Universality of Nonperturbative Effects in c<1 Noncritical String Theory

Nonperturbative effects in c<1 noncritical string theory are studied using the two-matrix model. Such effects are known to have the form fixed by the string equations but the numerical coefficients have not been known so far. Using the method proposed recently, we show that it is possible to determine the coefficients for (p,q) string theory. We find that they are indeed finite in the double scaling limit and universal in the sense that they do not depend on the detailed structure of the potential of the two-matrix model.Comment: 17 page

Transcriptional implications of intragenic DNA methylation in the oestrogen receptor alpha gene in breast cancer cells and tissues

Background DNA methylation variability regions (MVRs) across the oestrogen receptor alpha (ESR1) gene have been identified in peripheral blood cells from breast cancer patients and healthy individuals. In contrast to promoter methylation, gene body methylation may be important in maintaining active transcription. This study aimed to assess MVRs in ESR1 in breast cancer cell lines, tumour biopsies and exfoliated epithelial cells from expressed breast milk (EBM), to determine their significance for ESR1 transcription. Methods DNA methylation levels in eight MVRs across ESR1 were assessed by pyrosequencing bisulphite-converted DNA from three oestrogen receptor (ER)-positive and three ER-negative breast cancer cell lines. DNA methylation and expression were assessed following treatment with DAC (1 μM), or DMSO (controls). ESR1 methylation levels were also assayed in DNA from 155 invasive ductal carcinoma biopsies provided by the Breast Cancer Campaign Tissue Bank, and validated with DNA methylation profiles from the TCGA breast tumours (n = 356 ER-pos, n = 109 ER-neg). DNA methylation was profiled in exfoliated breast epithelial cells from EBM using the Illumina 450 K (n = 36) and pyrosequencing in a further 53 donor samples. ESR1 mRNA levels were measured by qRT-PCR. Results We show that ER-positive cell lines had unmethylated ESR1 promoter regions and highly methylated intragenic regions (median, 80.45%) while ER-negative cells had methylated promoters and lower intragenic methylation levels (median, 38.62%). DAC treatment increased ESR1 expression in ER-negative cells, but significantly reduced methylation and expression of ESR1 in ER-positive cells. The ESR1 promoter was unmethylated in breast tumour biopsies with high levels of intragenic methylation, independent of ER status. However, ESR1 methylation in the strongly ER-positive EBM DNA samples were very similar to ER-positive tumour cell lines. Conclusion DAC treatment inhibited ESR1 transcription in cells with an unmethylated ESR1 promoter and reduced intragenic DNA methylation. Intragenic methylation levels correlated with ESR1 expression in homogenous cell populations (cell lines and exfoliated primary breast epithelial cells), but not in heterogeneous tumour biopsies, highlighting the significant differences between the in vivo tumour microenvironment and individual homogenous cell types. These findings emphasise the need for care when choosing material for epigenetic research and highlights the presence of aberrant intragenic methylation levels in tumour tissue

The Trouble with de Sitter Space

In this paper we assume the de Sitter Space version of Black Hole Complementarity which states that a single causal patch of de Sitter space is described as an isolated finite temperature cavity bounded by a horizon which allows no loss of information. We discuss the how the symmetries of de Sitter space should be implemented. Then we prove a no go theorem for implementing the symmetries if the entropy is finite. Thus we must either give up the finiteness of the de Sitter entropy or the exact symmetry of the classical space. Each has interesting implications for the very long time behavior. We argue that the lifetime of a de Sitter phase can not exceed the Poincare recurrence time. This is supported by recent results of Kachru, Kallosh, Linde and Trivedi.Comment: 15 pages, 1 figure. v2: added fifth section with comments on long time stability of de Sitter space, in which we argue that the lifetime can not exceed the Poincare recurrence time. v3: corrected a minor error in the appendi

Scattered Results in 2D String Theory

The nonperturbative $1\to N$ tachyon scattering amplitude in 2D type 0A string theory is computed. The probability that $N$ particles are produced is a monotonically decreasing function of $N$ whenever $N$ is large enough that statistical methods apply. The results are compared with expectations from black hole thermodynamics.Comment: 22 pages, 5 figures, harvmac. v2: minor comments added, typos correcte

Nonperturbative effects and nonperturbative definitions in matrix models and topological strings

We develop techniques to compute multi-instanton corrections to the 1/N expansion in matrix models described by orthogonal polynomials. These techniques are based on finding trans-series solutions, i.e. formal solutions with exponentially small corrections, to the recursion relations characterizing the free energy. We illustrate this method in the Hermitian, quartic matrix model, and we provide a detailed description of the instanton corrections in the Gross-Witten-Wadia (GWW) unitary matrix model. Moreover, we use Borel resummation techniques and results from the theory of resurgent functions to relate the formal multi-instanton series to the nonperturbative definition of the matrix model. We study this relation in the case of the GWW model and its double-scaling limit, providing in this way a nice illustration of various mechanisms connecting the resummation of perturbative series to nonperturbative results, like the cancellation of nonperturbative ambiguities. Finally, we argue that trans-series solutions are also relevant in the context of topological string theory. In particular, we point out that in topological string models with both a matrix model and a large N gauge theory description, the nonperturbative, holographic definition involves a sum over the multi-instanton sectors of the matrix modelComment: 50 pages, 12 figures, comments and references added, small correction

An approximate renormalization-group transformation for Hamiltonian systems with three degrees of freedom

We construct an approximate renormalization transformation that combines Kolmogorov-Arnold-Moser (KAM)and renormalization-group techniques, to analyze instabilities in Hamiltonian systems with three degrees of freedom. This scheme is implemented both for isoenergetically nondegenerate and for degenerate Hamiltonians. For the spiral mean frequency vector, we find numerically that the iterations of the transformation on nondegenerate Hamiltonians tend to degenerate ones on the critical surface. As a consequence, isoenergetically degenerate and nondegenerate Hamiltonians belong to the same universality class, and thus the corresponding critical invariant tori have the same type of scaling properties. We numerically investigate the structure of the attracting set on the critical surface and find that it is a strange nonchaotic attractor. We compute exponents that characterize its universality class.Comment: 10 pages typeset using REVTeX, 7 PS figure

A toy model for the AdS/CFT correspondence

We study the large N gauged quantum mechanics for a single Hermitian matrix in the Harmonic oscillator potential well as a toy model for the AdS/CFT correspondence. We argue that the dual geometry should be a string in two dimensions with a curvature of stringy size. Even though the dual geometry is not weakly curved, one can still gain knowledge of the system from a detailed study of the open-closed string duality. We give a mapping between the basis of states made of traces (closed strings) and the eigenvalues of the matrix (D-brane picture) in terms of Schur polynomials. We connect this model with the study of giant gravitons in AdS_5 x S^5. We show that the two giant gravitons that expand along AdS_5 and S^5 can be interpreted in the matrix model as taking an eigenvalue from the Fermi sea and exciting it very much, or as making a hole in the Fermi sea respectively. This is similar to recent studies of the c=1 string. This connection gives new insight on how to perform calculations for giant gravitons.Comment: 19 pages JHEP, 4 figures. v2: comments added, typos fixed, additional refs. v3: The paper has been largely revised, to make the relation as a limit of N=4 SYM clear, also some proofs have been written in full rather than sketched. This updated version reflects the changes that were made in the published versio

Large D-instanton effects in string theory

By reduction along the time direction, black holes in 4 dimensions yield instantons in 3 dimensions. Each of these instantons contributes individually at order $\exp(-|Q|/g_s)$ to certain protected couplings in the three-dimensional effective action, but the number of distinct instantons is expected to be equal (or comparable) to the number of black hole micro-states, i.e. of order $\exp(Q^2)$. The same phenomenon also occurs for certain protected couplings in four dimensions, such as the hypermultiplet metric in type II string theories compactified on a Calabi-Yau threefold. In either case, the D-instanton series is therefore asymptotic, much like the perturbative expansion in any quantum field theory. By using a Borel-type resummation method, adapted to the Gaussian growth of the D-instanton series, we find that the total D-instanton sum has an inherent ambiguity of order $\exp(-1/g_s^2)$. We further suggest that this ambiguity can be lifted by including Kaluza-Klein monopole or NS5-brane instantons.Comment: 11 pages, uses JHEP3.cls, v2, typos fixed and added footnote, v3, minor correction

Quantum Black Holes as Holograms in AdS Braneworlds

We propose a new approach for using the AdS/CFT correspondence to study quantum black hole physics. The black holes on a brane in an AdS$_{D+1}$ braneworld that solve the classical bulk equations are interpreted as duals of {\it quantum-corrected} $D$-dimensional black holes, rather than classical ones, of a conformal field theory coupled to gravity. We check this explicitly in D=3 and D=4. In D=3 we reinterpret the existing exact solutions on a flat membrane as states of the dual 2+1 CFT. We show that states with a sufficiently large mass really are 2+1 black holes where the quantum corrections dress the classical conical singularity with a horizon and censor it from the outside. On a negatively curved membrane, we reinterpret the classical bulk solutions as quantum-corrected BTZ black holes. In D=4 we argue that the bulk solution for the brane black hole should include a radiation component in order to describe a quantum-corrected black hole in the 3+1 dual. Hawking radiation of the conformal field is then dual to classical gravitational bremsstrahlung in the AdS$_5$ bulk.Comment: 28 pages, JHEP latex, 1 .eps figure, v2: references and comments added, v3: comments and acknowledgements added to match the published pape