arXiv subjects

H. Samtleben

Publications and source records attributed to H. Samtleben.

31 records · Page 2Linked to original sources

arXiv2001

Maximal gauged supergravity in three dimensions

We construct maximally supersymmetric gauged N=16 supergravity in three dimensions, thereby obtaining an entirely new class of AdS supergravities. These models are not derivable from any known higher-dimensional theory, indicating the existence of a new type of supergravity beyond D=11. They are expected to be of special importance also for the conjectured AdS/CFT correspondence. One of their noteworthy features is a nonabelian generalization of the duality between scalar and vector fields in three dimensions. Among the possible gauge groups, SO(8)xSO(8) is distinguished as the maximal compact gauge group, but there are also more exotic possibilities such as F_4 x G_2.

hep-th↗

arXiv2000

Sequential Bethe vectors and the quantum Ernst system

We give a brief review on the use of Bethe ansatz techniques to construct solutions of recursive functional equations which emerged in a bootstrap approach to the quantum Ernst system. The construction involves two particular limits of a rational Bethe ansatz system with complex inhomogeneities. First, we pinch two insertions to the critical value. This links Bethe systems with different number of insertions and leads to the concept of sequential Bethe vectors. Second, we study the semiclassical limit of the system in which the scale parameter of the insertions tends to infinity.

math-ph↗

arXiv2000

An exceptional geometry for d=11 supergravity?

We analyze the algebraic constraints of the generalized vielbein in SO(1,2) x SO(16) invariant d=11 supergravity, and show that the bosonic degrees of freedom of d=11 supergravity, which become the physical ones upon reduction to d=3, can be assembled into an E_8-valued vielbein already in eleven dimensions. A crucial role in the construction is played by the maximal nilpotent commuting subalgebra of E_8, of dimension 36, suggesting a partial unification of general coordinate and tensor gauge transformations.

hep-th↗

arXiv1999

An Algebraic Bootstrap for Dimensionally Reduced Quantum Gravity

Cylindrical gravitational waves of Einstein gravity are described by an integrable system (Ernst system) whose quantization is a long standing problem. We propose to bootstrap the quantum theory along the following lines: The quantum theory is described in terms of matrix elements e.g. of the metric operator between spectral-transformed multi-vielbein configurations. These matrix elements are computed exactly as solutions of a recursive system of functional equations, which in turn is derived from an underlying quadratic algebra. The Poisson algebra emerging in its classical limit links the spectral-transformed vielbein and the non-local conserved charges and can be derived from first principles within the Ernst system. Among the noteworthy features of the quantum theory are: (i) The issue of (non-)renormalizability is sidestepped and (ii) there is an apparently unavoidable ``spontaneous'' breakdown of the SL(2,R) symmetry that is a remnant of the 4D diffeomorphism invariance in the compactified dimensions.

hep-th↗

arXiv1999

Schlesinger transformations for elliptic isomonodromic deformations

Schlesinger transformations are discrete monodromy preserving symmetry transformations of the classical Schlesinger system. Generalizing well-known results from the Riemann sphere we construct these transformations for isomonodromic deformations on genus one Riemann surfaces. Their action on the system's tau-function is computed and we obtain an explicit expression for the ratio of the old and the transformed tau-function.

solv-int↗

arXiv1999

On the Yangian Y(e_8) quantum symmetry of maximal supergravity in two dimensions

We present the algebraic framework for the quantization of the classical bosonic charge algebra of maximally extended (N=16) supergravity in two dimensions, thereby taking the first steps towards an exact quantization of this model. At the core of our construction is the Yangian algebra $Y(e_8)$ whose RTT presentation we discuss in detail. The full symmetry algebra is a centrally extended twisted version of the Yangian double $DY(e_8)_c$. We show that there exists only one special value of the central charge for which the quantum algebra admits an ideal by which the algebra can be divided so as to consistently reproduce the classical coset structure $E_{8(8)}/SO(16)$ in the limit $\hbar\to 0$.

hep-th↗

arXiv1998

Integrability and Canonical Structure of d=2, N=16 Supergravity

The canonical formulation of d=2, N=16 supergravity is presented. We work out the supersymmetry generators (including all higher order spinor terms) and the N=16 superconformal constraint algebra. We then describe the construction of the conserved non-local charges associated with the affine E_9 symmetry of the classical equations of motion. These charges are shown to commute weakly with the supersymmetry constraints, and hence with all other constraints. Under commutation, they close into a quadratic algebra of Yangian type, which is formally the same as that of the bosonic theory. The Lie-Poisson action of E_9 on the classical solutions is exhibited explicitly. Further implications of our results are discussed.

hep-th↗

arXiv1997

Yangian Symmetry in Integrable Quantum Gravity

Dimensional reduction of various gravity and supergravity models leads to effectively two-dimensional field theories described by gravity coupled G/H coset space sigma-models. The transition matrices of the associated linear system provide a complete set of conserved charges. Their Poisson algebra is a semi-classical Yangian double modified by a twist which is a remnant of the underlying coset structure. The classical Geroch group is generated by the Lie-Poisson action of these charges. Canonical quantization of the structure leads to a twisted Yangian double with fixed central extension at a critical level.

hep-th↗

arXiv1997

Canonical quantization of cylindrical gravitational waves with two polarizations

The canonical quantization of the essentially nonlinear midisuperspace model describing cylindrically symmetric gravitational waves with two polarizations is presented. A Fock space type representation is constructed. It is based on a complete set of quantum observables. Physical expectation values may be calculated in arbitrary excitations of the vacuum. Our approach provides a non-linear generalization of the quantization of the collinearly polarized Einstein-Rosen gravitational waves.

gr-qc↗

arXiv1997

Quantization of coset space sigma-models coupled to two-dimensional gravity

The mathematical framework for an exact quantization of the two-dimensional coset space sigma-models coupled to dilaton gravity, that arise from dimensional reduction of gravity and supergravity theories, is presented. Extending previous results the two-time Hamiltonian formulation is obtained, which describes the complete phase space of the model in the isomonodromic sector. The Dirac brackets arising from the coset constraints are calculated. Their quantization allows to relate exact solutions of the corresponding Wheeler-DeWitt equations to solutions of a modified (Coset) Knizhnik-Zamolodchikov system. On the classical level, a set of observables is identified, that is complete for essential sectors of the theory. Quantum counterparts of these observables and their algebraic structure are investigated. Their status in alternative quantization procedures is discussed, employing the link with Hamiltonian Chern-Simons theory.

hep-th↗

arXiv1996

Integrable Classical and Quantum Gravity

In these lectures we report recent work on the exact quantization of dimensionally reduced gravity, i.e. 2d non-linear (G/H)-coset space sigma-models coupled to gravity and a dilaton. Using methods developed in the context of flat space integrable systems, the Wheeler-DeWitt equations for these models can be reduced to a modified version of the Knizhnik-Zamolodchikov equations from conformal field theory, the insertions given by singularities in the spectral parameter plane. This basic result in principle permits the explicit construction of solutions, i.e. physical states of the quantized theory. In this way, we arrive at integrable models of quantum gravity with infinitely many self-interacting propagating degrees of freedom.

hep-th↗

arXiv1996

Poisson Realization and Quantization of the Geroch Group

The conserved nonlocal charges generating the Geroch group with respect to the canonical Poisson structure of the Ernst equation are found. They are shown to build a quadratic Poisson algebra, which suggests to identify the quantum Geroch algebra with Yangian structures.

gr-qc↗

arXiv1996

On $2D$ quantum gravity coupled to a $\s$-model

This contribution is a review of the method of isomonodromic quantization of dimensionally reduced gravity. Our approach is based on the complete separation of variables in the isomonodromic sector of the model and the related ``two-time" Hamiltonian structure. This allows an exact quantization in the spirit of the scheme developed in the framework of integrable systems. Possible ways to identify a quantum state corresponding to the Kerr black hole are discussed. In addition, we briefly describe the relation of this model with Chern Simons theory.

gr-qc↗