Two-dimensional Gravitation Research Articles

Horizon of quantum black holes in various dimensions

We adapt the horizon wave-function formalism to describe massive static spherically symmetric sources in a general $(1+D)$-dimensional space-time, for $D>3$ and including the $D=1$ case. We find that the probability $P_{\rm BH}$ that such objects are (quantum) black holes behaves similarly to the probability in the $(3+1)$ framework for $D> 3$. In fact, for $D\ge 3$, the probability increases towards unity as the mass grows above the relevant $D$-dimensional Planck scale $m_D$. At fixed mass, however, $P_{\rm BH}$ decreases with increasing $D$, so that a particle with mass $m\simeq m_D$ has just about $10\%$ probability to be a black hole in $D=5$, and smaller for larger $D$. This result has a potentially strong impact on estimates of black hole production in colliders. In contrast, for $D=1$, we find the probability is comparably larger for smaller masses, but $P_{\rm BH} < 0.5$, suggesting that such lower dimensional black holes are purely quantum and not classical objects. This result is consistent with recent observations that sub-Planckian black holes are governed by an effective two-dimensional gravitation theory. Lastly, we derive Generalised Uncertainty Principle relations for the black holes under consideration, and find a minimum length corresponding to a characteristic energy scale of the order of the fundamental gravitational mass $m_D$ in $D>3$. For $D=1$ we instead find the uncertainty due to the horizon fluctuations has the same form as the usual Heisenberg contribution, and therefore no fundamental scale exists.

Canonical analysis of the Jackiw–Teitelboim model in the temporal gauge: I. The classical theory

As a preparation for its quantization in the loop formalism, the two-dimensional gravitation model of Jackiw and Teitelboim is analysed in the classical canonical formalism. The dynamics is of pure constraints as is well known. A partial gauge fixing of the temporal type being performed, the resulting second class constraints are sorted out and the corresponding Dirac bracket algebra is worked out. Dirac observables of this classical theory are then calculated.

Two-dimensional gravitation and nonstationary Higgs field solitons

Some aspects of two-dimensional gravity coupled to nonstationary Higgs field solitons are examined. General properties of the nonstationary Higgs field model in flat space-time and their generalization to curved space-time are discussed. A solution which corresponds to cosmology is arrived at.

GAUGE THEORY BASED ON NONLINEAR LIE SUPERALGEBRAS AND STRUCTURE OF 2D DILATON SUPERGRAVITY

We construct a gauge theory based on general nonlinear Lie superalgebras. The generic form of "dilaton" supergravity is derived from nonlinear super-Poincaré algebra, which exhibits a gauge-theoretical formulation in two-dimensional gravitation theory, and clarifies the symmetry structure of two-dimensional dilaton supergravity.

General Form of Dilaton Gravity and Nonlinear Gauge Theory

We construct a gauge theory based on general nonlinear Lie algebras. The generic form of ‘dilaton’ gravity is derived from nonlinear Poincaré algebra, which exhibits a gauge-theoretical origin of the non-geometric scalar field in two-dimensional gravitation theory.

General Form of Dilaton Gravity and Nonlinear Gauge Theory

We construct a gauge theory based on general nonlinear Lie algebras. The generic form of `dilaton' gravity is derived from nonlinear Poincar{\' e} algebra, which exhibits a gauge-theoretical origin of the non-geometric scalar field in two-dimensional gravitation theory.

Generalized integrability and two-dimensional gravitation

We review the construction of generalized integrable hierarchies of partial differential equations, associated to affine Kac-Moody algebras, that include those considered by Drinfel'd and Sokolov. These hierarchies can be used to construct new models of 2D quantum or topological gravity, as well as new $\cal W$-algebras.

Nonlocal effective action in two dimensional curved space with torsion and cosmology

Local and nonlocal forms are obtained of the action induced by two-dimensional gravitation with torsion. It is shown that at the classical level this action can be rewritten in a form where there is no torsion. Cosmological applications and the possibility of the exact solvability are discussed.

Quantization of finite-gap potentials and nonlinear quasiclassical approximation in nonperturbative string theory

In recent articles [1]–[3], and ending with [4], there has been discovered a remarkable circumstance resulting from the combinatorial Kazakov–Migdal–Rostov approach in the continuous limit. In cases of nonperturbative conformal string theories interacting with a “two-dimensional gravitation” according to Polyakov’s scheme, as well as some other ones, when the central charge is c < 1, there appears a simple system of equations for the renormgroup, i.e., a set of Laks type equations with certain ordinary differential operators in x:

A new action for chiral bosons in two dimensions

We construct a new action for chiral bosons coupled to two-dimensional gravitation. Our action has no anomalous Siegel symmetries and can be quantized on S 1×S 1 unlike the Floreanini-Jackiw action. The gravitational anomalies are shown to be equal to those of a Weyl fermion. A conserved current which generates the U (1) Kač-Moody algebra is also constructed.