7,163 research outputs found
The Seiberg-Witten Kahler Potential as a Two-Sphere Partition Function
Recently it has been shown that the two-sphere partition function of a gauged
linear sigma model of a Calabi-Yau manifold yields the exact quantum Kahler
potential of the Kahler moduli space of that manifold. Since four-dimensional
N=2 gauge theories can be engineered by non-compact Calabi-Yau threefolds, this
implies that it is possible to obtain exact gauge theory Kahler potentials from
two-sphere partition functions. In this paper, we demonstrate that the
Seiberg-Witten Kahler potential can indeed be obtained as a two-sphere
partition function. To be precise, we extract the quantum Kahler metric of 4D
N=2 SU(2) Super-Yang-Mills theory by taking the field theory limit of the
Kahler parameters of the O(-2,-2) bundle over P1 x P1. We expect this method of
computing the Kahler potential to generalize to other four-dimensional N=2
gauge theories that can be geometrically engineered by toric Calabi-Yau
threefolds.Comment: 12 pages + appendix; v2: minor corrections, reference adde
Tall sections from non-minimal transformations
In previous work, we have shown that elliptic fibrations with two sections,
or Mordell-Weil rank one, can always be mapped birationally to a Weierstrass
model of a certain form, namely, the Jacobian of a model.
Most constructions of elliptically fibered Calabi-Yau manifolds with two
sections have been carried out assuming that the image of this birational map
was a "minimal" Weierstrass model. In this paper, we show that for some
elliptically fibered Calabi-Yau manifolds with Mordell-Weil rank-one, the
Jacobian of the model is not minimal. Said another way,
starting from a Calabi-Yau Weierstrass model, the total space must be blown up
(thereby destroying the "Calabi-Yau" property) in order to embed the model into
. In particular, we show that the elliptic fibrations studied
recently by Klevers and Taylor fall into this class of models.Comment: 16 page
A-twisted correlators and Hori dualities
The Hori-Tong and Hori dualities are infrared dualities between
two-dimensional gauge theories with supersymmetry, which
are reminiscent of four-dimensional Seiberg dualities. We provide additional
evidence for those dualities with , , and
gauge groups, by matching correlation functions of Coulomb branch operators on
a Riemann surface , in the presence of the topological -twist. The
theories studied, denoted by and , can be understood
as orbifolds of an theory. The correlators of these
theories on with are obtained by computing correlators with
-twisted boundary conditions and summing them up with weights
determined by the orbifold projection.Comment: 45 pages plus appendix; v2: updated bibliography and acknowledgement
Quantization of anomaly coefficients in 6D supergravity
We obtain new constraints on the anomaly coefficients of 6D
supergravity theories using local and global anomaly
cancellation conditions. We show how these constraints can be strengthened if
we assume that the theory is well-defined on any spin space-time with an
arbitrary gauge bundle. We distinguish the constraints depending on the gauge
algebra only from those depending on the global structure of the gauge group.
Our main constraint states that the coefficients of the anomaly polynomial for
the gauge group should be an element of where is the unimodular string charge lattice. We show
that the constraints in their strongest form are realized in F-theory
compactifications. In the process, we identify the cocharacter lattice, which
determines the global structure of the gauge group, within the homology lattice
of the compactification manifold.Comment: 42 pages. v3: Some clarifications, typos correcte
FPU physics with nanomechanical graphene resonators: intrinsic relaxation and thermalization from flexural mode coupling
Thermalization in nonlinear systems is a central concept in statistical
mechanics and has been extensively studied theoretically since the seminal work
of Fermi, Pasta and Ulam (FPU). Using molecular dynamics and continuum modeling
of a ring-down setup, we show that thermalization due to nonlinear mode
coupling intrinsically limits the quality factor of nanomechanical graphene
drums and turns them into potential test beds for FPU physics. We find the
thermalization rate to be independent of radius and scaling as
, where and
are effective resonator temperature and prestrain
On the Defect Group of a 6D SCFT
We use the F-theory realization of 6D superconformal field theories (SCFTs)
to study the corresponding spectrum of stringlike, i.e. surface defects. On the
tensor branch, all of the stringlike excitations pick up a finite tension, and
there is a corresponding lattice of string charges, as well as a dual lattice
of charges for the surface defects. The defect group is data intrinsic to the
SCFT and measures the surface defect charges which are not screened by
dynamical strings. When non-trivial, it indicates that the associated theory
has a partition vector rather than a partition function. We compute the defect
group for all known 6D SCFTs, and find that it is just the abelianization of
the discrete subgroup of U(2) which appears in the classification of 6D SCFTs
realized in F-theory. We also explain how the defect group specifies defining
data in the compactification of a (1,0) SCFT.Comment: 24 page
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