2,650 research outputs found
A Note on Domain Walls and the Parameter Space of N=1 Gauge Theories
We study the spectrum of BPS domain walls within the parameter space of N=1
U(N) gauge theories with adjoint matter and a cubic superpotential. Using a low
energy description obtained by compactifying the theory on R^3 x S^1, we
examine the wall spectrum by combining direct calculations at special points in
the parameter space with insight drawn from the leading order potential between
minimal walls, i.e those interpolating between adjacent vacua. We show that the
multiplicity of composite BPS walls -- as characterised by the CFIV index --
exhibits discontinuities on marginal stability curves within the parameter
space of the maximally confining branch. The structure of these marginal
stability curves for large N appears tied to certain singularities within the
matrix model description of the confining vacua.Comment: 33 pages, LaTeX, 6 eps figures; v2: references adde
BPS Graphs: From Spectral Networks to BPS Quivers
We define "BPS graphs" on punctured Riemann surfaces associated with
theories of class . BPS graphs provide a bridge between
two powerful frameworks for studying the spectrum of BPS states: spectral
networks and BPS quivers. They arise from degenerate spectral networks at
maximal intersections of walls of marginal stability on the Coulomb branch.
While the BPS spectrum is ill-defined at such intersections, a BPS graph
captures a useful basis of elementary BPS states. The topology of a BPS graph
encodes a BPS quiver, even for higher-rank theories and for theories with
certain partial punctures. BPS graphs lead to a geometric realization of the
combinatorics of Fock-Goncharov -triangulations and generalize them in
several ways.Comment: 48 pages, 44 figure
Unsteady undular bores in fully nonlinear shallow-water theory
We consider unsteady undular bores for a pair of coupled equations of
Boussinesq-type which contain the familiar fully nonlinear dissipationless
shallow-water dynamics and the leading-order fully nonlinear dispersive terms.
This system contains one horizontal space dimension and time and can be
systematically derived from the full Euler equations for irrotational flows
with a free surface using a standard long-wave asymptotic expansion.
In this context the system was first derived by Su and Gardner. It coincides
with the one-dimensional flat-bottom reduction of the Green-Naghdi system and,
additionally, has recently found a number of fluid dynamics applications other
than the present context of shallow-water gravity waves. We then use the
Whitham modulation theory for a one-phase periodic travelling wave to obtain an
asymptotic analytical description of an undular bore in the Su-Gardner system
for a full range of "depth" ratios across the bore. The positions of the
leading and trailing edges of the undular bore and the amplitude of the leading
solitary wave of the bore are found as functions of this "depth ratio". The
formation of a partial undular bore with a rapidly-varying finite-amplitude
trailing wave front is predicted for ``depth ratios'' across the bore exceeding
1.43. The analytical results from the modulation theory are shown to be in
excellent agreement with full numerical solutions for the development of an
undular bore in the Su-Gardner system.Comment: Revised version accepted for publication in Phys. Fluids, 51 pages, 9
figure
Irregular singularities in Liouville theory
Motivated by problems arising in the study of N=2 supersymmetric gauge
theories we introduce and study irregular singularities in two-dimensional
conformal field theory, here Liouville theory. Irregular singularities are
associated to representations of the Virasoro algebra in which a subset of the
annihilation part of the algebra act diagonally. In this paper we define
natural bases for the space of conformal blocks in the presence of irregular
singularities, describe how to calculate their series expansions, and how such
conformal blocks can be constructed by some delicate limiting procedure from
ordinary conformal blocks. This leads us to a proposal for the structure
functions appearing in the decomposition of physical correlation functions with
irregular singularities into conformal blocks. Taken together, we get a precise
prediction for the partition functions of some Argyres-Douglas type theories on
the four-sphere.Comment: 84 pages, 6 figure
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