12,654 research outputs found
Matching nuts and bolts optimally
The nuts and bolts problem is the following : Given a collection of nuts of distinct sizes and bolts of distinct sizes such that for each nut there is exactly one matching bolt, find for each nut its corresponding bolt subject to the restriction that we can {\em only} compare nuts to bolts. That is we can neither compare nuts to nuts, nor bolts to bolts. This humble restriction on the comparisons appears to make this problem quite difficult to solve. In this paper, we illustrate the existence of an algorithm for solving the nuts and bolts problem that makes nut-and-bolt comparisons. We show the existence of this algorithm by showing the existence of certain expander-based comparator networks. Our algorithm is asymptotically optimal in terms of the number of nut-and-bolt comparisons it does. Another view of this result is that we show the existence of a decision tree with depth that solves this problem
Partition functions on 3d circle bundles and their gravity duals
The partition function of a three-dimensional theory on the
manifold , an bundle of degree over a closed
Riemann surface , was recently computed via supersymmetric
localization. In this paper, we compute these partition functions at large
in a class of quiver gauge theories with holographic M-theory duals. We provide
the supergravity bulk dual having as conformal boundary such three-dimensional
circle bundles. These configurations are solutions to minimal
gauged supergravity and pertain to the class of Taub-NUT-AdS and Taub-Bolt-AdS
preserving of the supersymmetries. We discuss the conditions for the
uplift of these solutions to M-theory, and compute the on-shell action via
holographic renormalization. We show that the uplift condition and on-shell
action for the Bolt solutions are correctly reproduced by the large limit
of the partition function of the dual superconformal field theory. In
particular, the partition
function, which was recently shown to match the entropy of black holes,
and the free energy, occur as special cases of
our formalism, and we comment on relations between them.Comment: typos in eqs 5.51 and subsequent fixed, conclusions unaltere
New Taub-NUT-Reissner-Nordstr\"{o}m spaces in higher dimensions
We construct new charged solutions of the Einstein-Maxwell field equations
with cosmological constant. These solutions describe the nut-charged
generalisation of the higher dimensional Reissner-Nordstr\"{o}m spacetimes. For
a negative cosmological constant these solutions are the charged
generalizations of the topological nut-charged black hole solutions in higher
dimensions. Finally, we discuss the global structure of such solutions and
possible applications.Comment: 10 pages, v.2 References adde
Surface Terms as Counterterms in the AdS/CFT Correspondence
We examine the recently proposed technique of adding boundary counterterms to
the gravitational action for spacetimes which are locally asymptotic to anti-de
Sitter. In particular, we explicitly identify higher order counterterms, which
allow us to consider spacetimes of dimensions d<=7. As the counterterms
eliminate the need of ``background subtraction'' in calculating the action, we
apply this technique to study examples where the appropriate background was
ambiguous or unknown: topological black holes, Taub-NUT-AdS and Taub-Bolt-AdS.
We also identify certain cases where the covariant counterterms fail to render
the action finite, and we comment on the dual field theory interpretation of
this result. In some examples, the case of vanishing cosmological constant may
be recovered in a limit, which allows us to check results and resolve
ambiguities in certain asymptotically flat spacetime computations in the
literature.Comment: Revtex, 18 pages. References updated and few typo's fixed. Final
versio
Gravitational Entropy and Global Structure
The underlying reason for the existence of gravitational entropy is traced to
the impossibility of foliating topologically non-trivial Euclidean spacetimes
with a time function to give a unitary Hamiltonian evolution. In dimensions
the entropy can be expressed in terms of the obstructions to foliation,
bolts and Misner strings, by a universal formula. We illustrate with a number
of examples including spaces with nut charge. In these cases, the entropy is
not just a quarter the area of the bolt, as it is for black holes.Comment: 18 pages. References adde
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