293 research outputs found
On the Ground State Wave Function of Matrix Theory
We propose an explicit construction of the leading terms in the asymptotic
expansion of the ground state wave function of BFSS SU(N) matrix quantum
mechanics. Our proposal is consistent with the expected factorization property
in various limits of the Coulomb branch, and involves a different scaling
behavior from previous suggestions. We comment on some possible physical
implications.Comment: 21 page
Lengthening and Extending Binary Private Information Retrieval Codes
It was recently shown by Fazeli et al. that the storage overhead of a
traditional -server private information retrieval (PIR) protocol can be
significantly reduced using the concept of a -server PIR code. In this work,
we show that a family of -server PIR codes (with increasing dimensions and
blocklengths) can be constructed from an existing -server PIR code through
lengthening by a single information symbol and code extension by at most
code symbols. Furthermore, by extending a code
construction notion from Steiner systems by Fazeli et al., we obtain a specific
family of -server PIR codes. Based on a code construction technique that
lengthens and extends a -server PIR code simultaneously, a basic algorithm
to find good (i.e., small blocklength) -server PIR codes is proposed. For
the special case of , we find provably optimal PIR codes for code
dimensions , while for all we find codes of smaller
blocklength than the best known codes from the literature. Furthermore, in the
case of , we also find better codes for . Numerical
results show that most of the best found -server PIR codes can be
constructed from the proposed family of codes connected to Steiner systems.Comment: The shorter version of this paper will appear in the proceedings of
2018 International Zurich Seminar on Information and Communicatio
Optimal Joint Routing and Scheduling in Millimeter-Wave Cellular Networks
Millimeter-wave (mmWave) communication is a promising technology to cope with
the expected exponential increase in data traffic in 5G networks. mmWave
networks typically require a very dense deployment of mmWave base stations
(mmBS). To reduce cost and increase flexibility, wireless backhauling is needed
to connect the mmBSs. The characteristics of mmWave communication, and
specifically its high directional- ity, imply new requirements for efficient
routing and scheduling paradigms. We propose an efficient scheduling method,
so-called schedule-oriented optimization, based on matching theory that
optimizes QoS metrics jointly with routing. It is capable of solving any
scheduling problem that can be formulated as a linear program whose variables
are link times and QoS metrics. As an example of the schedule-oriented
optimization, we show the optimal solution of the maximum throughput fair
scheduling (MTFS). Practically, the optimal scheduling can be obtained even for
networks with over 200 mmBSs. To further increase the runtime performance, we
propose an efficient edge-coloring based approximation algorithm with provable
performance bound. It achieves over 80% of the optimal max-min throughput and
runs 5 to 100 times faster than the optimal algorithm in practice. Finally, we
extend the optimal and approximation algorithms for the cases of multi-RF-chain
mmBSs and integrated backhaul and access networks.Comment: To appear in Proceedings of INFOCOM '1
On Higher Derivative Couplings in Theories with Sixteen Supersymmetries
We give simple arguments for new non-renormalization theorems on higher
derivative couplings of gauge theories to supergravity, with sixteen
supersymmetries, by considerations of brane-bulk superamplitudes. This leads to
some exact results on the effective coupling of D3-branes in type IIB string
theory. We also derive exact results on higher dimensional operators in the
torus compactification of the six dimensional (0, 2) superconformal theory.Comment: 31 pages, 10 figures, section 2 reconstructured, new result in
section 3.2, additional clarifications adde
(2,2) Superconformal Bootstrap in Two Dimensions
We find a simple relation between two-dimensional BPS N=2 superconformal
blocks and bosonic Virasoro conformal blocks, which allows us to analyze the
crossing equations for BPS 4-point functions in unitary (2,2) superconformal
theories numerically with semidefinite programming. We constrain gaps in the
non-BPS spectrum through the operator product expansion of BPS operators, in
ways that depend on the moduli of exactly marginal deformations through chiral
ring coefficients. In some cases, our bounds on the spectral gaps are observed
to be saturated by free theories, by N=2 Liouville theory, and by certain
Landau-Ginzburg models.Comment: 56 pages, 14 figure
Supersymmetry Constraints and String Theory on K3
We study supervertices in six dimensional (2,0) supergravity theories, and
derive supersymmetry non-renormalization conditions on the 4- and 6-derivative
four-point couplings of tensor multiplets. As an application, we obtain exact
non-perturbative results of such effective couplings in type IIB string theory
compactified on K3 surface, extending previous work on type II/heterotic
duality. The weak coupling limit thereof, in particular, gives certain
integrated four-point functions of half-BPS operators in the nonlinear sigma
model on K3 surface, that depend nontrivially on the moduli, and capture
worldsheet instanton contributions.Comment: 47 pages, 4 figure
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