Shocks and Universal Statistics in (1+1)-Dimensional Relativistic Turbulence

We propose that statistical averages in relativistic turbulence exhibit universal properties. We consider analytically the velocity and temperature differences structure functions in the (1+1)-dimensional relativistic turbulence in which shock waves provide the main contribution to the structure functions in the inertial range. We study shock scattering, demonstrate the stability of the shock waves, and calculate the anomalous exponents. We comment on the possibility of finite time blowup singularities.Comment: 37 pages, 7 figure

The Pure Spinor Formulation of Superstrings

In this lectures we outline the construction of pure spinor superstrings. We consider both the open and closed pure spinor superstrings in critical and noncritical dimensions and on flat and curved target spaces with RR flux. We exhibit the integrability properties of pure spinor superstrings on curved backgrounds with RR fluxes.Comment: These lectures have been given in the RTN Winter School on Strings, Supergravity and Gauge Theories, CERN (2008). 32 pages, a typo correcte

Perturbative Computation of Glueball Superpotentials for SO(N) and USp(N)

We use the superspace method of hep-th/0211017 to prove the matrix model conjecture for N=1 USp(N) and SO(N) gauge theories in four dimensions. We derive the prescription to relate the matrix model to the field theory computations. We perform an explicit calculation of glueball superpotentials. The result is consistent with field theory expectations.Comment: 24 pages, 10 figure

Gravitational F-terms of N=1 Supersymmetric Gauge Theories

We consider four-dimensional N=1 supersymmetric gauge theories in a supergravity background. We use generalized Konishi anomaly equations and R-symmetry anomaly to compute the exact perturbative and non-perturbative gravitational F-terms. We study two types of theories: The first model breaks supersymmetry dynamically, and the second is based on a $G_2$ gauge group. The results are compared with the corresponding vector models. We discuss the diagrammatic expansion of the $G_2$ theory.Comment: LaTeX2e, 23 pages, 2 figures. Added a reference and converted into JHEP styl

Anomalies in Superfluids and a Chiral Electric Effect

We analyze the chiral transport terms in relativistic superfluid hydrodynamics. In addition to the spontaneously broken symmetry current, we consider an arbitrary number of unbroken symmetries and extend the results of arXiv:1105.3733. We suggest an interpretation of some of the new transport coefficients in terms of chiral and gravitational anomalies. In particular, we show that with unbroken gauged charges in the system, one can observe a chiral electric conductivity - a current in a perpendicular direction to the applied electric field. We present a motivated proposal for the value of the associated transport coefficient, linking it to the triangle anomaly. Along the way we present new arguments regarding the interpretation of the anomalous transport coefficients in normal fluids. We propose a natural generalization of the chiral transport terms to the case of an arbitrary number of spontaneously broken symmetry currents.Comment: 30 pages; v2: Onsager-relations argument corrected, references added; v3: fixed missing line in eq. (38

Supersymmetry Breaking Vacua from M Theory Fivebranes

We consider intersecting brane configurations realizing N=2 supersymmetric gauge theories broken to N=1 by multitrace superpotentials, and softly to N=0. We analyze, in the framework of M5-brane wrapping a curve, the supersymmetric vacua and the analogs of spontaneous supersymmetry breaking and soft supersymmetry breaking in gauge theories. We show that the M5-brane does not exhibit the analog of metastable spontaneous supersymmetry breaking, and does not have non-holomorphic minimal volume curves with holomorphic boundary conditions. However, we find that any point in the N=2 moduli space can be rotated to a non-holomorphic minimal volume curve, whose boundary conditions break supersymmetry. We interpret these as the analogs of soft supersymmetry breaking vacua in the gauge theory.Comment: 32 pages, 8 figures, harvmac; v2: corrections in eq. 3.6 and in section 6, reference adde

One-Parameter Squeezed Gaussian States of Time-Dependent Harmonic Oscillator and Selection Rule for Vacuum States

By using the invariant method we find one-parameter squeezed Gaussian states for both time-independent and time-dependent oscillators. The squeezing parameter is expressed in terms of energy expectation value for time-independent case and represents the degree of mixing positive and negative frequency solutions for time-dependent case. A {\it minimum uncertainty proposal} is advanced to select uniquely vacuum states at each moment of time. We show that the Gaussian states with minimum uncertainty coincide with the true vacuum state for time-independent oscillator and the Bunch-Davies vacuum for a massive scalar field in a de Sitter spacetime.Comment: 13 Pages, ReVTeX, no figure

On the fermionic T-duality of the AdS_4 \times CP^3 sigma-model

In this note we consider a fermionic T-duality of the coset realization of the type IIA sigma-model on AdS_4 \times CP^3 with respect to the three flat directions in AdS_4, six of the fermionic coordinates and three of the CP^3 directions. We show that the Buscher procedure fails as it leads to a singular transformation and discuss the result and its implications.Comment: LaTeX2e, 9 pages, no figures, JHEP style; v2: minor clarifications; v3: typos fixed, matches the published versio

Beta Functions of Orbifold Theories and the Hierarchy Problem

We examine a class of gauge theories obtained by projecting out certain fields from an N=4 supersymmetric SU(N) gauge theory. These theories are non-supersymmetric and in the large N limit are known to be conformal. Recently it was proposed that the hierarchy problem could be solved by embedding the standard model in a theory of this kind with finite N. In order to check this claim one must find the conformal points of the theory. To do this we calculate the one-loop beta functions for the Yukawa and quartic scalar couplings. We find that with the beta functions set to zero the one-loop quadratic divergences are not canceled at sub-leading order in N; thus the hierarchy between the weak scale and the Planck scale is not stabilized unless N is of the order 10^28 or larger. We also find that at sub-leading orders in N renormalization induces new interactions, which were not present in the original Lagrangian.Comment: 21 pages, LaTeX, 6 figures. Minor clarifications, references adde