Functional integration on two-dimensional Regge geometries

@article{Menotti1996FunctionalIO,
  title={Functional integration on two-dimensional Regge geometries},
  author={Pietro Menotti and Pier Paolo Peirano},
  journal={Nuclear Physics},
  year={1996},
  volume={473},
  pages={426-454}
}
By adopting the standard definition of diffeomorphisms for a Regge surface we give an exact expression of the Liouville action both for the sphere and the torus topology in the discretized case. The results are obtained in a general way by choosing the unique self-adjoint extension of the Lichnerowicz operator satisfying the Riemann-Roch relation. We also give the explicit form of the integration measure for the conformal factor. For the sphere topology the theory is exactly invariant under the… Expand
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References

SHOWING 1-10 OF 26 REFERENCES
Conformal gauge fixing and Faddeev-Popov determinant in 2-dimensional Regge gravity
By regularizing the conical singularities by means of a segment of a sphere or pseudosphere and then taking the regulator to zero, we compute exactly the Faddeev--Popov determinant related to theExpand
Conformal-invariant Green functions without ultraviolet divergences
It is known that conformal invariance, with anomalous dimensions, determines the 2- and 3-point functions in relativistic quantum field theory up to some constants. It is then natural to use these toExpand
Failure of the Regge approach in two dimensional quantum gravity
Abstract Regge's method for regularizing euclidean quantum gravity is applied to two dimensional gravity. We use two different strategies to simulate the Regge path integral at a fixed value of theExpand
Theory of Strings with Boundaries: Fluctuations, Topology, and Quantum Geometry
We discuss Polyakov's quantization of the string in the presence of a boundary allowing for an arbitrary topology for the world sheet. In addition to the dynamical conformal factor discovered byExpand
Lattice gravity near the continuum limit
Abstract We prove that the lattice gravity always approaches the usual continuum limit when the link length l → 0, provided that certain general boundary conditions are satisfied. This result holdsExpand
Further results on Functional Determinants of Laplacians in Simplicial Complexes
We investigate the functional determinant of the laplacian on piece-wise flat two-dimensional surfaces, with conical singularities in the interior and/or corners on the boundary. Our results extendExpand
Critical Ising correlation functions in the plane and on the torus
Abstract Explicit expressions are given for all correlation functions of spin, disorder and energy operators of the critical Ising model in the plane or on the torus. Formulae for insertions ofExpand
On d = 2 Regge calculus without triangulation: The supersymmetric case
Abstract The supersymmetric version of a previously developed Regge calculus for d = 2 euclidean gravity is given. In the context of string theory, a continuum theory is likely to exist for D
Evaluation of the one loop string path integral
We evaluate Polyakov's path integral for the sum over all closed surfaces with the topology of a torus, in the critical dimensiond = 26. The result is applied to the partition function andExpand
Measure for moduli The Polyakov string has no nonlocal anomalies
Abstract The functional measure of the bosonic Polyakov string contains nonlocal determinantal factors which seem to spoil its gauge invariances even in the critical dimension. We show that in factExpand
...
1
2
3
...