141 research outputs found
Three-dimensional AdS gravity and extremal CFTs at c=8m
We note that Witten's proposed duality between extremal c=24k CFTs and
three-dimensional anti-de Sitter gravity may possibly be extended to central
charges that are multiples of 8, for which extremal self-dual CFTs are known to
exist up to c=40. All CFTs of this type with central charge 24 or higher,
provided that they exist, have the required mass gap and may serve as candidate
duals to three-dimensional gravity at the corresponding values of the
cosmological constant. Here, we compute the genus one partition function of
these theories up to c=88, we give exact and approximate formulas for the
degeneracies of states, and we determine the genus two partition functions of
the theories up to c=40.Comment: 17 pages, harvmac; v2: references added, version accepted in JHE
Topological Strings and (Almost) Modular Forms
The B-model topological string theory on a Calabi-Yau threefold X has a
symmetry group Gamma, generated by monodromies of the periods of X. This acts
on the topological string wave function in a natural way, governed by the
quantum mechanics of the phase space H^3(X). We show that, depending on the
choice of polarization, the genus g topological string amplitude is either a
holomorphic quasi-modular form or an almost holomorphic modular form of weight
0 under Gamma. Moreover, at each genus, certain combinations of genus g
amplitudes are both modular and holomorphic. We illustrate this for the local
Calabi-Yau manifolds giving rise to Seiberg-Witten gauge theories in four
dimensions and local P_2 and P_1 x P_1. As a byproduct, we also obtain a simple
way of relating the topological string amplitudes near different points in the
moduli space, which we use to give predictions for Gromov-Witten invariants of
the orbifold C^3/Z_3.Comment: 62 pages, 1 figure; v2: minor correction
Direct Integration and Non-Perturbative Effects in Matrix Models
We show how direct integration can be used to solve the closed amplitudes of
multi-cut matrix models with polynomial potentials. In the case of the cubic
matrix model, we give explicit expressions for the ring of non-holomorphic
modular objects that are needed to express all closed matrix model amplitudes.
This allows us to integrate the holomorphic anomaly equation up to holomorphic
modular terms that we fix by the gap condition up to genus four. There is an
one-dimensional submanifold of the moduli space in which the spectral curve
becomes the Seiberg--Witten curve and the ring reduces to the non-holomorphic
modular ring of the group . On that submanifold, the gap conditions
completely fix the holomorphic ambiguity and the model can be solved explicitly
to very high genus. We use these results to make precision tests of the
connection between the large order behavior of the 1/N expansion and
non-perturbative effects due to instantons. Finally, we argue that a full
understanding of the large genus asymptotics in the multi-cut case requires a
new class of non-perturbative sectors in the matrix model.Comment: 51 pages, 8 figure
Direct Integration of the Topological String
We present a new method to solve the holomorphic anomaly equations governing
the free energies of type B topological strings. The method is based on direct
integration with respect to the non-holomorphic dependence of the amplitudes,
and relies on the interplay between non-holomorphicity and modularity
properties of the topological string amplitudes. We develop a formalism valid
for any Calabi-Yau manifold and we study in detail two examples, providing
closed expressions for the amplitudes at low genus, as well as a discussion of
the boundary conditions that fix the holomorphic ambiguity. The first example
is the non-compact Calabi-Yau underlying Seiberg-Witten theory and its
gravitational corrections. The second example is the Enriques Calabi-Yau, which
we solve in full generality up to genus six. We discuss various aspects of this
model: we obtain a new method to generate holomorphic automorphic forms on the
Enriques moduli space, we write down a new product formula for the fiber
amplitudes at all genus, and we analyze in detail the field theory limit. This
allows us to uncover the modularity properties of SU(2), N=2 super Yang-Mills
theory with four massless hypermultiplets.Comment: 75 pages, 3 figure
Counting points on hyperelliptic curves over finite fields
International audienceWe describe some algorithms for computing the cardinality of hyperelliptic curves and their Jacobians over finite fields. They include several methods for obtaining the result modulo small primes and prime powers, in particular an algorithm à la Schoof for genus 2 using Cantor's division polynomials. These are combined with a birthday paradox algorithm to calculate the cardinality. Our methods are practical and we give actual results computed using our current implementation. The Jacobian groups we handle are larger than those previously reported in the literature
Metastasis to the breast from an adenocarcinoma of the lung with extensive micropapillary component: a case report and review of the literature
Breast metastasis from extra-mammary malignancy is rare. Based on the literature an incidence of 0.4-1.3% is reported. The primary malignancies most commonly metastasizing to the breast are leukemia-lymphoma, and malignant melanoma. We present a case of metastasis to the breast from a pulmonary adenocarcinoma, with extensive micropapillary component, diagnosed concomitantly with the primary tumor. A 73-year-old female presented with dyspnea and dry cough of 4 weeks duration and a massive pleural effusion was found on a chest radiograph. Additionally, on physical examination a poorly defined mass was noted in the upper outer quadrant of the left breast. The patient underwent bronchoscopy, excisional breast biopsy and medical thoracoscopy. By cytology, histology and immunohistochemistry primary lung adenocarcinoma with metastasis to the breast and parietal pleura was diagnosed. Both the primary and metastatic anatomic sites demonstrated histologically extensive micropapillary component, which is recently recognized as an important prognostic factor. The patient received chemotherapy but passed away within 7 months. Accurate differentiation of metastatic from primary carcinoma is of crucial importance because the treatment and prognosis differ significantly
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