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

No N=4 Strings on Wolf Spaces

We generalize the standard $N=2$ supersymmetric Kazama-Suzuki coset construction to the $N=4$ case by requiring the {\it non-linear} (Goddard-Schwimmer) $N=4~$ quasi-superconformal algebra to be realized on cosets. The constraints that we find allow very simple geometrical interpretation and have the Wolf spaces as their natural solutions. Our results obtained by using components-level superconformal field theory methods are fully consistent with standard results about $N=4$ supersymmetric two-dimensional non-linear sigma-models and $N=4$ WZNW models on Wolf spaces. We construct the actions for the latter and express the quaternionic structure, appearing in the $N=4$ coset solution, in terms of the symplectic structure associated with the underlying Freudenthal triple system. Next, we gauge the $N=4~$ QSCA and build a quantum BRST charge for the $N=4$ string propagating on a Wolf space. Surprisingly, the BRST charge nilpotency conditions rule out the non-trivial Wolf spaces as consistent string backgrounds.Comment: 31 pages, LaTeX, special macros are include

Non-geometric flux vacua, S-duality and algebraic geometry

The four dimensional gauged supergravities descending from non-geometric string compactifications involve a wide class of flux objects which are needed to make the theory invariant under duality transformations at the effective level. Additionally, complex algebraic conditions involving these fluxes arise from Bianchi identities and tadpole cancellations in the effective theory. In this work we study a simple T and S-duality invariant gauged supergravity, that of a type IIB string compactified on a $T^6/(Z_2 x Z_2)$ orientifold with O3/O7-planes. We build upon the results of recent works and develop a systematic method for solving all the flux constraints based on the algebra structure underlying the fluxes. Starting with the T-duality invariant supergravity, we find that the fluxes needed to restore S-duality can be simply implemented as linear deformations of the gauge subalgebra by an element of its second cohomology class. Algebraic geometry techniques are extensively used to solve these constraints and supersymmetric vacua, centering our attention on Minkowski solutions, become systematically computable and are also provided to clarify the methods.Comment: 47 pages, 10 tables, typos corrected, Accepted for Publication in Journal of High Energy Physic

Towards a string bit formulation of N=4 super Yang-Mills

We show that planar cal N=4 Yang-Mills theory at zero 't Hooft coupling can be efficiently described in terms of 8 bosonic and 8 fermionic oscillators. We show that these oscillators can serve as world-sheet variables, the string bits, of a discretized string. There is a one to one correspondence between the on shell gauge invariant words of the free Y-M theory and the states in the oscillators' Hilbert space, obeying a local gauge and cyclicity constraints. The planar two-point functions and the three-point functions of all gauge invariant words are obtained by the simple delta-function overlap of the corresponding discrete string world sheet. At first order in the 't Hooft coupling, i.e. at one-loop in the Y-M theory, the logarithmic corrections of the planar two-point and the three-point functions can be incorporated by nearest neighbour interactions among the discretized string bits. In the SU(2) sub-sector we show that the one-loop corrections to the structure constants can be uniquely determined by the symmetries of the bit picture. For the SU(2) sub-sector we construct a gauged, linear, discrete world-sheet model for the oscillators, with only nearest neighbour couplings, which reproduces the anomalous dimension Hamiltonian up to two loops. This model also obeys BMN scaling to all loops.Comment: 64 pages, 6 figures, typos fixed, references adde

Quadratic programming methods applied on the real-time clipping of audiosignals

Import 05/08/2014Tato bakalářská práce se zabývá řešením úlohy kvadratického programování. Popisuje algoritmy používané pro řešení této úlohy jak bez omezení, tak i s jednoduchými lineárními omezeními a aplikuje je na vybrané úlohy modelování průhybu struny a ořezání zvukového záznamu.This bachelor thesis deals with quadratic programming problems. It describes algorithms, which are used for solving such problems without constraints and with simple linear inequality constraints. Thess algorithms are then used for modeling of string deflection and clipping of audiosignals.470 - Katedra aplikované matematikyvýborn

Action of WW-type operators on Schur functions and Schur Q-functions

In this paper, we investigate a series of W-type differential operators, which appear naturally in the symmetry algebras of KP and BKP hierarchies. In particular, they include all operators in the W-constraints for tau functions of higher KdV hierarchies which satisfy the string equation. We will give simple uniform formulas for actions of these operators on all ordinary Schur functions and Schur's Q-functions. As applications of such formulas, we will give new simple proofs for Alexandrov's conjecture and Mironov-Morozov's formula, which express the Br\'{e}zin-Gross-Witten and Kontsevich-Witten tau-functions as linear combinations of Q-functions with simple coefficients respectively.Comment: 31 pages. Added an application for Kontsevich-Witten mode

Twining Genera of (0,4) Supersymmetric Sigma Models on K3

Conformal field theories with (0,4) worldsheet supersymmetry and K3 target can be used to compactify the E8xE8 heterotic string to six dimensions in a supersymmetric manner. The data specifying such a model includes an appropriate configuration of 24 gauge instantons in the E8xE8 gauge group to satisfy the constraints of anomaly cancellation. In this note, we compute twining genera - elliptic genera with appropriate insertions of discrete symmetry generators in the trace - for (0,4) theories with various instanton embeddings. We do this by constructing linear sigma models which flow to the desired conformal field theories, and using the techniques of localization. We present several examples of such twining genera which are consistent with a moonshine relating these (0,4) models to the finite simple sporadic group M24.Comment: 22 pages, 3 tables. We thank T. Eguchi and K. Hikami for permission to copy our Tables 2 and 3 (M24 character table and q-expansions of some twining genera in the (4,4) sigma model with K3 target) from their article arXiv:1008.492

Wilson Loops in 2D Yang Mills: Euler characters and Loop equations

We give a simple diagrammatic algorithm for writing the chiral large $N$ expansion of intersecting Wilson loops in $2D$ $SU(N)$ and $U(N)$Yang Mills theory in terms of symmetric groups, generalizing the result of Gross and Taylor for partition functions. We prove that these expansions compute Euler characters of a space of holomorphic maps from string worldsheets with boundaries. We prove that the Migdal-Makeenko equations hold for the chiral theory and show that they can be expressed as linear constraints on perturbations of the chiral $YM2$ partition functions. We briefly discuss finite $N$ , the non-chiral expansion, and higher dimensional lattice models.Comment: 55 pages, harvmac, 35 figure