269 research outputs found
A Simple Method for Computing Soliton Statistics
I provide an extremely simple argument that the kink-type solitons in certain
theories are fermionic. The argument is based on the Witten index, but can in
fact be used to determine soliton statistics in non-supersymmetric theories as
well.Comment: 9 pages, harvmac, HWS-92/09. (Added substantial details in one
section.
Duality, Partial Supersymmetry, and Arithmetic Number Theory
We find examples of duality among quantum theories that are related to
arithmetic functions by identifying distinct Hamiltonians that have identical
partition functions at suitably related coupling constants or temperatures. We
are led to this after first developing the notion of partial supersymmetry-in
which some, but not all, of the operators of a theory have superpartners-and
using it to construct fermionic and parafermionic thermal partition functions,
and to derive some number theoretic identities. In the process, we also find a
bosonic analogue of the Witten index, and use this, too, to obtain some number
theoretic results related to the Riemann zeta function.Comment: 14 pages, harvmac, no figures; revised to add references, fix typos,
add paragraph in Section
N=0 Supersymmetry and the Non-Relativistic Monopole
We study some of the algebraic properties of the non-relativistic monopole.
We find that we can construct theories that possess an exotic conserved
fermionic charge that squares to the Casimir of the rotation group, yet do not
possess an ordinary supersymmetry. This is in contrast to previous known
examples with such exotic fermionic charges. We proceed to show that the
presence of the exotic fermionic charge in the non-supersymmetric theory can
nonetheless be understood using supersymmetric techniques, providing yet
another example of the usefulness of supersymmetry in understanding
non-supersymmetric theories.Comment: 9 pages, harvmac, no figure
Anyon Statistics and the Witten Index
Using the theory of supersymmetric anyons, I extend the definition of the
Witten index to 2+1 dimensions so as to accommodate the existence of anyon spin
and statistics. I then demonstrate that, although in general the index receives
irrational and complex contributions from anyonic states, the overall index is
always integral, and I consider some of the implications and interpretations of
this result.Comment: 10 pages, harvmac, no figures; revised to elaborate on two detail
Minimal Length Uncertainty Relations and New Shape Invariant Models
This paper identifies a new class of shape invariant models. These models are
based on extensions of conventional quantum mechanics that satisfy a
string-motivated minimal length uncertainty relation. An important feature of
our construction is the pairing of operators that are not adjoints of each
other. The results in this paper thus show the broader applicability of shape
invariance to exactly solvable systems.Comment: 11 pages, no figure
Duality and Central Charges in Supersymmetric Quantum Mechanics
We identify a class of point-particle models that exhibit a target-space
duality. This duality arises from a construction based on supersymmetric
quantum mechanics with a non-vanishing central charge. Motivated by analogies
to string theory, we are led to speculate regarding mechanisms for restricting
the background geometry.Comment: 10 pages, 1 figure, late
Applications of Partial Supersymmetry
I examine quantum mechanical Hamiltonians with partial supersymmetry, and
explore two main applications. First, I analyze a theory with a logarithmic
spectrum, and show how to use partial supersymmetry to reveal the underlying
structure of this theory. This method reveals an intriguing equivalence between
two formulations of this theory, one of which is one-dimensional, and the other
of which is infinite-dimensional. Second, I demonstrate the use of partial
supersymmetry as a tool to obtain the asymptotic energy levels in
non-relativistic quantum mechanics in an exceptionally easy way. In the end, I
discuss possible extensions of this work, including the possible connections
between partial supersymmetry and renormalization group arguments.Comment: 11 pages, harvmac, no figures; typo corrected in identifying info on
title pag
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