Unification of the complex Langevin method and the Lefschetz-thimble method

Recently there has been remarkable progress in solving the sign problem, which occurs in investigating statistical systems with a complex weight. The two promising methods, the complex Langevin method and the Lefschetz thimble method, share the idea of complexifying the dynamical variables, but their relationship has not been clear. Here we propose a unified formulation, in which the sign problem is taken care of by both the Langevin dynamics and the holomorphic gradient flow. We apply our formulation to a simple model in three different ways and show that one of them interpolates the two methods by changing the flow time.Comment: 8 pages, 12 figures, presented at the 35th International Symposium on Lattice Field Theory (Lattice 2017), 18-24 June 2017, Granada, Spai

The spatiotemporal expression pattern of the bone morphogenetic protein family in rat ovary cell types during the estrous cycle.

In the mammalian ovary, great interest in the expression and function of the bone morphogenetic protein (BMP) family has been recently generated from evidence of their critical role in determining folliculogenesis and female fertility. Despite extensive work, there is a need to understand the cellular sites of expression of these important regulatory molecules, and how their gene expression changes within the basic ovary cell types through the cycle. Here we have performed a detailed in situ hybridization analysis of the spatial and temporal expression patterns of the BMP ligands (BMP-2, -3, -3b, -4, -6, -7, -15), receptors (BMPR-IA, -IB, -II), and BMP antagonist, follistatin, in rat ovaries over the normal estrous cycle. We have found that: i) all of the mRNAs are expressed in a cell-specific manner in the major classes of ovary cell types (oocyte, granulosa, theca interstitial, theca externa, corpora lutea, secondary interstitial, vascular and ovary surface epithelium); and ii) most undergo dynamic changes during follicular and corpora luteal morphogenesis and histogenesis. The general principle to emerge from these studies is that the developmental programs of folliculogenesis (recruitment, selection, atresia), ovulation, and luteogenesis (luteinization, luteolysis) are accompanied by rather dramatic spatial and temporal changes in the expression patterns of these BMP genes. These results lead us to hypothesize previously unanticipated roles for the BMP family in determining fundamental developmental events that ensure the proper timing and developmental events required for the generation of the estrous cycle

Emergent bubbling geometries in gauge theories with SU(2|4) symmetry

We study the gauge/gravity duality between bubbling geometries in type IIA supergravity and gauge theories with SU(2|4) symmetry, which consist of N=4 super Yang-Mills on $R\times S^3/Z_k$, N=8 super Yang-Mills on $R\times S^2$ and the plane wave matrix model. We show that the geometries are realized as field configurations in the strong coupling region of the gauge theories. On the gravity side, the bubbling geometries can be mapped to electrostatic systems with conducting disks. We derive integral equations which determine the charge densities on the disks. On the gauge theory side, we obtain a matrix integral by applying the localization to a 1/4-BPS sector of the gauge theories. The eigenvalue densities of the matrix integral turn out to satisfy the same integral equations as the charge densities on the gravity side. Thus we find that these two objects are equivalent.Comment: 29 pages, 3 figures; v2: typos corrected and a reference adde

Complex Langevin simulation of QCD at finite density and low temperature using the deformation technique

We study QCD at finite density and low temperature by using the complex Langevin method. We employ the gauge cooling to control the unitarity norm and introduce a deformation parameter in the Dirac operator to avoid the singular-drift problem. The reliability of the obtained results are judged by the probability distribution of the magnitude of the drift term. By making extrapolations with respect to the deformation parameter using only the reliable results, we obtain results for the original system. We perform simulations on a $4^3\times 3$ lattice and show that our method works well even in the region where the reweighting method fails due to the severe sign problem. As a result we observe a delayed onset of the baryon number density as compared with the phase-quenched model, which is a clear sign of the Silver Blaze phenomenon.Comment: 8 pages, 6 figures, presented at the 35th International Symposium on Lattice Field Theory (Lattice 2017), 18-24 June 2017, Granada, Spai