Gauge Threshold Corrections for Local String Models

We study gauge threshold corrections for local brane models embedded in a large compact space. A large bulk volume gives important contributions to the Konishi and super-Weyl anomalies and the effective field theory analysis implies the unification scale should be enhanced in a model-independent way from M_s to R M_s. For local D3/D3 models this result is supported by the explicit string computations. In this case the scale R M_s comes from the necessity of global cancellation of RR tadpoles sourced by the local model. We also study D3/D7 models and discuss discrepancies with the effective field theory analysis. We comment on phenomenological implications for gauge coupling unification and for the GUT scale.Comment: 30 pages; v2: references added, minor typos correcte

On the Effective Description of Large Volume Compactifications

We study the reliability of the Two-Step moduli stabilization in the type-IIB Large Volume Scenarios with matter and gauge interactions. The general analysis is based on a family of N=1 Supergravity models with a factorizable Kaehler invariant function, where the decoupling between two sets of fields without a mass hierarchy is easily understood. For the Large Volume Scenario particular analyses are performed for explicit models, one of such developed for the first time here, finding that the simplified version, where the Dilaton and Complex structure moduli are regarded as frozen by a previous stabilization, is a reliable supersymmetric description whenever the neglected fields stand at their leading F-flatness conditions and be neutral. The terms missed by the simplified approach are either suppressed by powers of the Calabi-Yau volume, or are higher order operators in the matter fields, and then irrelevant for the moduli stabilization rocedure. Although the power of the volume suppressing such corrections depends on the particular model, up to the mass level it is independent of the modular weight for the matter fields. This at least for the models studied here but we give arguments to expect the same in general. These claims are checked through numerical examples. We discuss how the factorizable models present a context where despite the lack of a hierarchy with the supersymmetry breaking scale, the effective theory still has a supersymmetric description. This can be understood from the fact that it is possible to find vanishing solution for the auxiliary components of the fields being integrated out, independently of the remaining dynamics. Our results settle down the question on the reliability of the way the Dilaton and Complex structure are treated in type-IIB compactifications with large compact manifold volumina.Comment: 23 pages + 2 appendices (38 pages total). v2: minor improvements, typos fixed. Version published in JHE

On two problems in graph Ramsey theory

We study two classical problems in graph Ramsey theory, that of determining the Ramsey number of bounded-degree graphs and that of estimating the induced Ramsey number for a graph with a given number of vertices. The Ramsey number r(H) of a graph H is the least positive integer N such that every two-coloring of the edges of the complete graph $K_N$ contains a monochromatic copy of H. A famous result of Chv\'atal, R\"{o}dl, Szemer\'edi and Trotter states that there exists a constant c(\Delta) such that r(H) \leq c(\Delta) n for every graph H with n vertices and maximum degree \Delta. The important open question is to determine the constant c(\Delta). The best results, both due to Graham, R\"{o}dl and Ruci\'nski, state that there are constants c and c' such that 2^{c' \Delta} \leq c(\Delta) \leq 2^{c \Delta \log^2 \Delta}. We improve this upper bound, showing that there is a constant c for which c(\Delta) \leq 2^{c \Delta \log \Delta}. The induced Ramsey number r_{ind}(H) of a graph H is the least positive integer N for which there exists a graph G on N vertices such that every two-coloring of the edges of G contains an induced monochromatic copy of H. Erd\H{o}s conjectured the existence of a constant c such that, for any graph H on n vertices, r_{ind}(H) \leq 2^{c n}. We move a step closer to proving this conjecture, showing that r_{ind} (H) \leq 2^{c n \log n}. This improves upon an earlier result of Kohayakawa, Pr\"{o}mel and R\"{o}dl by a factor of \log n in the exponent.Comment: 18 page

On 'Light' Fermions and Proton Stability in 'Big Divisor' D3/D7 Swiss Cheese Phenomenology

Building up on our earlier work [1,2], we show the possibility of generating "light" fermion mass scales of MeV-GeV range (possibly related to first two generations of quarks/leptons) as well as eV (possibly related to first two generations of neutrinos) in type IIB string theory compactified on Swiss-Cheese orientifolds in the presence of a mobile space-time filling D3-$brane restricted to (in principle) stacks of fluxed D7-branes wrapping the "big" divisor \Sigma_B. This part of the paper is an expanded version of the latter half of section 3 of a published short invited review [3] written up by one of the authors [AM]. Further, we also show that there are no SUSY GUT-type dimension-five operators corresponding to proton decay, as well as estimate the proton lifetime from a SUSY GUT-type four-fermion dimension-six operator to be 10^{61} years. Based on GLSM calculations in [1] for obtaining the geometric Kaehler potential for the "big divisor", using further the Donaldson's algorithm, we also briefly discuss in the first of the two appendices, obtaining a metric for the Swiss-Cheese Calabi-Yau used, that becomes Ricci flat in the large volume limit.Comment: v2: 1+25 pages, Title modified and text thoroughly expanded including a brief discussion on obtaining Ricci-flat Swiss Cheese Calabi-Yau metrics using the Donaldson's algorithm, references added, to appear in EPJ

Ground State Energy of the Low Density Bose Gas

Now that the properties of low temperature Bose gases at low density, $\rho$, can be examined experimentally it is appropriate to revisit some of the formulas deduced by many authors 4-5 decades ago. One of these is that the leading term in the energy/particle is $2\pi \hbar^2 \rho a/m$, where $a$ is the scattering length. Owing to the delicate and peculiar nature of bosonic correlations, four decades of research have failed to establish this plausible formula rigorously. The only known lower bound for the energy was found by Dyson in 1957, but it was 14 times too small. The correct bound is proved here.Comment: 4 pages, Revtex, reference 12 change

Bounds for graph regularity and removal lemmas

We show, for any positive integer k, that there exists a graph in which any equitable partition of its vertices into k parts has at least ck^2/\log^* k pairs of parts which are not \epsilon-regular, where c,\epsilon>0 are absolute constants. This bound is tight up to the constant c and addresses a question of Gowers on the number of irregular pairs in Szemer\'edi's regularity lemma. In order to gain some control over irregular pairs, another regularity lemma, known as the strong regularity lemma, was developed by Alon, Fischer, Krivelevich, and Szegedy. For this lemma, we prove a lower bound of wowzer-type, which is one level higher in the Ackermann hierarchy than the tower function, on the number of parts in the strong regularity lemma, essentially matching the upper bound. On the other hand, for the induced graph removal lemma, the standard application of the strong regularity lemma, we find a different proof which yields a tower-type bound. We also discuss bounds on several related regularity lemmas, including the weak regularity lemma of Frieze and Kannan and the recently established regular approximation theorem. In particular, we show that a weak partition with approximation parameter \epsilon may require as many as 2^{\Omega(\epsilon^{-2})} parts. This is tight up to the implied constant and solves a problem studied by Lov\'asz and Szegedy.Comment: 62 page

The critical window for the classical Ramsey-Tur\'an problem

The first application of Szemer\'edi's powerful regularity method was the following celebrated Ramsey-Tur\'an result proved by Szemer\'edi in 1972: any K_4-free graph on N vertices with independence number o(N) has at most (1/8 + o(1)) N^2 edges. Four years later, Bollob\'as and Erd\H{o}s gave a surprising geometric construction, utilizing the isoperimetric inequality for the high dimensional sphere, of a K_4-free graph on N vertices with independence number o(N) and (1/8 - o(1)) N^2 edges. Starting with Bollob\'as and Erd\H{o}s in 1976, several problems have been asked on estimating the minimum possible independence number in the critical window, when the number of edges is about N^2 / 8. These problems have received considerable attention and remained one of the main open problems in this area. In this paper, we give nearly best-possible bounds, solving the various open problems concerning this critical window.Comment: 34 page

Unification, KK-thresholds and the top Yukawa coupling in F-theory GUTs

In a class of F-theory SU(5) GUTs the low energy chiral mass spectrum is obtained from rank one fermion mass textures with a hierarchical structure organised by U(1) symmetries embedded in the exceptional E_8 group. In these theories chiral fields reside on matter `curves' and the tree level masses are computed from integrals of overlapping wavefuctions of the particles at the triple intersection points. This calculation requires knowledge of the exact form of the wavefuctions. In this work we propose a way to obtain a reliable estimate of the various quantities which determine the strength of the Yukawa couplings. We use previous analysis of KK threshold effects to determine the (ratios of) heavy mass scales of the theory which are involved in the normalization of the wave functions. We consider similar effects from the chiral spectrum of these models and discuss possible constraints on the emerging matter content. In this approach, we find that the Yukawa couplings can be determined solely from the U(1) charges of the states in the `intersection' and the torsion which is a topological invariant quantity. We apply the results to a viable SU(5) model with minimal spectrum which satisfies all the constraints imposed by our analysis. We use renormalization group analysis to estimate the top and bottom masses and find that they are in agreement with the experimental values.Comment: 28 pages, 2 figure

Motif Discovery through Predictive Modeling of Gene Regulation

We present MEDUSA, an integrative method for learning motif models of transcription factor binding sites by incorporating promoter sequence and gene expression data. We use a modern large-margin machine learning approach, based on boosting, to enable feature selection from the high-dimensional search space of candidate binding sequences while avoiding overfitting. At each iteration of the algorithm, MEDUSA builds a motif model whose presence in the promoter region of a gene, coupled with activity of a regulator in an experiment, is predictive of differential expression. In this way, we learn motifs that are functional and predictive of regulatory response rather than motifs that are simply overrepresented in promoter sequences. Moreover, MEDUSA produces a model of the transcriptional control logic that can predict the expression of any gene in the organism, given the sequence of the promoter region of the target gene and the expression state of a set of known or putative transcription factors and signaling molecules. Each motif model is either a $k$-length sequence, a dimer, or a PSSM that is built by agglomerative probabilistic clustering of sequences with similar boosting loss. By applying MEDUSA to a set of environmental stress response expression data in yeast, we learn motifs whose ability to predict differential expression of target genes outperforms motifs from the TRANSFAC dataset and from a previously published candidate set of PSSMs. We also show that MEDUSA retrieves many experimentally confirmed binding sites associated with environmental stress response from the literature.Comment: RECOMB 200

Phenomenology of a Pseudo-Scalar Inflaton: Naturally Large Nongaussianity

Many controlled realizations of chaotic inflation employ pseudo-scalar axions. Pseudo-scalars \phi are naturally coupled to gauge fields through c \phi F \tilde{F}. In the presence of this coupling, gauge field quanta are copiously produced by the rolling inflaton. The produced gauge quanta, in turn, source inflaton fluctuations via inverse decay. These new cosmological perturbations add incoherently with the "vacuum" perturbations, and are highly nongaussian. This provides a natural mechanism to generate large nongaussianity in single or multi field slow-roll inflation. The resulting phenomenological signatures are highly distinctive: large nongaussianity of (nearly) equilateral shape, in addition to detectably large values of both the scalar spectral tilt and tensor-to-scalar ratio (both being typical of large field inflation). The WMAP bound on nongaussianity implies that the coupling, c, of the pseudo-scalar inflaton to any gauge field must be smaller than about 10^{2} M_p^{-1}.Comment: 45 pages, 7 figure