discuss some general aspects of D-dimensional gravity coupled to scalar
fields in the coset SL(N,R)/SO(N).Comment: 46 pages, latex. v2: typos corrected and some references added. v3:
minor corrections and improvements, references added, to appear in ATM
Riemann surfaces and Schrodinger potentials of gauged supergravity
Supersymmetric domain-wall solutions of maximal gauged supergravity are
classified in 4, 5 and 7 dimensions in the presence of non-trivial scalar
fields taking values in the coset SL(N, R)/SO(N) for N=8, 6 and 5 respectively.
We use an algebro-geometric method based on the Christoffel-Schwarz
transformation, which allows for the characterization of the solutions in terms
of Riemann surfaces whose genus depends on the isometry group. The
uniformization of the curves can be carried out explicitly for models of low
genus and results into trigonometric and elliptic solutions for the scalar
fields and the conformal factor of the metric. The Schrodinger potentials for
the quantum fluctuations of the graviton and scalar fields are derived on these
backgrounds and enjoy all properties of supersymmetric quantum mechanics.
Special attention is given to a class of elliptic models whose quantum
fluctuations are commonly described by the generalized Lame potential
\mu(\mu+1)P(z) + \nu(\nu+1)P(z+\omega_1)+ \kappa(\kappa+1)P(z+\omega_2) +
\lambda(\lambda+1)P(z+\omega_1 +\omega_2) for the Weierstrass function P(z) of
the underlying Riemann surfaces with periods 2\omega_1 and 2\omega_2, for
different half-integer values of the coupling constants \mu, \nu, \kappa,
\lambda.Comment: 13 pages, latex; contribution to the proceedings of the TMR meeting
"Quantum Aspects of Gauge Theories, Supersymmetry and Unification" held in
Paris in September 199
Power Range: Forward Private Multi-Client Symmetric Searchable Encryption with Range Queries Support
Symmetric Searchable Encryption (SSE) is an encryption technique that allows users to search directly over their outsourced encrypted data while preserving the privacy of both the files and the queries. In this paper, we present Power Range -- a dynamic SSE scheme (DSSE) that supports range queries in the multi-client model. We prove that our construction captures the very crucial notion of forward privacy in the sense that additions and deletions of files do not reveal any information about the content of past queries. Finally, to deal with the problem of synchronization in the multi-client model, we exploit the functionality offered by Trusted Execution Environments and Intel's SGX
Statistical state dynamics of weak jets in barotropic beta-plane turbulence
Zonal jets in a barotropic setup emerge out of homogeneous turbulence through
a flow-forming instability of the homogeneous turbulent state (`zonostrophic
instability') which occurs as the turbulence intensity increases. This has been
demonstrated using the statistical state dynamics (SSD) framework with a
closure at second order. Furthermore, it was shown that for small
supercriticality the flow-forming instability follows Ginzburg-Landau (G-L)
dynamics. Here, the SSD framework is used to study the equilibration of this
flow-forming instability for small supercriticality. First, we compare the
predictions of the weakly nonlinear G-L dynamics to the fully nonlinear SSD
dynamics closed at second order for a wide ranges of parameters. A new branch
of jet equilibria is revealed that is not contiguously connected with the G-L
branch. This new branch at weak supercriticalities involves jets with larger
amplitude compared to the ones of the G-L branch. Furthermore, this new branch
continues even for subcritical values with respect to the linear flow-forming
instability. Thus, a new nonlinear flow-forming instability out of homogeneous
turbulence is revealed. Second, we investigate how both the linear flow-forming
instability and the novel nonlinear flow-forming instability are equilibrated.
We identify the physical processes underlying the jet equilibration as well as
the types of eddies that contribute in each process. Third, we propose a
modification of the diffusion coefficient of the G-L dynamics that is able to
capture the asymmetric evolution for weak jets at scales other than the
marginal scale (side-band instabilities) for the linear flow-forming
instability.Comment: 27 pages, 17 figure
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