26,980 research outputs found
Tropical Geometry and Five Dimensional Higgs Branches at Infinite Coupling
Superconformal five dimensional theories have a rich structure of phases and
brane webs play a crucial role in studying their properties. This paper is
devoted to the study of a three parameter family of SQCD theories, given by the
number of colors for an gauge theory, number of fundamental
flavors , and the Chern Simons level . The study of their infinite
coupling Higgs branch is a long standing problem and reveals a rich pattern of
moduli spaces, depending on the 3 values in a critical way. For a generic
choice of the parameters we find a surprising number of 3 different components,
with intersections that are closures of height 2 nilpotent orbits of the flavor
symmetry. This is in contrast to previous studies where except for one case
(), the parameters were restricted to the cases of Higgs branches
that have only one component. The new feature is achieved thanks to a concept
in tropical geometry which is called stable intersection and allows for a
computation of the Higgs branch to almost all the cases which were previously
unknown for this three parameter family apart form certain small number of
exceptional theories with low rank gauge group. A crucial feature in the
construction of the Higgs branch is the notion of dressed monopole operators.Comment: 49 page
Boundaries of Amplituhedra and NMHV Symbol Alphabets at Two Loops
In this sequel to arXiv:1711.11507 we classify the boundaries of amplituhedra
relevant for determining the branch points of general two-loop amplitudes in
planar super-Yang-Mills theory. We explain the connection to
on-shell diagrams, which serves as a useful cross-check. We determine the
branch points of all two-loop NMHV amplitudes by solving the Landau equations
for the relevant configurations and are led thereby to a conjecture for the
symbol alphabets of all such amplitudes.Comment: 42 pages, 6 figures, 8 tables; v2: minor corrections and improvement
Persistent Homology Over Directed Acyclic Graphs
We define persistent homology groups over any set of spaces which have
inclusions defined so that the corresponding directed graph between the spaces
is acyclic, as well as along any subgraph of this directed graph. This method
simultaneously generalizes standard persistent homology, zigzag persistence and
multidimensional persistence to arbitrary directed acyclic graphs, and it also
allows the study of more general families of topological spaces or point-cloud
data. We give an algorithm to compute the persistent homology groups
simultaneously for all subgraphs which contain a single source and a single
sink in arithmetic operations, where is the number of vertices in
the graph. We then demonstrate as an application of these tools a method to
overlay two distinct filtrations of the same underlying space, which allows us
to detect the most significant barcodes using considerably fewer points than
standard persistence.Comment: Revised versio
Acylindrical hyperbolicity of cubical small-cancellation groups
We provide an analogue of Strebel's classification of geodesic triangles in
classical groups for groups given by Wise's cubical presentations
satisfying sufficiently strong metric cubical small cancellation conditions.
Using our classification, we prove that, except in specific degenerate cases,
such groups are acylindrically hyperbolic.Comment: Added figures. Exposition improved in Section 3,
correction/simplification in Section 5, background added and citations
updated in Section
5d/6d DE instantons from trivalent gluing of web diagrams
We propose a new prescription for computing the Nekrasov partition functions
of five-dimensional theories with eight supercharges realized by gauging
non-perturbative flavor symmetries of three five-dimensional superconformal
field theories. The topological vertex formalism gives a way to compute the
partition functions of the matter theories with flavor instanton backgrounds,
and the gauging is achieved by summing over Young diagrams. We apply the
prescription to calculate the Nekrasov partition functions of various
five-dimensional gauge theories such as gauge theories with
or without hypermultiplets in the vector representation and also pure gauge theories. Furthermore, the technique can be applied to
computations of the Nekrasov partition functions of five-dimensional theories
which arise from circle compactifications of six-dimensional minimal
superconformal field theories characterized by the gauge groups
. We exemplify our method by
comparing some of the obtained partition functions with known results and find
perfect agreement. We also present a prescription of extending the gluing rule
to the refined topological vertex.Comment: 66 pages, 28 figures; v2: typos corrected, references added and a
Mathematica notebook for some checks adde
- β¦