199 research outputs found
The geometry of finite dimensional algebras with vanishing radical square
Let be a basic finite dimensional algebra over an algebraically
closed field, with the property that the square of the Jacobson radical
vanishes. We determine the irreducible components of the module variety
for any dimension vector . Our description
leads to a count of the components in terms of the underlying Gabriel quiver. A
closed formula for the number of components when is local extends
existing counts for the two-loop quiver to quivers with arbitrary finite sets
of loops.
For any algebra with , our criteria for identifying the
components of permit us to characterize the
modules parametrized by the individual irreducible components. Focusing on such
a component, we explore generic properties of the corresponding modules by
establishing a geometric bridge between the algebras with zero radical square
on one hand and their stably equivalent hereditary counterparts on the other.
The bridge links certain closed subvarieties of Grassmannians parametrizing the
modules with fixed top over the two types of algebras. By way of this
connection, we transfer results of Kac and Schofield from the hereditary case
to algebras of Loewy length . Finally, we use the transit of information to
show that any algebra of Loewy length which enjoys the dense orbit property
in the sense of Chindris, Kinser and Weyman has finite representation type
Quantum hypermultiplet moduli spaces in N=2 string vacua: a review
The hypermultiplet moduli space M_H in type II string theories compactified
on a Calabi-Yau threefold X is largely constrained by supersymmetry (which
demands quaternion-K\"ahlerity), S-duality (which requires an isometric action
of SL(2, Z)) and regularity. Mathematically, M_H ought to encode all
generalized Donaldson-Thomas invariants on X consistently with wall-crossing,
modularity and homological mirror symmetry. We review recent progress towards
computing the exact metric on M_H, or rather the exact complex contact
structure on its twistor space.Comment: 31 pages; Contribution to the Proceedings of String Math 2012; v2:
references added, misprints corrected, published versio
Holographic Lattices, Dimers, and Glasses
We holographically engineer a periodic lattice of localized fermionic
impurities within a plasma medium by putting an array of probe D5-branes in the
background produced by N D3-branes. Thermodynamic quantities are computed in
the large N limit via the holographic dictionary. We then dope the lattice by
replacing some of the D5-branes by anti-D5-branes. In the large N limit, we
determine the critical temperature below which the system dimerizes with bond
ordering. Finally, we argue that for the special case of a square lattice our
system is glassy at large but finite N, with the low temperature physics
dominated by a huge collection of metastable dimerized configurations without
long-range order, connected only through tunneling events.Comment: 20 pages, 7 figures; v2: minor revisions mad
Toric Methods in F-theory Model Building
In this review article we discuss recent constructions of global F-theory GUT
models and explain how to make use of toric geometry to do calculations within
this framework. After introducing the basic properties of global F-theory GUTs
we give a self-contained review of toric geometry and introduce all the tools
that are necessary to construct and analyze global F-theory models. We will
explain how to systematically obtain a large class of compact Calabi-Yau
fourfolds which can support F-theory GUTs by using the software package PALP.Comment: 19 pages. Prepared for the special issue "Computational Algebraic
Geometry in String and Gauge Theory" of Advances in High Energy Physics, v2:
references added, typos correcte
Massless interacting particles
We show that classical electrodynamics of massless charged particles and the
Yang--Mills theory of massless quarks do not experience rearranging their
initial degrees of freedom into dressed particles and radiation. Massless
particles do not radiate. We consider a version of the direct interparticle
action theory for these systems following the general strategy of Wheeler and
Feynman.Comment: LaTeX; 20 pages; V4: discussion is slightly modified to clarify some
important points, relevant references are adde
T-duality simplifies bulk-boundary correspondence: some higher dimensional cases
Recently we introduced T-duality in the study of topological insulators, and
used it to show that T-duality trivialises the bulk-boundary correspondence in
2 dimensions. In this paper, we partially generalise these results to higher
dimensions and briefly discuss the 4D quantum Hall effect.Comment: 25 pages. To appear in Ann. Henri Poincar
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