17,898 research outputs found
Charge Lattices and Consistency of 6D Supergravity
We extend the known consistency conditions on the low-energy theory of
six-dimensional N = 1 supergravity. We review some facts about the theory of
two-form gauge fields and conclude that the charge lattice Gamma for such a
theory has to be self-dual. The Green-Schwarz anomaly cancellation conditions
in the supergravity theory determine a sublattice of Gamma. The condition that
this sublattice can be extended to a self-dual lattice Gamma leads to a strong
constraint on theories that otherwise appear to be self-consistent.Comment: 15 pages. v2: minor changes; references, additional example added;
v3: minor corrections and clarifications added, JHEP versio
Massless Higher Spins and Holography
We treat free large N superconformal field theories as holographic duals of
higher spin (HS) gauge theories expanded around AdS spacetime with radius R.
The HS gauge theories contain massless and light massive AdS fields. The HS
current correlators are written in a crossing symmetric form including only
exchange of other HS currents. This and other arguments point to the existence
of a consistent truncation to massless HS fields. A survey of massless HS
theories with 32 supersymmetries in D=4,5,7 (where the 7D results are new) is
given and the corresponding composite operators are discussed. In the case of
AdS_4, the cubic couplings of a minimal bosonic massless HS gauge theory are
described. We examine high energy/small tension limits giving rise to massless
HS fields in the Type IIB string on AdS_5 x S^5 and M theory on AdS_{4/7} x
S^{7/4}. We discuss breaking of HS symmetries to the symmetries of ordinary
supergravity, and a particularly natural Higgs mechanism in AdS_5 x S^5 and
AdS_4 x S^7 where the HS symmetry is broken by finite g_{YM}. In AdS_5 x S^5 it
is shown that the supermultiplets of the leading Regge trajectory cross over
into the massless HS spectrum. We propose that g_{YM}=0 corresponds to a
critical string tension of order 1/R^2 and a finite string coupling of order
1/N. In AdS_7 x S^4 we give a rotating membrane solution coupling to the
massless HS currents, and describe these as limits of Wilson surfaces in the
A_{N-1}(2,0) SCFT, expandable in terms of operators with anomalous dimensions
that are asymptotically small for large spin. The minimal energy configurations
have semi-classical energy E=s for all s and the geometry of infinitely
stretched strings with energy and spin density concentrated at the endpoints.Comment: 77 pages, latex, minor corrections to eqs 4.26-30, a refined
discussion of long strings in Sec
Conic Optimization Theory: Convexification Techniques and Numerical Algorithms
Optimization is at the core of control theory and appears in several areas of
this field, such as optimal control, distributed control, system
identification, robust control, state estimation, model predictive control and
dynamic programming. The recent advances in various topics of modern
optimization have also been revamping the area of machine learning. Motivated
by the crucial role of optimization theory in the design, analysis, control and
operation of real-world systems, this tutorial paper offers a detailed overview
of some major advances in this area, namely conic optimization and its emerging
applications. First, we discuss the importance of conic optimization in
different areas. Then, we explain seminal results on the design of hierarchies
of convex relaxations for a wide range of nonconvex problems. Finally, we study
different numerical algorithms for large-scale conic optimization problems.Comment: 18 page
A Recursive Definition of the Holographic Standard Signature
We provide a recursive description of the signatures realizable on the
standard basis by a holographic algorithm. The description allows us to prove
tight bounds on the size of planar matchgates and efficiently test for standard
signatures. Over finite fields, it allows us to count the number of n-bit
standard signatures and calculate their expected sparsity.Comment: Fixed small typo in Section 3.
Bosonisation and Duality Symmetry in the Soldering Formalism
We develop a technique that solders the dual aspects of some symmetry. Using
this technique it is possible to combine two theories with such symmetries to
yield a new effective theory. Some applications in two and three dimensional
bosonisation are discussed. In particular, it is shown that two apparently
independent three dimensional massive Thirring models with same coupling but
opposite mass signatures, in the long wavelegth limit, combine by the process
of bosonisation and soldering to yield an effective massive Maxwell theory.
Similar features also hold for quantum electrodynamics in three dimensions. We
also provide a systematic derivation of duality symmetric actions and show that
the soldering mechanism leads to a master action which is duality invariant
under a bigger set of symmetries than is usually envisaged. The concept of
duality swapping is introduced and its implications are analysed. The example
of electromagnetic duality is discussed in details.Comment: LaTex file, 38 pages, this paper is a revised combination of
hep-th/9709105 and hep-th/9710060. Ref-Journal: Nucl. Phys. B, to appea
Ignorance and indifference
The epistemic state of complete ignorance is not a probability distribution. In it, we assign the same, unique, ignorance degree of belief to any contingent outcome and each of its contingent, disjunctive parts. That this is the appropriate way to represent complete ignorance is established by two instruments, each individually strong enough to identify this state. They are the principle of indifference (PI) and the notion that ignorance is invariant under certain redescriptions of the outcome space, here developed into the 'principle of invariance of ignorance' (PII). Both instruments are so innocuous as almost to be platitudes. Yet the literature in probabilistic epistemology has misdiagnosed them as paradoxical or defective since they generate inconsistencies when conjoined with the assumption that an epistemic state must be a probability distribution. To underscore the need to drop this assumption, I express PII in its most defensible form as relating symmetric descriptions and show that paradoxes still arise if we assume the ignorance state to be a probability distribution. Copyright 2008 by the Philosophy of Science Association. All rights reserved
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