4,281 research outputs found
Rigid Limit in N=2 Supergravity and Weak-Gravity Conjecture
We analyze the coupled N=2 supergravity and Yang-Mills system using
holomorphy, near the rigid limit where the former decouples from the latter. We
find that there appears generically a new mass scale around g M_{pl} where g is
the gauge coupling constant and M_{pl} is the Planck scale. This is in accord
with the weak-gravity conjecture proposed recently. We also study the scale
dependence of the gauge theory prepotential from its embedding into
supergravity.Comment: 17 pages, minor correction
Superconformal Algebras and Mock Theta Functions
It is known that characters of BPS representations of extended superconformal
algebras do not have good modular properties due to extra singular vectors
coming from the BPS condition. In order to improve their modular properties we
apply the method of Zwegers which has recently been developed to analyze
modular properties of mock theta functions. We consider the case of N=4
superconformal algebra at general levels and obtain the decomposition of
characters of BPS representations into a sum of simple Jacobi forms and an
infinite series of non-BPS representations.
We apply our method to study elliptic genera of hyper-Kahler manifolds in
higher dimensions. In particular we determine the elliptic genera in the case
of complex 4 dimensions of the Hilbert scheme of points on K3 surfaces K^{[2]}
and complex tori A^{[[3]]}.Comment: 28 page
A comparsion of force sensors for atomic force microscopy based on quartz tuning forks and length extensional resonators
The force sensor is key to the performance of atomic force microscopy (AFM).
Nowadays, most AFMs use micro-machined force sensors made from silicon, but
piezoelectric quartz sensors are applied at an increasing rate, mainly in
vacuum. These self sensing force sensors allow a relatively easy upgrade of a
scanning tunneling microscope to a combined scanning tunneling/atomic force
microscope. Two fundamentally different types of quartz sensors have achieved
atomic resolution: the 'needle sensor' that is based on a length extensional
resonator and the 'qPlus sensor' that is based on a tuning fork. Here, we
calculate and measure the noise characteristics of these sensors. We find four
noise sources: deflection detector noise, thermal noise, oscillator noise and
thermal drift noise. We calculate the effect of these noise sources as a factor
of sensor stiffness, bandwidth and oscillation amplitude. We find that for self
sensing quartz sensors, the deflection detector noise is independent of sensor
stiffness, while the remaining three noise sources increase strongly with
sensor stiffness. Deflection detector noise increases with bandwidth to the
power of 1.5, while thermal noise and oscillator noise are proportional to the
square root of the bandwidth. Thermal drift noise, however, is inversely
proportional to bandwidth. The first three noise sources are inversely
proportional to amplitude while thermal drift noise is independent of the
amplitude. Thus, we show that the earlier finding that quoted optimal
signal-to-noise ratio for oscillation amplitudes similar to the range of the
forces is still correct when considering all four frequency noise
contributions. Finally, we suggest how the signal-to-noise ratio of the sensors
can be further improved and briefly discuss the challenges of mounting tips.Comment: 40 pages, 14 figure
Numerical results from large N reduced QCD_2
Some results in QCD_2 at large N are presented using the reduced model on the
lattice. Overlap fermions are used to compute meson propagators.Comment: 3 pages, contribution to Lattice 2002, Bosto
Comments on Non-holomorphic Modular Forms and Non-compact Superconformal Field Theories
We extend our previous work arXiv:1012.5721 [hep-th] on the non-compact N=2
SCFT_2 defined as the supersymmetric SL(2,R)/U(1)-gauged WZW model. Starting
from path-integral calculations of torus partition functions of both the
axial-type (`cigar') and the vector-type (`trumpet') models, we study general
models of the Z_M-orbifolds and M-fold covers with an arbitrary integer M. We
then extract contributions of the degenerate representations (`discrete
characters') in such a way that good modular properties are preserved. The
`modular completion' of the extended discrete characters introduced in
arXiv:1012.5721 [hep-th] are found to play a central role as suitable building
blocks in every model of orbifolds or covering spaces. We further examine a
large M-limit (the `continuum limit'), which `deconstructs' the spectral flow
orbits while keeping a suitable modular behavior. The discrete part of
partition function as well as the elliptic genus is then expanded by the
modular completions of irreducible discrete characters, which are parameterized
by both continuous and discrete quantum numbers modular transformed in a mixed
way. This limit is naturally identified with the universal cover of trumpet
model. We finally discuss a classification of general modular invariants based
on the modular completions of irreducible characters constructed above.Comment: 1+40 pages, no figure; v2 some points are clarified with respect to
the `continuum limit', typos corrected, to appear in JHEP; v3 footnotes added
in pages 18, 23 for the relation with arXiv:1407.7721[hep-th
Two-dimensional Gross-Neveu Model with Wilson Fermion Action at Finite Temperature and Density
We analytically investigate the 2-dimensional Gross-Neveu model at finite
temperature and density using Wilson fermion action. The relation between the
phase structure on the lattice and that in the continuum is clarified.Comment: LATTICE98(hightemp), 3 pages, 3 eps figure
Lorentz Invariance and Origin of Symmetries
In this letter we reconsider the role of Lorentz invariance in the dynamical
generation of the observed internal symmetries. We argue that, generally,
Lorentz invariance can only be imposed in the sense that all Lorentz
non-invariant effects caused by the spontaneous breakdown of Lorentz symmetry
are physically unobservable. Remarkably, the application of this principle to
the most general relativistically invariant Lagrangian, with arbitrary
couplings for all the fields involved, leads by itself to the appearance of a
symmetry and, what is more, to the massless vector fields gauging this symmetry
in both Abelian and non-Abelian cases. In contrast, purely global symmetries
are only generated as accidental consequences of the gauge symmetry.Comment: 10 page LaTeX fil
The non-compact elliptic genus: mock or modular
We analyze various perspectives on the elliptic genus of non-compact
supersymmetric coset conformal field theories with central charge larger than
three. We calculate the holomorphic part of the elliptic genus via a free field
description of the model, and show that it agrees with algebraic expectations.
The holomorphic part of the elliptic genus is directly related to an
Appell-Lerch sum and behaves anomalously under modular transformation
properties. We analyze the origin of the anomaly by calculating the elliptic
genus through a path integral in a coset conformal field theory. The path
integral codes both the holomorphic part of the elliptic genus, and a
non-holomorphic remainder that finds its origin in the continuous spectrum of
the non-compact model. The remainder term can be shown to agree with a function
that mathematicians introduced to parameterize the difference between mock
theta functions and Jacobi forms. The holomorphic part of the elliptic genus
thus has a path integral completion which renders it non-holomorphic and
modular.Comment: 13 page
Towards A Topological G_2 String
We define new topological theories related to sigma models whose target space
is a 7 dimensional manifold of G_2 holonomy. We show how to define the
topological twist and identify the BRST operator and the physical states.
Correlation functions at genus zero are computed and related to Hitchin's
topological action for three-forms. We conjecture that one can extend this
definition to all genus and construct a seven-dimensional topological string
theory. In contrast to the four-dimensional case, it does not seem to compute
terms in the low-energy effective action in three dimensions.Comment: 15 pages, To appear in the proceedings of Cargese 2004 summer schoo
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