Current-density functional theory of time-dependent linear response in quantal fluids: recent progress

Vignale and Kohn have recently formulated a local density approximation to the time-dependent linear response of an inhomogeneous electron system in terms of a vector potential for exchange and correlation. The vector potential depends on the induced current density through spectral kernels to be evaluated on the homogeneous electron-gas. After a brief review of their theory, the case of inhomogeneous Bose superfluids is considered, with main focus on dynamic Kohn-Sham equations for the condensate in the linear response regime and on quantal generalized hydrodynamic equations in the weak inhomogeneity limit. We also present the results of calculations of the exchange-correlation spectra in both electron and superfluid boson systems.Comment: 12 pages, 2 figures, Postscript fil

Gluon Scattering Amplitudes in Finite Temperature Gauge/Gravity Dualities

We examine the gluon scattering amplitude in N=4 super Yang-Mills at finite temperature with nonzero R-charge densities, and in Non-Commutative gauge theory at finite temperature. The gluon scattering amplitude is defined as a light-like Wilson loop which lives at the horizon of the T-dual black holes of the backgrounds we consider. We study in detail a special amplitude, which corresponds to forward scattering of a low energy gluon off a high energy one. For this kinematic configuration in the considered backgrounds, we find the corresponding minimal surface which is directly related to the gluon scattering amplitude. We find that for increasing the chemical potential or the non-commutative parameter, the on-shell action corresponding to our Wilson loop in the T-dual space decreases. For all of our solutions the length of the short side of the Wilson loop is constrained by an upper bound which depends on the temperature, the R-charge density and the non-commutative parameter. Due to this constraint, in the limit of zeroth temperature our approach breaks down since the upper bound goes to zero, while by keeping the temperature finite and letting the chemical potential or the non-commutative parameter to approach to zero the limit is smooth.Comment: 30 pages, 16 figures, minor corrections (plus improved numerical computation for the non-commutative case

The Effects of Twitter Sentiment on Stock Price Returns

Social media are increasingly reflecting and influencing behavior of other complex systems. In this paper we investigate the relations between a well-know micro-blogging platform Twitter and financial markets. In particular, we consider, in a period of 15 months, the Twitter volume and sentiment about the 30 stock companies that form the Dow Jones Industrial Average (DJIA) index. We find a relatively low Pearson correlation and Granger causality between the corresponding time series over the entire time period. However, we find a significant dependence between the Twitter sentiment and abnormal returns during the peaks of Twitter volume. This is valid not only for the expected Twitter volume peaks (e.g., quarterly announcements), but also for peaks corresponding to less obvious events. We formalize the procedure by adapting the well-known "event study" from economics and finance to the analysis of Twitter data. The procedure allows to automatically identify events as Twitter volume peaks, to compute the prevailing sentiment (positive or negative) expressed in tweets at these peaks, and finally to apply the "event study" methodology to relate them to stock returns. We show that sentiment polarity of Twitter peaks implies the direction of cumulative abnormal returns. The amount of cumulative abnormal returns is relatively low (about 1-2%), but the dependence is statistically significant for several days after the events

Wilson loops stability in the gauge/string correspondence

We study the stability of some classical string worldsheet solutions employed for computing the potential energy between two static fundamental quarks in confining and non-confining gravity duals. We discuss the fixing of the diffeomorphism invariance of the string action, its relation with the fluctuation orientation and the interpretation of the quark mass substraction worldsheet needed for computing the potential energy in smooth (confining) gravity background. We consider various dual gravity backgrounds and show by a numerical analysis the existence of instabilities under linear fluctuations for classical string embedding solutions having positive length function derivative $L'(r_0)>0$. Finally we make a brief discussion of 't Hooft loops in non-conformal backgrounds.Comment: 34 pages, 36 figures. Reference added. Final version JHEP accepte

Exact Results and Holography of Wilson Loops in N=2 Superconformal (Quiver) Gauge Theories

Using localization, matrix model and saddle-point techniques, we determine exact behavior of circular Wilson loop in N=2 superconformal (quiver) gauge theories. Focusing at planar and large `t Hooft couling limits, we compare its asymptotic behavior with well-known exponential growth of Wilson loop in N=4 super Yang-Mills theory. For theory with gauge group SU(N) coupled to 2N fundamental hypermultiplets, we find that Wilson loop exhibits non-exponential growth -- at most, it can grow a power of `t Hooft coupling. For theory with gauge group SU(N) x SU(N) and bifundamental hypermultiplets, there are two Wilson loops associated with two gauge groups. We find Wilson loop in untwisted sector grows exponentially large as in N=4 super Yang-Mills theory. We then find Wilson loop in twisted sector exhibits non-analytic behavior with respect to difference of two `t Hooft coupling constants. By letting one gauge coupling constant hierarchically larger/smaller than the other, we show that Wilson loops in the second type theory interpolate to Wilson loop in the first type theory. We infer implications of these findings from holographic dual description in terms of minimal surface of dual string worldsheet. We suggest intuitive interpretation that in both type theories holographic dual background must involve string scale geometry even at planar and large `t Hooft coupling limit and that new results found in the gauge theory side are attributable to worldsheet instantons and infinite resummation therein. Our interpretation also indicate that holographic dual of these gauge theories is provided by certain non-critical string theories.Comment: 52 pages, 7 figures v2. more figures embedded v3. minor stylistic changes, v4. published versio

Revealed Preference Dimension via Matrix Sign Rank

Given a data-set of consumer behaviour, the Revealed Preference Graph succinctly encodes inferred relative preferences between observed outcomes as a directed graph. Not all graphs can be constructed as revealed preference graphs when the market dimension is fixed. This paper solves the open problem of determining exactly which graphs are attainable as revealed preference graphs in $d$-dimensional markets. This is achieved via an exact characterization which closely ties the feasibility of the graph to the Matrix Sign Rank of its signed adjacency matrix. The paper also shows that when the preference relations form a partially ordered set with order-dimension $k$, the graph is attainable as a revealed preference graph in a $k$-dimensional market.Comment: Submitted to WINE `1

BPS States in Omega Background and Integrability

We reconsider string and domain wall central charges in N=2 supersymmetric gauge theories in four dimensions in presence of the Omega background in the Nekrasov-Shatashvili (NS) limit. Existence of these charges entails presence of the corresponding topological defects in the theory - vortices and domain walls. In spirit of the 4d/2d duality we discuss the worldsheet low energy effective theory living on the BPS vortex in N=2 Supersymmetric Quantum Chromodynamics (SQCD). We discuss some aspects of the brane realization of the dualities between various quantum integrable models. A chain of such dualities enables us to check the AGT correspondence in the NS limit.Comment: 48 pages, 10 figures, minor changes, references added, typos correcte

Causality violation, gravitational shockwaves and UV completion

The effective actions describing the low-energy dynamics of QFTs involving gravity generically exhibit causality violations. These may take the form of superluminal propagation or Shapiro time advances and allow the construction of "time machines", i.e. spacetimes admitting closed non-spacelike curves. Here, we discuss critically whether such causality violations may be used as a criterion to identify unphysical effective actions or whether, and how, causality problems may be resolved by embedding the action in a fundamental, UV complete QFT. We study in detail the case of photon scattering in an Aichelburg-Sexl gravitational shockwave background and calculate the phase shifts in QED for all energies, demonstrating their smooth interpolation from the causality-violating effective action values at low-energy to their manifestly causal high-energy limits. At low energies, these phase shifts may be interpreted as backwards-in-time coordinate jumps as the photon encounters the shock wavefront, and we illustrate how the resulting causality problems emerge and are resolved in a two-shockwave time machine scenario. The implications of our results for ultra-high (Planck) energy scattering, in which graviton exchange is modelled by the shockwave background, are highlighted.Comment: 42 pages, 15 figures, updated reference

Automatic Network Fingerprinting through Single-Node Motifs

Complex networks have been characterised by their specific connectivity patterns (network motifs), but their building blocks can also be identified and described by node-motifs---a combination of local network features. One technique to identify single node-motifs has been presented by Costa et al. (L. D. F. Costa, F. A. Rodrigues, C. C. Hilgetag, and M. Kaiser, Europhys. Lett., 87, 1, 2009). Here, we first suggest improvements to the method including how its parameters can be determined automatically. Such automatic routines make high-throughput studies of many networks feasible. Second, the new routines are validated in different network-series. Third, we provide an example of how the method can be used to analyse network time-series. In conclusion, we provide a robust method for systematically discovering and classifying characteristic nodes of a network. In contrast to classical motif analysis, our approach can identify individual components (here: nodes) that are specific to a network. Such special nodes, as hubs before, might be found to play critical roles in real-world networks.Comment: 16 pages (4 figures) plus supporting information 8 pages (5 figures