Non-perturbative path integral of 2d dilaton gravity and two-loop effects from scalar matter

Kummer, Wolfgang; Liebl, H.; Vassilevich, D. V.

doi:10.1016/s0550-3213(97)00796-7

Cited by 25 publications

(35 citation statements)

References 48 publications

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“…Similarities to the analysis of non-minimally coupled scalars interacting with a one-dilaton theory [31] which is based upon the simpler results obtained for the minimally coupled case [17,32,33] may well occur. In fact, for simple factorizable theories the constraint algebra is already known [31] and differs only slightly from the simpler algebra obtained in [32]. Non-simple, but conformally simple factorizable models fit into this theoretical frame only through a conformal transformation.…”

Section: Discussionmentioning

confidence: 64%

Two-Dilaton Theories in Two Dimensions from Dimensional Reduction

2001

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Dimensional reduction of generalized gravity theories or string theories generically yields dilaton fields in the lower-dimensional effective theory. Thus at the level of D=4 theories, and cosmology many models contain more than just one scalar field (e.g. inflaton, Higgs, quintessence). Our present work is restricted to two-dimensional gravity theories with only two dilatons which nevertheless allow a large class of physical applications. The notions of factorizability, simplicity and conformal simplicity, Einstein form and Jordan form are the basis of an adequate classification. We show that practically all physically motivated models belong either to the class of factorizable simple theories (e.g. dimensionally reduced gravity, bosonic string) or to factorizable conformally simple theories (e.g. spherically reduced Scalar-Tensor theories). For these theories a first order formulation is constructed straightforwardly. As a consequence an absolute conservation law can be established.

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Section: Discussionmentioning

confidence: 64%

Two-Dilaton Theories in Two Dimensions from Dimensional Reduction

2001

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“…Preliminary computations show that the 'minimal' supergravity actions, provided by the PSM approach, also seem to be most appropriate for a Hamiltonian analysis leading eventually to a quantum 2d supergravity, extending the analogous result for a purely bosonic case [39,43,[55][56][57]. The role of the obstruction for real supersymmetric extensions, encountered for some of the models within this paper, has to be reconsidered carefully in this context.…”

Section: Discussionmentioning

confidence: 78%

“…Moreover, also the change of variables in a path integral corresponding to the 'torsion' description of dilaton theories (Y -dependent potential (4)) seems advantageous over the one in the 'conformal' description. In this description even interactions with (scalar) matter can be included in a systematic perturbation theory, starting from the (trivially) exact path integral for the geometric part (2) [55][56][57]. Therefore when describing dilaton theories within the present paper we will primarily focus on potentials (3), linear in Y .…”

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confidence: 99%

General two-dimensional supergravity from Poisson superalgebras

Ertl

Kummer

Strobl

2001

J. High Energy Phys.

121

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We provide the geometric actions for most general N = 1 supergravity in two spacetime dimensions. Our construction implies an extension to arbitrary N . This provides a supersymmetrization of any generalized dilaton gravity theory or of any theory with an action being an (essentially) arbitrary function of curvature and torsion.Technically we proceed as follows: The bosonic part of any of these theories may be characterized by a generically nonlinear Poisson bracket on a three-dimensional target space. In analogy to a given ordinary Lie algebra, we derive all possible N = 1 extensions of any of the given Poisson (or W -) algebras. Using the concept of graded Poisson Sigma Models, any extension of the algebra yields a possible supergravity extension of the original theory, local Lorentz and super-diffeomorphism invariance follow by construction. Our procedure automatically restricts the fermionic extension to the minimal one; thus local supersymmetry is realized on-shell. By avoiding a superfield approach we are also able to circumvent in this way the introduction of constraints and their solution. For many well-known dilaton theories different supergravity extensions are derived. In generic cases their field equations are solved explicitly.

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“…Much of the recent progress [7,[15][16][17][18] to understand bosonic gravity theories in two dimensions also at the quantum level is based upon the equivalence [19,20] of a torsion free general dilaton theory [21][22][23][24][25] and a Hamiltonian action of the type of a Poisson-Sigma model (PSM) [26,27]. A (graded) PSM ((g)PSM) is defined by the action (1.1)…”

Section: Introductionmentioning

confidence: 99%

Graded Poisson-sigma models and dilaton-deformed 2D supergravity algebra

Bergamin

Kummer

2003

J. High Energy Phys.

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Fermionic extensions of generic 2d gravity theories obtained from the graded Poisson-Sigma model (gPSM) approach show a large degree of ambiguity. In addition, obstructions may reduce the allowed range of fields as given by the bosonic theory, or even prohibit any extension in certain cases. In our present work we relate the finite W-algebras inherent in the gPSM algebra of constraints to algebras which can be interpreted as supergravities in the usual sense (Neuveu-Schwarz or Ramond algebras resp.), deformed by the presence of the dilaton field. With very straightforward and natural assumptions on them -like demanding rigid supersymmetry in a certain flat limit, or linking the anti-commutator of certain fermionic charges to the Hamiltonian constraint-in the "genuine" supergravity obtained in this way the ambiguities disappear, as well as the obstructions referred to above. Thus all especially interesting bosonic models (spherically reduced gravity, the Jackiw-Teitelboim model etc.) under these conditions possess a unique fermionic extension and are free from new singularities. The superspace supergravity model of Howe is found as a special case of this supergravity action. For this class of models the relation between bosonic potential and prepotential does not introduce obstructions as well.

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Non-perturbative path integral of 2d dilaton gravity and two-loop effects from scalar matter

Cited by 25 publications

References 48 publications

Two-Dilaton Theories in Two Dimensions from Dimensional Reduction

Two-Dilaton Theories in Two Dimensions from Dimensional Reduction

General two-dimensional supergravity from Poisson superalgebras

Graded Poisson-sigma models and dilaton-deformed 2D supergravity algebra

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