1,218 research outputs found
Extended Bernoulli and Stirling matrices and related combinatorial identities
In this paper we establish plenty of number theoretic and combinatoric
identities involving generalized Bernoulli and Stirling numbers of both kinds.
These formulas are deduced from Pascal type matrix representations of Bernoulli
and Stirling numbers. For this we define and factorize a modified Pascal matrix
corresponding to Bernoulli and Stirling cases.Comment: Accepted for publication in Linear Algebra and its Application
Quantum Deconstruction of 5D SQCD
We deconstruct the fifth dimension of 5D SCQD with general numbers of colors
and flavors and general 5D Chern-Simons level; the latter is adjusted by adding
extra quarks to the 4D quiver. We use deconstruction as a non-stringy UV
completion of the quantum 5D theory; to prove its usefulness, we compute
quantum corrections to the SQCD_5 prepotential. We also explore the
moduli/parameter space of the deconstructed SQCD_5 and show that for |K_CS| <
N_F/2 it continues to negative values of 1/(g_5)^2. In many cases there are
flop transitions connecting SQCD_5 to exotic 5D theories such as E0, and we
present several examples of such transitions. We compare deconstruction to
brane-web engineering of the same SQCD_5 and show that the phase diagram is the
same in both cases; indeed, the two UV completions are in the same universality
class, although they are not dual to each other. Hence, the phase structure of
an SQCD_5 (and presumably any other 5D gauge theory) is inherently
five-dimensional and does not depends on a UV completion.Comment: LaTeX+PStricks, 108 pages, 41 colored figures. Please print in colo
Superconductors are topologically ordered
We revisit a venerable question: what is the nature of the ordering in a
superconductor? We find that the answer is properly that the superconducting
state exhibits topological order in the sense of Wen, i.e. that while it lacks
a local order parameter, it is sensitive to the global topology of the
underlying manifold and exhibits an associated fractionalization of quantum
numbers. We show that this perspective unifies a number of previous
observations on superconductors and their low lying excitations and that this
complex can be elegantly summarized in a purely topological action of the
``'' type and its elementary quantization. On manifolds with boundaries,
the action correctly predicts non-chiral edge states, gapped in general,
but crucial for fractionalization and establishing the ground state degeneracy.
In all of this the role of the physical electromagnetic fields is central. We
also observe that the action describes the topological order in several
other physically distinct systems thus providing an example of topological
universality
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