Dark energy, Ricci-nonflat spaces, and the Swampland

It was recently pointed out that the existence of dark energy imposes highly restrictive constraints on effective field theories that satisfy the Swampland conjectures. We provide a critical confrontation of these constraints with the cosmological framework emerging from the Salam-Sezgin model and its string realization by Cvetic, Gibbons, and Pope. We also discuss the implication of the constraints for string model building.Comment: Matching version to be published in PL

Comments on the global constraints in light-cone string and membrane theories

In the light-cone closed string and toroidal membrane theories, we associate the global constraints with gauge symmetries. In the closed string case, we show that the physical states defined by the BRS charge satisfy the level-matching condition. In the toroidal membrane case, we show that the Faddeev-Popov ghost and anti-ghost corresponding to the global constraints are essentially free even if we adopt any gauge fixing condition for the local constraint. We discuss the quantum double-dimensional reduction of the wrapped supermembrane with the global constraints.Comment: 12 pages, typos corrected, to appear in JHE

Axion Couplings and Effective Cut-Offs in Superstring Compactifications

We use the linear supermultiplet formalism of supergravity to study axion couplings and chiral anomalies in the context of field-theoretical Lagrangians describing orbifold compactifications beyond the classical approximation. By matching amplitudes computed in the effective low energy theory with the results of string loop calculations we determine the appropriate counterterm in this effective theory that assures modular invariance to all loop order. We use supersymmetry consistency constraints to identify the correct ultra-violet cut-offs for the effective low energy theory. Our results have a simple interpretation in terms of two-loop unification of gauge coupling constants at the string scale.Comment: 25 page

What is decidable about string constraints with the ReplaceAll function

The theory of strings with concatenation has been widely argued as the basis of constraint solving for verifying string-manipulating programs. However, this theory is far from adequate for expressing many string constraints that are also needed in practice; for example, the use of regular constraints (pattern matching against a regular expression), and the string-replace function (replacing either the first occurrence or all occurrences of a ``pattern'' string constant/variable/regular expression by a ``replacement'' string constant/variable), among many others. Both regular constraints and the string-replace function are crucial for such applications as analysis of JavaScript (or more generally HTML5 applications) against cross-site scripting (XSS) vulnerabilities, which motivates us to consider a richer class of string constraints. The importance of the string-replace function (especially the replace-all facility) is increasingly recognised, which can be witnessed by the incorporation of the function in the input languages of several string constraint solvers. Recently, it was shown that any theory of strings containing the string-replace function (even the most restricted version where pattern/replacement strings are both constant strings) becomes undecidable if we do not impose some kind of straight-line (aka acyclicity) restriction on the formulas. Despite this, the straight-line restriction is still practically sensible since this condition is typically met by string constraints that are generated by symbolic execution. In this paper, we provide the first systematic study of straight-line string constraints with the string-replace function and the regular constraints as the basic operations. We show that a large class of such constraints (i.e. when only a constant string or a regular expression is permitted in the pattern) is decidable. We note that the string-replace function, even under this restriction, is sufficiently powerful for expressing the concatenation operator and much more (e.g. extensions of regular expressions with string variables). This gives us the most expressive decidable logic containing concatenation, replace, and regular constraints under the same umbrella. Our decision procedure for the straight-line fragment follows an automata-theoretic approach, and is modular in the sense that the string-replace terms are removed one by one to generate more and more regular constraints, which can then be discharged by the state-of-the-art string constraint solvers. We also show that this fragment is, in a way, a maximal decidable subclass of the straight-line fragment with string-replace and regular constraints. To this end, we show undecidability results for the following two extensions: (1) variables are permitted in the pattern parameter of the replace function, (2) length constraints are permitted

Detecting k-(Sub-)Cadences and Equidistant Subsequence Occurrences

The equidistant subsequence pattern matching problem is considered. Given a pattern string $P$ and a text string $T$, we say that $P$ is an \emph{equidistant subsequence} of $T$ if $P$ is a subsequence of the text such that consecutive symbols of $P$ in the occurrence are equally spaced. We can consider the problem of equidistant subsequences as generalizations of (sub-)cadences. We give bit-parallel algorithms that yield $o(n^2)$ time algorithms for finding $k$-(sub-)cadences and equidistant subsequences. Furthermore, $O(n\log^2 n)$ and $O(n\log n)$ time algorithms, respectively for equidistant and Abelian equidistant matching for the case $|P| = 3$, are shown. The algorithms make use of a technique that was recently introduced which can efficiently compute convolutions with linear constraints

Gauge invariant finite size spectrum of the giant magnon

It is shown that the finite size corrections to the spectrum of the giant magnon solution of classical string theory, computed using the uniform light-cone gauge, are gauge invariant and have physical meaning. This is seen in two ways: from a general argument where the single magnon is made gauge invariant by putting it on an orbifold as a wrapped state obeying the level matching condition as well as all other constraints, and by an explicit calculation where it is shown that physical quantum numbers do not depend on the uniform light-cone gauge parameter. The resulting finite size effects are exponentially small in the $R$-charge and the exponent (but not the prefactor) agrees with gauge theory computations using the integrable Hubbard model.Comment: 12 pages, some clarifications, references adde

E-ELT constraints on runaway dilaton scenarios

We use a combination of simulated cosmological probes and astrophysical tests of the stability of the fine-structure constant $\alpha$, as expected from the forthcoming European Extremely Large Telescope (E-ELT), to constrain the class of string-inspired runaway dilaton models of Damour, Piazza and Veneziano. We consider three different scenarios for the dark sector couplings in the model and discuss the observational differences between them. We improve previously existing analyses investigating in detail the degeneracies between the parameters ruling the coupling of the dilaton field to the other components of the universe, and studying how the constraints on these parameters change for different fiducial cosmologies. We find that if the couplings are small (e.g., $\alpha_b=\alpha_V\sim0$) these degeneracies strongly affect the constraining power of future data, while if they are sufficiently large (e.g., $\alpha_b\gtrsim10^{-5}-\alpha_V\gtrsim0.05$, as in agreement with current constraints) the degeneracies can be partially broken. We show that E-ELT will be able to probe some of this additional parameter space.Comment: 16 pages, 8 figures. Updated version matching the one accepted by JCA

Antisymmetric tensors in holographic approaches to QCD

We study real (massive) antisymmetric tensors of rank two in holographic models of QCD based on the gauge/string duality. Our aim is to understand in detail how the AdS/CFT correspondence describes correlators with tensor currents in QCD. To this end we study a set of bootstrapped correlators with spin-1 vector and tensor currents, imposing matching to QCD at the partonic level. We show that a consistent description of this set of correlators yields a very predictive picture. For instance, it imposes strong constraints on infrared boundary conditions and precludes the introduction of dilatonic backgrounds as a mechanism to achieve linear confinement. Additionally, correlators with tensor currents turn out to be especially sensitive to chiral symmetry breaking, thus offering an ideal testing ground for genuine QCD effects. Several phenomenological consequences are explored, such as the nontrivial interplay between $1^{+-}$ states and conventional $1^{--}$ vector mesons.Comment: 15 pages, 2 figures. Minor changes to match the journal versio

String Searching with Ranking Constraints and Uncertainty

Strings play an important role in many areas of computer science. Searching pattern in a string or string collection is one of the most classic problems. Different variations of this problem such as document retrieval, ranked document retrieval, dictionary matching has been well studied. Enormous growth of internet, large genomic projects, sensor networks, digital libraries necessitates not just efficient algorithms and data structures for the general string indexing, but indexes for texts with fuzzy information and support for queries with different constraints. This dissertation addresses some of these problems and proposes indexing solutions. One such variation is document retrieval query for included and excluded/forbidden patterns, where the objective is to retrieve all the relevant documents that contains the included patterns and does not contain the excluded patterns. We continue the previous work done on this problem and propose more efficient solution. We conjecture that any significant improvement over these results is highly unlikely. We also consider the scenario when the query consists of more than two patterns. The forbidden pattern problem suffers from the drawback that linear space (in words) solutions are unlikely to yield a solution better than O(root(n/occ)) per document reporting time, where n is the total length of the documents and occ is the number of output documents. Continuing this path, we introduce a new variation, namely document retrieval with forbidden extension query, where the forbidden pattern is an extension of the included pattern.We also address the more general top-k version of the problem, which retrieves the top k documents, where the ranking is based on PageRank relevance metric. This problem finds motivation from search applications. It also holds theoretical interest as we show that the hardness of forbidden pattern problem is alleviated in this problem. We achieve linear space and optimal query time for this variation. We also propose succinct indexes for both these problems. Position restricted pattern matching considers the scenario where only part of the text is searched. We propose succinct index for this problem with efficient query time. An important application for this problem stems from searching in genomic sequences, where only part of the gene sequence is searched for interesting patterns. The problem of computing discriminating(resp. generic) words is to report all minimal(resp. maximal) extensions of a query pattern which are contained in at most(resp. at least) a given number of documents. These problems are motivated from applications in computational biology, text mining and automated text classification. We propose succinct indexes for these problems. Strings with uncertainty and fuzzy information play an important role in increasingly many applications. We propose a general framework for indexing uncertain strings such that a deterministic query string can be searched efficiently. String matching becomes a probabilistic event when a string contains uncertainty, i.e. each position of the string can have different probable characters with associated probability of occurrence for each character. Such uncertain strings are prevalent in various applications such as biological sequence data, event monitoring and automatic ECG annotations. We consider two basic problems of string searching, namely substring searching and string listing. We formulate these well known problems for uncertain strings paradigm and propose exact and approximate solution for them. We also discuss a constrained variation of orthogonal range searching. Given a set of points, the task of orthogonal range searching is to build a data structure such that all the points inside a orthogonal query region can be reported. We introduce a new variation, namely shared constraint range searching which naturally arises in constrained pattern matching applications. Shared constraint range searching is a special four sided range reporting query problem where two constraints has sharing among them, effectively reducing the number of independent constraints. For this problem, we propose a linear space index that can match the best known bound for three dimensional dominance reporting problem. We extend our data structure in the external memory model