16,142 research outputs found
1/2, 1/4 and 1/8 BPS Equations in SUSY Yang-Mills-Higgs Systems -- Field Theoretical Brane Configurations --
We systematically classify 1/2, 1/4 and 1/8 BPS equations in SUSY gauge
theories in d=6, 5, 4, 3 and 2 with eight supercharges, with gauge groups and
matter contents being arbitrary. Instantons (strings) and vortices (3-branes)
are only allowed 1/2 BPS solitons in d=6 with N=1 SUSY. We find two 1/4 BPS
equations and the unique 1/8 BPS equation in d=6 by considering configurations
made of these field theory branes. All known BPS equations are rederived while
several new 1/4 and 1/8 BPS equations are found in dimension less than six by
dimensional reductions.Comment: 41 pages, no figures, v2: 49 pages, no figures, typos corrected,
references added, the final version in NP
On the self-adjointness of certain reduced Laplace-Beltrami operators
The self-adjointness of the reduced Hamiltonian operators arising from the
Laplace-Beltrami operator of a complete Riemannian manifold through quantum
Hamiltonian reduction based on a compact isometry group is studied. A simple
sufficient condition is provided that guarantees the inheritance of essential
self-adjointness onto a certain class of restricted operators and allows us to
conclude the self-adjointness of the reduced Laplace-Beltrami operators in a
concise way. As a consequence, the self-adjointness of spin Calogero-Sutherland
type reductions of `free' Hamiltonians under polar actions of compact Lie
groups follows immediately.Comment: 9 pages, minor changes, updated references in v
On the confluence of lambda-calculus with conditional rewriting
The confluence of untyped \lambda-calculus with unconditional rewriting is
now well un- derstood. In this paper, we investigate the confluence of
\lambda-calculus with conditional rewriting and provide general results in two
directions. First, when conditional rules are algebraic. This extends results
of M\"uller and Dougherty for unconditional rewriting. Two cases are
considered, whether \beta-reduction is allowed or not in the evaluation of
conditions. Moreover, Dougherty's result is improved from the assumption of
strongly normalizing \beta-reduction to weakly normalizing \beta-reduction. We
also provide examples showing that outside these conditions, modularity of
confluence is difficult to achieve. Second, we go beyond the algebraic
framework and get new confluence results using a restricted notion of
orthogonality that takes advantage of the conditional part of rewrite rules
Definability of linear equation systems over groups and rings
Motivated by the quest for a logic for PTIME and recent insights that the
descriptive complexity of problems from linear algebra is a crucial aspect of
this problem, we study the solvability of linear equation systems over finite
groups and rings from the viewpoint of logical (inter-)definability. All
problems that we consider are decidable in polynomial time, but not expressible
in fixed-point logic with counting. They also provide natural candidates for a
separation of polynomial time from rank logics, which extend fixed-point logics
by operators for determining the rank of definable matrices and which are
sufficient for solvability problems over fields. Based on the structure theory
of finite rings, we establish logical reductions among various solvability
problems. Our results indicate that all solvability problems for linear
equation systems that separate fixed-point logic with counting from PTIME can
be reduced to solvability over commutative rings. Moreover, we prove closure
properties for classes of queries that reduce to solvability over rings, which
provides normal forms for logics extended with solvability operators. We
conclude by studying the extent to which fixed-point logic with counting can
express problems in linear algebra over finite commutative rings, generalising
known results on the logical definability of linear-algebraic problems over
finite fields
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