Strings in plane wave backgrounds

I review aspects of string theory on plane wave backgrounds emphasising the connection to gauge theory given by the BMN correspondence. Topics covered include the Penrose limit and its role in deriving the BMN duality from AdS/CFT, light-cone string field theory in the maximally supersymmetric plane wave and extensions of the correspondence to less supersymmetric backgrounds.Comment: 85 pages, based on PhD thesis, Humboldt University, Berlin; v2: added reference

PP-Wave Light-Cone Superstring Field Theory

We construct the cubic interaction vertex and dynamically generated supercharges in light-cone superstring field theory in the pp-wave background. We show that these satisfy the pp-wave superalgebra at first order in string coupling. The cubic interaction vertex and dynamical supercharges presented here differ from the expressions previously given in the literature. Using this vertex we compute various string theory three-point functions and comment on their relation to gauge theory in the BMN limit.Comment: 32 pages, 1 figure; v2: typos corrected, reference adde

Resolving the Holography in the Plane-Wave Limit of AdS/CFT Correspondence

The issue of holographic mapping between bulk and boundary in the plane-wave limit of AdS/SYM correspondence is reexamined from the viewpoint of correlation functions. We first study the limit of large angular momentum for the so-called GKP-W relation in supergeravity approximation, connecting directly the effective action in the bulk and the generating functional of correlation functions on the boundary. The spacetime tunneling picture which has been proposed in our previous works naturally emerges. This gives not only a justification of our previous proposal, with some important refinements, on the mapping between bulk effective interaction and the CFT coefficients on the boundary in the plane-wave limit, but also implies various insights on the interpretation of holography in the plane-wave limit. Based on this result, we construct a new `holographic' string field theory. We confirm for several nontrivial examples that this gives the CFT coefficients derived by perturbation theory on the gauge-theory side. Our results are useful for understanding how apparently different duality maps proposed from different standpoints are consistent with each other and with our definite spacetime picture for the AdS holography in the plane-wave limit.Comment: corrected typos, 57 page

The individual taxpayer utility function with tax optimization and fiscal fraud environment

In this paper I examine a taxpayer utility function determined by the extended set of variables - i.e. consumption, labor and tax-evasion propensity. This constitutes the main framework for the analysis of taxpayer's decision making process under assumption that in the economy there exist two main reduction methods: a) access to tax optimization techniques, which may decrease effective tax burden and are fully compliant with binding laws, but generate transactional costs and 2) possibility of fiscal fraud in particular tax evasion, as the alternative method of reducing tax due, which has no direct transactional costs, but involves tax litigation risk

Impurity Non-Preserving 3-Point Correlators of BMN Operators from PP-Wave Holography II : Fermionic Excitations

The holographic principle in the pp-wave limit proposed in our previous works is further confirmed by studying impurity non-preserving processes which contain a fermionic BMN operator with one scalar and one fermion impurities. We show that the previously proposed duality relation between the matrix elements of the three point interaction Hamiltonian in the holographic string field theory and the OPE coefficients in super Yang-Mills theory holds to the leading order in the large $\mu$ limit. Operator mixing is required to obtain the BMN operator of definite conformal dimension which corresponds to the string state with one scalar and one fermion excitations. The mixing term plays a crucial role for our duality relation to be valid. Our results, combined with those in the previous papers, provide a positive support that our duality relation holds for the general process regardless of the kind of impurities and of whether impurities conserve or not.Comment: 44 pages, 6 figure

Poszukiwanie znaczeń sztuki naskalnej na podstawie badań poświęconych współczesnej twórczości dzieci

Child art has long been a subject of research. Books and papers on the issue inspired me to look at rock art through the prism of studies on the artistic works of the little ones. This paper discusses a pilot study that I have conducted and offers some theoretical considerations on reading art

Superstring on PP-Wave Orbifold from Large-N Quiver Gauge Theory

We extend the proposal of Berenstein, Maldacena and Nastase to Type IIB superstring propagating on pp-wave over ${\bf R}^4/{\bf Z}_k$ orbifold. We show that first-quantized free string theory is described correctly by the large $N$, fixed gauge coupling limit of ${\cal N}=2$ $[U(N)]^k$ quiver gauge theory. We propose a precise map between gauge theory operators and string states for both untwisted and twisted sectors. We also compute leading-order perturbative correction to the anomalous dimensions of these operators. The result is in agreement with the value deduced from string energy spectrum, thus substantiating our proposed operator-state map.Comment: 11 pages, Late

On the Uniqueness of Plane-wave String Field Theory

We prove that the two interaction Hamiltonians of light-cone closed superstring field theory in the plane-wave background present in the literature are identical.Comment: 15 pages late

New aspects of the BMN correspondence beyond the planar limit

Motivated by recent disagreements in the context of AdS/CFT, we study the non-planar sector of the BMN correspondence. In particular, we reconsider the energy shift of states with two stringy excitations in light-cone string field theory and explicitly determine its complete perturbative contribution from the impurity-conserving channel. Surprisingly, our result neither agrees with earlier leading order computations, nor reproduces the gauge theory prediction. More than that, it features half-integer powers of the effective gauge coupling $\lambda'$ representing a qualitative difference to gauge theory. Based on supersymmetry we argue that the above truncation is not suited for conclusive tests of the BMN duality.Comment: 20 pages, 1 figur

Model-Based Calibration of Filter Imperfections in the Random Demodulator for Compressive Sensing

The random demodulator is a recent compressive sensing architecture providing efficient sub-Nyquist sampling of sparse band-limited signals. The compressive sensing paradigm requires an accurate model of the analog front-end to enable correct signal reconstruction in the digital domain. In practice, hardware devices such as filters deviate from their desired design behavior due to component variations. Existing reconstruction algorithms are sensitive to such deviations, which fall into the more general category of measurement matrix perturbations. This paper proposes a model-based technique that aims to calibrate filter model mismatches to facilitate improved signal reconstruction quality. The mismatch is considered to be an additive error in the discretized impulse response. We identify the error by sampling a known calibrating signal, enabling least-squares estimation of the impulse response error. The error estimate and the known system model are used to calibrate the measurement matrix. Numerical analysis demonstrates the effectiveness of the calibration method even for highly deviating low-pass filter responses. The proposed method performance is also compared to a state of the art method based on discrete Fourier transform trigonometric interpolation.Comment: 10 pages, 8 figures, submitted to IEEE Transactions on Signal Processin