Right-moving Sector Research Articles

Hawking Radiation from the Boundary Scalar Field and the Information Loss Paradox

Hawking radiation is an essential property of the quantum black hole. It results in the information loss paradox and provides an important clue with regard to the unification of quantum mechanics and general relativity. In previous work, the boundary scalar fields on the horizon of black holes were used to determine the microstates of BTZ black holes and Kerr black holes. They account for Bekenstein–Hawking entropy. In this paper, we show that the Hawking radiation can also be derived from those scalar fields. Hawking radiation is a mixture of the thermal radiation of right- and left-moving sectors at different temperatures. Based on this result, for static BTZ black holes and Schwarzschild black holes, we propose a simple solution for the information loss paradox; i.e., the Hawking radiation is pure due to its entanglement between the left-moving sector and the right-moving sector. This entanglement may be detected in an analogue black hole in the near future.

Small Landau-Ginzburg theories

We classify (0,2) Landau-Ginzburg theories that can flow to compact IR fixed points with equal left and right central charges strictly bounded by 3. Our result is a (0,2) generalization of the ADE classification of (2,2) Landau-Ginzburg theories that flow to N=2 minimal models. Unitarity requires the right-moving supersymmetric sector to fall into the standard N=2 minimal model representations, but the left-moving sector need not have supersymmetry. The Landau-Ginzburg realizations provide a simple way to compute the chiral algebra and other characteristics of these fixed points. While our results pertain to isolated superconformal theories, tensor products lead to (0,2) superconformal theories with higher central charge, and the Landau-Ginzburg realization provides a model for a class of marginal and relevant deformations of such theories.

Thermodynamics of two-dimensional conformal field theory dual to black holes

In this letter we investigate the first law of thermodynamics of the two-dimensional conformal field theory (CFT) that is dual to black holes. We start from the Cardy formula and get the CFT thermodynamics with minimal reasonable assumptions. We use both the microcanonical ensemble and canonical ensemble versions of the Cardy formula. In the black hole/CFT correspondence the black hole is dual to a CFT with excitations, and the black hole mass M and charge N correspond to the energy and charge of the excited CFT. The CFT left- and right-moving central charges cL,R should be quantized, and so we assume that they are mass-independent. Also we assume the difference of the left- and right-moving sector levels NL–NR is mass-independent dual to level matching condition. The thermodynamics of two-dimensional CFT we get is universal and supports the thermodynamics method of black hole/CFT correspondence.

Non-singular string cosmology in a 2d hybrid model

The existence of non-singular string cosmologies is established in a class of two-dimensional supersymmetric Hybrid models at finite temperature. The left-moving sector of the Hybrid models gives rise to 16 real ( N 4 = 4 ) spacetime supercharges as in the usual superstring models. The right-moving sector is non-supersymmetric at the massless level, but is characterized by MSDS symmetry, which ensures boson/fermion degeneracy of the right-moving massive levels. Finite temperature configurations, which are free of Hagedorn instabilities, are constructed in the presence of non-trivial “gravito-magnetic” fluxes. These fluxes inject non-trivial winding charge into the thermal vacuum and restore the thermal T-duality symmetry associated with the Euclidean time circle. Thanks to the unbroken right-moving MSDS symmetry, the one-loop string partition function is exactly calculable beyond any α ′ -approximation. At the self-dual point new massless thermal states appear, sourcing localized spacelike branes, which can be used to connect a contracting thermal Universe to an expanding one. The resulting bouncing cosmology is free of any curvature singularities and the string coupling remains perturbative throughout the cosmological evolution.

THE SUPERSTRING WORLD SHEET IN CURVED SPACE–TIME

The heterotic superstring theory is formulated on the world sheet hab(τ,σ), in a flat space–time background [Formula: see text], by combining a 26-dimensional left-moving sector, consisting only of bosonic fields [Formula: see text], with a 10-dimensional right-moving sector, consisting of bosonic fields [Formula: see text] and Majorana–Weyl fermionic fields ψA(τ - σ), the string coordinates in 10-dimensional space–time being the sum [Formula: see text] and the right-moving sector supersymmetric due to the decoupling of left- and right-moving modes for closed strings. Here, we generalize the background to a curved space–time ĝAB(XC). The equation of motion for XA(τ,σ), given by Short, is then a non-linear modification of the linear wave equation □XA = 0 which yields decoupled left- and right-moving sectors in flat space–time. The linearity of the transverse modes can be maintained, however, if the metric, after reduction to four dimensions, is allowed to depend only upon co-moving time t ∝ X0, although it can be anisotropic, gij = gij(X0). Specializing to the isotropic, Friedmann cosmological space–time ds2 = dt2 - r2(t) dx2, where the radius function of the three-space dx2, assumed flat, is r(t), with d ln r/dt = 2/3γt for a perfect-fluid source whose pressure and energy-density are related by p = (γ - 1)ρ, we find that the string coordinates Xα(τ,σ)(α = 1,2,3), multiplied by the overall prefactor r ≡ t2/3γ, are purely oscillatory only in Minkowski space or for the value γ = 2/3. This result is equivalent to requiring that the Nordström energy-density ρ N ≡ (3γ - 2)ρ vanish. The case ρ = 2/3 corresponds to a space–time generated by an ensemble of cosmic strings, including the superstrings themselves in a self-consistent solution containing no other matter, and defines the Milne universe. The string is only world-sheet-supersymmetric if ρ N = 0, that is if ρ = 0 or γ = 2/3.

SU(3) × SU(3) compactification and mirror duals of magnetic fluxes

This paper analyses type II string theories in backgrounds which admit an SU(3) x SU(3) structure. Such backgrounds are designed to linearly realize eight out of the original 32 supercharges and as a consequence the low-energy effective action can be written in terms of couplings which are closely related to the couplings of four-dimensional N=2 theories. This generalizes the previously studied case of SU(3) backgrounds in that the left- and right-moving sector each have a different globally defined spinor. Given a truncation to a finite number of modes, these backgrounds lead to a conventional four-dimensional low-energy effective theory. The results are manifestly mirror symmetric and give terms corresponding to the mirror dual couplings of Calabi-Yau compactifications with magnetic fluxes. It is argued, however, that generically such backgrounds are non-geometric and hence the supergravity analysis is not strictly valid. Remarkably, the naive generalization of the geometrical expressions nonetheless appears to give the correct low-energy effective theory.

Greybody factors for black holes in four dimensions: Particles with spin

We compute the emission spectrum of minimally coupled particles with spin that are Hawking radiated from four dimensional black holes in string theory. For a range of the black hole parameters the result has a product structure that may be interpreted in terms of the respective right- and left-moving thermal correlation functions of an effective string model. For spin-one and spin-two particles a novel cancellation between contributions to the wave function is needed to ensure this outcome. The form of the spectra suggests that the four-dimensional effective string description is ``heterotic'': particles with spin are emitted from the right-moving sector, only.

Self-dual supergravity from N = 2 strings

A new heterotic N = 2 string with manifest target space supersymmetry is constructed by combining a conventional N = 2 string in the right-moving sector and a Green-Schwarz-Berkovits type string in the left-moving sector. The corresponding sigma mode] is then obtained by turning on background fields for the massless excitations. We compute the beta functions and we partially check the OPE's of the superconformal algebra perturbatively in αt', all in superspace. The resulting field equations describe N = 1 self-dual supergravity.

ON THE BRST APPROACH TO TWO-DIMENSIONAL GRAVITY IN THE LIGHT-CONE GAUGE

The BRST approach to two-dimensional gravity coupled to conformal field theories is discussed. The ordinary BRST symmetry acts only on the left-moving sector of the theory. It is found that there exists a BRST-like symmetry also in the right-moving sector. The conserved charge of this new symmetry is found to be nilpotent. This symmetry is a result of a redundancy of the parametrization of the gravitational field in terms of a scalar field. We propose that the physical states of the theory should belong to the cohomology of this BRST-like charge to eliminate the redundancy. It is also discussed how to derive the BRST charge from the action and the transformation laws of fields.