356 research outputs found
N=4 Topological Amplitudes and Black Hole Entropy
We study the effects of N=4 topological string amplitudes on the entropy of
black holes. We analyse the leading contribution associated to six-derivative
terms and find one particular operator which can correct the entropy of N=4
black holes. This operator is BPS-like and appears in the effective action of
type II string theory on K3 x T^2 or equivalently its heterotic dual on T^6. In
both descriptions the leading contribution arises at one-loop, which we
calculate explicitly on the heterotic side. We then consider whether this term
has any consequences for the entropy of (large) N=4 black holes and find that
it makes indeed a contribution at subleading order. Repeating the computation
for small black holes with vanishing horizon area at the classical level, we
prove that this coupling lifts certain flat directions in the entropy function
thereby being responsible for the attractor equations of some moduli fields.Comment: 33 pages, references added, section 3.3 adde
N=4 superconformal Ward identities for correlation functions
In this paper we study the four-point correlation function of the
energy-momentum supermultiplet in theories with N=4 superconformal symmetry in
four dimensions. We present a compact form of all component correlators as an
invariant of a particular abelian subalgebra of the N=4 superconformal algebra.
This invariant is unique up to a single function of the conformal cross-ratios
which is fixed by comparison with the correlation function of the lowest
half-BPS scalar operators. Our analysis is independent of the dynamics of a
specific theory, in particular it is valid in N=4 super Yang-Mills theory for
any value of the coupling constant. We discuss in great detail a subclass of
component correlators, which is a crucial ingredient for the recent study of
charge-flow correlations in conformal field theories. We compute the latter
explicitly and elucidate the origin of the interesting relations among
different types of flow correlations previously observed in arXiv:1309.1424.Comment: 41 page
Topological Amplitudes and Physical Couplings in String Theory
In these lectures, we review the main properties of the topological theory obtained by twisting the N=2 two-dimensional superconformal algebra, associated to supersymmetric string compactifications. In particular, we describe a set of physical quantities in string theory that are computed by topological amplitudes. These are in general higher-dimensional F-terms in the low energy effective supergravity, or fermion masses after supersymmetry breaking. We discuss N=2 compactifications of type II strings, N=1 compactifications of heterotic and type I strings, as well as N=4 string vacua. Particular emphasis is put on alternative string dual representations allowing calculability, and on the generalization of N=2 holomorphicity and its anomaly
Worldsheet Realization of the Refined Topological String
A worldsheet realization of the refined topological string is proposed in
terms of physical string amplitudes that compute generalized N=2 F-terms of the
form F_{g,n} W^{2g}Y^{2n} in the effective supergravity action. These terms
involve the chiral Weyl superfield W and a superfield Y defined as an N=2
chiral projection of a particular anti-chiral T-bar vector multiplet. In
Heterotic and Type I theories, obtained upon compactification on the
six-dimensional manifold K3xT2, T is the usual K\"ahler modulus of the T2
torus. These amplitudes are computed exactly at the one-loop level in string
theory. They are shown to reproduce the correct perturbative part of the
Nekrasov partition function in the field theory limit when expanded around an
SU(2) enhancement point of the string moduli space. The two deformation
parameters epsilon_- and epsilon_+ of the Omega-supergravity background are
then identified with the constant field-strength backgrounds for the
anti-self-dual graviphoton and self-dual gauge field of the T-bar vector
multiplet, respectively.Comment: 35 pages, typos corrected, published in NP
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How organized is deep convection over Germany?
Deep moist convection shows a tendency to organize into mesoscale structures. To be able to understand the potential effect of convective organization on the climate, one needs first to characterize organization. In this study, we systematically characterize the organizational state of convection over Germany based on two years of cloud-top observations derived from the Meteosat Second Generation satellite and of precipitation cores detected by the German C-band radar network. The organizational state of convection is characterized by commonly employed organization indices, which are mostly based on the object numbers, sizes and nearest-neighbour distances. According to the organization index Iorg, cloud tops and precipitation cores are found to be in an organized state for 69% and 92% of the time, respectively. There is an increase in rainfall when the number of objects and their sizes increase, independently of the organizational state. Case-studies of specific days suggest that convectively organized states correspond to either local multi-cell clusters, with less numerous, larger objects close to each other, or to scattered clusters, with more numerous, smaller organized objects spread out over the domain. For those days, simulations are performed with the large-eddy model ICON with grid spacings of 625, 312 and 156?m. Although the model underestimates rainfall and shows a too large cold cloud coverage, the organizational state is reasonably well represented without significant differences between the grid spacings
From correlation functions to event shapes
We present a new approach to computing event shape distributions or, more
precisely, charge flow correlations in a generic conformal field theory (CFT).
These infrared finite observables are familiar from collider physics studies
and describe the angular distribution of global charges in outgoing radiation
created from the vacuum by some source. The charge flow correlations can be
expressed in terms of Wightman correlation functions in a certain limit. We
explain how to compute these quantities starting from their Euclidean analogues
by means of a non-trivial analytic continuation which, in the framework of CFT,
can elegantly be performed in Mellin space. The relation between the charge
flow correlations and Euclidean correlation functions can be reformulated
directly in configuration space, bypassing the Mellin representation, as a
certain Lorentzian double discontinuity of the correlation function integrated
along the cuts. We illustrate the general formalism in N=4 SYM, making use of
the well-known results on the four-point correlation function of half-BPS
scalar operators. We compute the double scalar flow correlation in N=4 SYM, at
weak and strong coupling and show that it agrees with known results obtained by
different techniques. One of the remarkable features of the N=4 theory is that
the scalar and energy flow correlations are proportional to each other.
Imposing natural physical conditions on the energy flow correlations
(finiteness, positivity and regularity), we formulate additional constraints on
the four-point correlation functions in N=4 SYM that should be valid at any
coupling and away from the planar limit.Comment: 40 pages, 1 figure; v2: typos correcte
Energy-energy correlations in N=4 SYM
We present a new approach to computing energy-energy correlations in gauge
theories that exploits their relation to correlation functions and bypasses the
use of scattering amplitudes. We illustrate its power by calculating
energy-energy correlations in the maximally supersymmetric Yang-Mills theory
(N=4 SYM) in the next-to-leading order approximation.Comment: 5 page
Event shapes in N=4 super-Yang-Mills theory
We study event shapes in N=4 SYM describing the angular distribution of
energy and R-charge in the final states created by the simplest half-BPS scalar
operator. Applying the approach developed in the companion paper
arXiv:1309.0769, we compute these observables using the correlation functions
of certain components of the N=4 stress-tensor supermultiplet: the half-BPS
operator itself, the R-symmetry current and the stress tensor. We present
master formulas for the all-order event shapes as convolutions of the Mellin
amplitude defining the correlation function of the half-BPS operators, with a
coupling-independent kernel determined by the choice of the observable. We find
remarkably simple relations between various event shapes following from N=4
superconformal symmetry. We perform thorough checks at leading order in the
weak coupling expansion and show perfect agreement with the conventional
calculations based on amplitude techniques. We extend our results to strong
coupling using the correlation function of half-BPS operators obtained from the
AdS/CFT correspondence.Comment: 52 pages, 6 figures; v2: typos correcte
Non-Perturbative Nekrasov Partition Function from String Theory
We calculate gauge instanton corrections to a class of higher derivative
string effective couplings introduced in [1]. We work in Type I string theory
compactified on K3xT2 and realise gauge instantons in terms of D5-branes
wrapping the internal space. In the field theory limit we reproduce the
deformed ADHM action on a general {\Omega}-background from which one can
compute the non-perturbative gauge theory partition function using
localisation. This is a non-perturbative extension of [1] and provides further
evidence for our proposal of a string theory realisation of the
{\Omega}-background.Comment: 23 page
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